text:
How to build cities in Catan without any ore?
When playing in a Catan game (basic edition) last week, I got a couple of good starting spots, with dice rolls 5,4, and 6 and 10, 5, and 8. Except that there was no ore in those settlements, and none that was obtainable on the map. I was able to quickly get 7 points (5 settlements + longest road) before any of my opponents had 5, but I couldn't get any more quickly enough because of my lack of ore, and ultimately ended the game with 9 points in second place. In the future, I feel like this is possibly a good starting strategy, but how can I plan my endgame for this strategy so that I can get the cities or points necessary to win?

Yes, those are good numbers and might be worth not having access to ore. It's hard to tell without seeing the rest of the board.

Convince other players to trade ore with you; even though they'll probably notice you don't have access to ore, you might hold other resources that they absolutely need.
Use a harbor to trade with the bank in better ratios than 4:1.

Yes, this could potentially work, but wouldn't other players be wary of trading with me if I am ahead of them? (And not so far ahead that I can afford to do 3:1 or 4:1 trades with them)

If they're smart players, yes. That's why you need something that's vital to them; if e.g. wool is scarce and you have plenty, you can use that as leverage.

We like to play the fishermen extension; fish tokens can be a valuable resource too to bridge the time to reaching an ore location! Or, add in the harbourmaster option and just focus on gaining harbours, and you can win without cities if you play it well. Those fish tokens earned from being adjacent to water make road building easier too so I’ve won more than once with HM + LR, and no access to ore..

@JoeKerr The standard for trading is 4:1, so unless they're willing to act on a 2:1 deal, they're going to lose out on those resources. If they'll only go for a 3:1, I'd rather just starve them out and do a neutral trade to keep them hungry for later. Additionally, by having the resources needed to build roads and settlements, you can quickly isolate your opponents into a starving position, forcing them to trade with you.

Using the strategy that you did, you can start off with no ore in the first two settlements, and get off to a "quick" start (many settlements). But you have to use that "quick start" to remedy your deficiency.
The first thing to do is to use your third (or subsequent) settlement to build next to an ore hex. Even a 4 or 3, 10 or 11 may do.(You probably won't get a good ore hex). The second is to build on a 2 to 1 port and trade the other good for ore at that ratio. Note that building new settlements (as opposed to cities) does not require ore.
When you roll sevens, move the robber onto the hex of a player that has a lot of ore and hope to steal some from him or her.
When you do get your first ore, buy development cards and hope to get a year of plenty or monopoly card that allow you get more ore. Even a knight will allow you to move the robber and possibly steal ore.
Just about every Catan player has a deficiency somewhere. The ones who win are those that remedy their deficiency the fastest. You have identified ore as your deficiency, so concentrate your early game efforts on the remedies described above.


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In mahjong, how will joker tiles change the game strategy?
I'm developing a new ruleset of mahjong. It's supposed to be a hybrid of Japanese rule and Chinese rule. I'm also considering including the joker tile, also known as baida (百塔). Here is the sketch of how it works:

There are 8 joker tiles in total.

Upon calling Mahjong (和了):

if you have 2 joker tiles, they are considered as an arbitrary Pair (対子).

if you have 3 joker tiles, they are considered as an arbitrary Chow/Pong  (順子) / (刻子).

if you declared a concealed Kong with joker tiles, they are considered as an arbitrary Kong (槓子).

It is possible to declare Pon, Kan, or Ron to a joker tile.

It is not possible to declare Chi to a joker tile.

A Dora tile declares itself as a Dora. This also applies to a joker tile. But if the tile is a flower tile, it doesn't declare a Dora.

But I'm unsure how this will change the game strategy. How will the game strategy change, and why didn't Japanese rule and Chinese rule use joker tiles at the first place?

I've not played Mah Jong for years so can't answer question but my advice would just be play test and see.  From my own designs you will often find when playing with people things will happen you hadn't considered, then test changes with as many different people as possible and see what happens.

I don
t see that this would significantly change strategy or play. I concur that playtesting would be a good idea.
My understanding is that the "joker" was never a part of the traditional game, and was added when the "American" rules were defined. I learned to play with slightly modified Chinese rules, and the jokers were never used. But if you are defining a new rules set, you can use them however you wish, of course.

source: Stack Exchange

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

sort: votes


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Does a player rolling a 7 have to discard half their cards if they have more than 7?
If I roll a "7" every player that has 8 or more cards has to give to the bank the half. Does that include the player who rolled the "7"?
If playing with then Seafarers expansion I can choose the Pirate after rolling "7" Does every player have to discard half of their cards when pirate is selected?

A small correction that I don't think constitutes its own answer but the Robber only affects you when you have 8+ resource cards. Having 7 and below will not cause you to discard down. The relevant rule is in L. Scott's answer

Yes, every player, including yourself / the player who rolled the 7.
From the rules:

every player who has more than 7 resource cards must select half...

With SeaFarers, you can choose to move the pirate instead of moving the robber. But that's the only difference. The discard half applies either way.
The rules specify only the pirate/robber choice. Leaving it up to the reader to remember that there's also the discard. But for confirmation, see this blog post:

Rolling seven is the same as in the original Catan in that the player who rolls seven gets to move the robber, and can take a resource from any player effected [sic] by where they move it to. Additionally any player with seven or more cards in their hand still has to discard half of them (the lesser half in the case of an odd number, i.e. if I have 9 cards with a seven is rolled I must discard 4).

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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What board and card games have professional players?
Can we provide a listing of what board games or card games are played by full-time professionals? I define such a professional as someone whose income arises primarily from competing and winning events (against other competitive players, rather than against a stable benchmark like a casino for example) and/or teaching (so, for example, a full-time coach who hardly ever plays competitively still counts). There don't need to be many - if it's possible to confirm even one such full-time professional that is enough to mention the game.
So far I am aware of:

Poker
Chess
Go
Bridge
Magic: the Gathering

And possibly Shogi, Xiangqi, though confirmation on these would be valuable. Can anyone add to this list?
EDIT: Since this question has been reopened I will offer some further
thoughts that I felt evolved from our discussion. They could be useless to someone who has already researched this and knows better:

We should not need to look far for these games; they are likely to have been in the public eye for decades at a minimum. Of the established examples of games sustaining full-time professionals, from chess/Go to Magic: The Gathering, every game has done so for at least 25 years now. Since full-time professional players undertake considerable risk, they would not likely commit themselves to a game without strong pedigree. (Counter-examples always welcome)

I will venture - from very limited experience - a list of games which seem vaguely plausible for which I'm curious whether they have full-time professionals, as a starting point for someone who doesn't feel confident to answer because they suspect they will be missing some category or the other (e.g. Asian board-games) but might know about these particular games:

Trick Taking games: Whist, Hearts, Spades, Euchre, Skat, ...
Other Card games: Rummy, Cribbage, ...
Abstract games: Checkers, Backgammon, Reversi, ...
Trading Card games: MTG, ...
Board games: ...

Obviously an extremely incomplete list but maybe a few possibilities that occurred to me to start brainstorming.

Comments are not for extended discussion; this conversation has been moved to chat.

Given that this question was already reopened once, I feel it should not be deleted. Even if it's to remain closed, it ought to stand on the record given that several members of the community have found it interesting and worthwhile.

And it's been closed twice. If it was worth keeping, it would be open or it would be locked, and it is neither. Deletion is the inevitable result for a post that is deemed inappropriate, for whatever reason, on Stack Exchange.

@Nij That sad, this question is more interesting and important than 100 question about the rules of Monopoly.

@Nij Wrong: deletion is not the 'inevitable result' for anything. As that Meta post makes clear, deletion is the result of a post that 'no longer adds anything to the site'; in this case the post is felt valuable by a substantial proportion of the community, and whether for that reason or because a larger still proportion vehemently feels it is inappropriate, it should remain as a signal of the community's decision in an interesting/ambiguous case.

I'll add that, you can imagine, I don't have much skin in the game seeing as, deleted or not (and probably even closed or not - perhaps the fact it was opened a long time and no-one really answered in that period is some sort of vindication of the closure, though I'm not sure), it's unlikely I'll get the answers I want. However, in general I find the attitude of people on smaller SEs to VTC questions they simply don't like or personally feel is outside the type of content they are accustomed to, rather than objectively low-quality, to be quite pernicious.

What is a VTC question?

VTC = "vote to close"

Duplicate bridge certainly has full-time professional players who earn their living playing, although most of them are also teachers, and play with students for pay. There at least used to be professional players of Chemin de fer (a gambling game) and still are for blackjack and other casino gambling games.

Thanks for confirming bridge. Chemin de fer = baccarat? Note that as I defined professional players, they need to win from competition with one another, not against 'the house', so blackjack doesn't count. I don't know if other 'casino gambling games' fit these terms - of course poker does, but are there others?

Note that bridge is weird; even those that make their living from playing as opposed to teaching or mentoring don't make their money from prizes or sponsorship in the classic sense; they play team-of-4 matches at high level 5-pros-and-the client, who pays for everything.  Since the clients are people like the former CEOs of Adidas, Bear Stearns, and Standard Oil, or "came back last week from Italy, where he was looking for a winery to buy", 5 pros can be paid a good living out of "petty cash".  There are very few bridge events (almost none in North America) with significant prize pools.

@Mycroft that's very interesting. How then do they become those pros? Is there an element of competition? Do they have to win extremely competitive events and the winners are then de facto sponsored by wealthy clients to play with those clients?

I'm not the person to ask; I went down a different path (I'm PT, but does "full time organizer and referee" count as "professional"?)  I know a few full-time pros well, and several others to "hello" to when I'm working; I know a few players who get paid for teaching sessions, or paid by playing pros to fill in their teams, but it's definitely a sideline only for them (now, at least).  It's a weird world, and I wouldn't want it; but for those who can, it's very rewarding.

@Mobeus Zoom ther are several different routes to professional status in bridge.  One interesting case is the famous "Dallas Aces". A wealthy bridge player (Ira Corn) wanted the US to do better in international events which had been dominated by italy for 10+ years. So he hired 6 players who were near the top of the US tourney lists and had done well in international play, and seemed likely to play well together. They were paid full-time ($800-950/Mth, 1968) to practice and play high-level bridge. Corn also paid for coaches and a dedicated computer.  Some other pros followed this path ...

... Many other pros earn by writing and publishing books, and giving personal lessons. Culbertson and Goren followed this path, and many others after them Often such a pro will play with a client in a major event, as a "playing lesson" but if the pair or team wins, the client shares in the masterpoint award, and part of the fee is for helping the client do well. (Sometimes a team is 2 pros, each partnered with a client.

@MobeusZoom: There are also lower-level bridge pros.  Making Life Master rank in N. America requires a certain amount of Gold Points, which one earns by placing well (or at least not too badly) in Regional Tournaments.  Some basically competent but far from expert players who are well-to-do but by no means wealthy will hire a pro as a partner for a Regional to help them win some Gold Points.  Probably a few dozen pros make a living primarily this way, and more make some money this way to supplement their retirement.  They basically get clients through word-of-mouth.

There are a number of Magic: the Gathering players who derive all their income from the game, whether that be:

A direct contract from Wizards of the Coast, given to the players with the best competitive results
Prize money from winning tournaments
1:1 lessons
Writing about the game
Streaming-related income
Sponsorship related to all the above

The split between those sources will obviously vary between individuals, with others supplementing their Magic-related income with "regular" employment.
[ Update four days after I wrote this answer: Wizards of the Coast have canned their professional contracts... ]
While it may be strictly off-topic for this site as it doesn't have a physical version, I believe there are also Hearthstone pros who earn a living in a similar manner.

Thanks, good answer, I don't know why this question was closed - I've asked - but this is the kind of answer I was hoping for.

Backgammon has pros; see e.g. https://en.wikipedia.org/wiki/Akiko_Yazawa or  https://www.reddit.com/r/backgammon/comments/2sje8f/iama_professional_backgammon_player_voted_5_in/ .


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Identify a card game where you need to play a higher card or pickup the discard pile?
The first time I played was elementary and no one remembered the name so we've called it "the game with no name" for years.
Setup: The game starts with three cards dealt to each player, face down on the table, these will be the final cards a player uses. Then five cards to each players hand.
Play: The lowest card goes first, players draw to always have 5 cards in their hand, until the draw pile is empty. Players go around the table discarding higher cards or picking up the discard pile when they can't play. After the discard pile is empty, a player wins when they play their three cards on the table.
Special cards: 2's reset the discard pile, Aces are the highest, 10s or four of the same card in a row "blow up" the pile and those cards are out of play for the rest of the game.

I fear the description is far from complete, and wouldn't be enough to play the game. It is not clear to me which cards can be played at  given time. when one picks up the pile is it added to one's hand? what does it mean to "reset the discard pile"? But I am fairly sure I have never played this.

I should prob make this clearer in my answer as I recognised enough of Shithead from the question.   Players take it in turns to play cards to a shared discard pile.  the card they play must be equal or higher than the last card.   if they are unable to do so they take all the cards into there hand.  a 2 "reset" the discard pile back to start so that a card of value 3 becomes legal to play again.

I believe you are describing Shithead, or one of its MANY variants.
I played this at school in 1990's and when I went to University people from different places had the numbers special powers have slightly different names.  But what I played broadly matches your description.  As stated in the wikipedia link the game does have many regional variations. I am describing this from UK.
In the version of Shithead I played there were 3 cards face down to each player.  3 face up on those cards and players could then swap those face up cards with ones in their hand.  In the version I played all cards were dealt out and sometimes we played with multiple decks in a large group.
In the version I played 2's reset the deck.  7's were transparent and could be played on anything and 10s 'burnt' the stack removing them from the game.
Once a player had emptied their hand they would play with the 3 face up cards and then finally the 3 face down cards were played blind on a players turn.

This is definitely the game, just a variant I played. 7s weren't special, but everything else matches. Thank you!

I see your new to stack exchange.  If you get a 'correct' answer to your question don't forget to upvote an accept it as the correct answer.

I believe the game you are talking about is called Castle.
REQUIRED:
2+ players
52 card deck(with or without Jokers)
SETUP:
Each player is dealt three cards face down, and then three more cards face up. Although you typically don't get to see the face down cards, some variants exist that allow you to choose the better cards for later play. Each player is then dealt 5 cards, which they use to play. The remainder of the deck is placed in the center of the table.
GAMEPLAY:
Cards from lowest to highest are 3, 4, 5, 6, 7, 8, 9, Jack, Queen, King, and Ace. 2, 10, and Joker are special cards (see below.) Suites do not constitute to card hierarchy. The player with the lowest card usually goes first, but can play any card. The next card must either match or succeed the card just below it in rank(i.e., the next card can't be lower.) The deck and player's current hand must be empty in order for the face up cards to be played; the face down cards follow next, but, depending on the rules, you usually can't look at them until you play them. Players take turns playing a card or cards, and the first player to play all their face down card wins.
SPECIAL CARDS(can be played on top of any card, regardless of rank):
2: 2's "reset" the deck, meaning you can then place any card on it afterward (build), or place nothing else and move on to the next player's turn (hold).
10: 10's "clear" the deck, which means all the cards beneath the deck are removed from the game and cannot be used later on.
Jokers: The Jokers can be used as either a 2 or 10, but not both of them. The player must also declare which card they want action they wish to perform with it (clear or build/hold).
4-Of-A-Kind: While not technically a special card, 4 cards played in a row clears the deck automatically. However, all 4 cards don't have to be played by one person; as long as there are 4 of the same cards in a row, the discard pile is cleared and removed from the game.
But, wait! What if I can't play any card???
The unfortunate player who can't play any card (all the cards in their hand are lower than the last discard card, and they don't have a 2, 10, or Joker) must pick up the discard pile, and add it to their own hand.


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Unbeatable Nine Men's Morris AI?
Supposedly Nine Men's Morris is a solved game that always ends in a draw if both players play perfectly. Has anybody successfully implemented an AI that achieves this perfect level of play? If so, how can I play against it?

If you cant get an answer here, try also at AI stack exchange https://ai.stackexchange.com/

Yes, Gábor E. Gévay et al. have made such an engine.
The program and instructions for downloading the databases necessary for perfect play can be found here.


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Discarding before laying down a hand
Can I throw out my discard, and then lay down my hand?
Or am I then supposed to wait until the next turn to lay it down?
If I do lay down after I discard is that cheating?
My Stepdad throwed his discard and then laid down his hand. He had a fit when I told him he couldn't do that since that it is cheating. Am I right?
I know that in any card game I played you must lay down your hand before discarding, but I can not find anything on this anywhere.

This sounds more like a question of sportsmanship and the play-style of people you choose to play with rather than an actual rules question.
Yes, discarding is the last thing you do on your turn; when you make a meld you do so during your turn before discarding your card.
However, as long as the next player has not taken a turn, or provided any additional information, there is no reason to not allow a player to still play their meld.
It is unclear from your question why your opponent did not lay down the meld first. In Phase 10 there is never a reason to hold onto a meld that you could play instead. So is it that he didn’t notice that he didn’t have the meld until just after he discarded? Or he didn’t understand that melding should happen before discarding? Or was it just his style of laying down all his cards to lay down the discard right before the meld; just messing around? In any of these cases, I and the people I play games with would consider it poor sportsmanship to tell the person that they cannot play their meld because technically the discard card hit the table before the meld cards did. What matters is that they all happened on the same turn.
This could be different in other similar games where there is sometimes a reason to not play a meld when you can. In that case a person could choose to not play a meld, but then change their mind at last second after they discard a card; perhaps because something in their opponent's face told them that the card they chose to discard means that this turn was their last chance to meld. But in Phase 10, laying down your meld as soon as you have the required cards is an automatic decision; there is no skill or strategy in deciding when to meld.


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I am wondering how in the world the number 136,694 of directly dealt out Gin hands was arrived at
Some kind person on here said that when dealing out hands from a standard 52-card
deck in the game of Rummy, there are 136,694 possible 10-card hands that can be declared "Gin."
I am just wondering how that number was found - can it be done using pencil and paper and combinatorics
or does a computer program have to be written to do it?

The number seems to come from this question, for reference.

And in a comment on that post I've found the solution, which I'll post as an answer.

According to the accepted answer on the post containing that number, it originates in the book How to Win at Gin Rummy: Playing for Fun and Profit by Pramod Shankar. Unfortunately, the book doesn't seem to have a source or proof for it.
Thankfully, though, a comment on that post does give an answer. A blog called Entropy Clay steps through the calculations, breaking down all the possible ways the hand could contain Gin and a full calculation of the number of such hands in terms of fairly standard combinatorics. I won't repeat the whole thing, but the top level results are:

Hand composition
Number of hands

Two runs of 5
526

Three sets (4, 3, 3)
13,728

Three runs (4, 3, 3)
25,452

Set of 4, two runs of 3
6,636

Set of 3, two runs (4, 3)
47,272

Two sets (4, 3), run of 3
17,120

Two sets (3, 3), run of 4
25,960

Total
136,694

That seems to be missing some combinations, such as a run of 6, 4 and a run of 7, 3.

In that scenario, the 6 & 7 runs would be split into separate runs of 3s and a 4.

I was initially skeptical, but after looking over the calculations in the linked blog post they do appear correct.  The common mistakes that students make with overcounting seem to all be handled correctly.

Wow, I could have worked on this until Doom's Day and never solved it !


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Barbarian attack In Catan - Cities and Knights
4 of us were playing Catan - Cities and Knights, the barbarians attacked and the situation was as follows:

Player 1 has 2 cities and 1 knight.
Player 2 and 3 each have 1 city and 1 knight.
Player 4 has 0 cities and 0 knights.

Who loses a city?

Players 1, 2, and 3 will each have 1 city pillaged.
You say that players 2 and 3 are protected, but this is not correct. It doesn't matter if an individual player has as many knights as they do cities. All that matters is the total number of cities among all players compared to the total number of active knights among all players.
From the rules:

The strength of the barbarians is equal to the number of cities (including metropolises) owned by all players. Add up all the cities owned by all of the players anywhere on the island to determine this strength.

All active knights of all players (even those who do not own any cities) will defend against the barbarians. Only the active knights are counted, the inactive knights do not assist in defending the island in any way. Remember that the strength of each knight is based upon its type: basic (1), strong (2), or mighty (3). Sum up the value of all the active knights to determine the strength of the defending army.

The Barbarians win the attack because they have a total strength of 4 (for 4 total cities on the board), and the Knights have a total strength of 3 (assuming all Knights you mention are activated and level 1).
When the Barbarians win, they pillage a city belonging to the player(s) who contributed the least defense. However, players who do not have any cities are not counted for this purpose. Of the players who have cities, there is a 3-way tie for who contributed the least.

If the barbarians are stronger, they are victorious! If the barbarians win the battle, they pillage one or more cities. Pillaged cities are reduced to settlements (replace the city piece with a settlement). The barbarians pillage one city belonging to the player who had the lowest total strength of active knights when the barbarians attacked. Any player who contributed no knights are automatically considered to have the lowest total strength of active knights. If various players rie for having the lowest total strength of active knights, each of those player loses 1 of their own cities.

Important: When determining which player has contributed the weakest group of knights, do not count any player who has no cities or any player who has only metropolises. These players are immune to the effects of the barbarian attack.

As an aside, it is a very powerful strategy for player 1 to try to intentionally cause this to happen leaving them with the only remaining city on the board.  This allows them to continue with developing commodities and improvements while the rest of the players struggle to salvage their game state.  It is seen as rude or poor sportsmanship by some, but it is highly effective and can lead to huge point spreads like winning 15-5-4.


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in Citadels, the Fort card ability does it affect whole city or just the card?
The Fort card ability makes it immune to the tier 8 character ability. Does it apply to the whole city or just to the Fort?
It might be that the Fort ability is unclear in my language edition.

Welcome to Board and card games. The question is a bit hard to understand. Can you please edit the question and add some more information.

I wonder, what does it say in your language then? Like Eric Nolan's answer says, it's rather clear in the English text, and it's similar in the other translations I saw on boardgamegeek.

Assuming you are referring to the Keep card as it is called in the English edition the text is quite clear that only that specific building is protected.


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What does this card mean in Everdell?
This card confuses me.  It's from the second edition of Everdell.

What does it mean?  It could be...

Draw two meadow cards.  Play one of them for one resource less than it would normally cost.

Draw two meadow cards.  Play one of them for one resource (likely less than the original cost of playing that item).

Draw two meadow cards.  Play one and gain a free resource.  This seems unlikely, but isn't that what paying -1 resources means?

Option 1 is correct.
The designer James Wilson has clarified this on a BGG Forum Post
He clarified the following was correct (copy and pasted from the post)

"draw two Meadow cards, and then play one of those cards you just
drew with a discount of 1 on any resource."


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Last stone in hand landing in Mancala
When your last stone in your hand lands in your store (Mancala), is it  optional or required to take an extra turn?

Maybe I am not understanding something but how can you take another turn if you have no stones left?

Last stone in hand, I presume.  Since this is the trigger for getting an extra turn.

You Must take another turn.

When the last seed in your hand lands in your store, take another turn.

Source: mancala_rules


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Which Ranking system is best for my group that play Hearts?
I have put together an advanced Excel spreadsheet that I use to keep score.
I currently track a year to date average which is a raw average. A yearly average that has a minimum of 12 games played to tabulate and a lifetime average that uses the yearly averages to show your average of all time.
I would like to have a sheet that tracks your average based on the number of games you play, but I am not sure how to do this.
David plays the most games and statistically I think his score would be the greatest risk/reward and in some cases he plays hundreds more games than another player.
Is this assumption correct?
If so how would be the best way to look at this?
Here is a copy of the current sheet: Scoresheet

I did not understand, can you explain a bit more what are you asking?  Are you looking for something else than average? Do you wish to give players that play more often more or less points?  Are you looking for some Ranking criteria? If so, you can look at ELO or GLICKO rating systems.

I may be looking for a "weighted average" although I am not sure.

Are you looking for something else than average? Maybe I am, I am not sure. I just want to have the most accurate information on player "ranking"
Do you wish to give players that play more often more or less points? Not more or less points just looking to tabulate a ranking on the players based on scores and games played.
Are you looking for some Ranking criteria? If so, you can look at ELO or GLICKO rating systems.  Those look interesting but I am not sure how to incorporate that into my sheet

From what I understand, I think that you are looking for some players-rating system.  The most known system is ELO. In a nutshell, the ELO compute the probability for player A to win player B (and players C & D).
I would start by reading Understanding the Elo Rating System. If you want a bit more theory, check wikipedia.
BGA explains well their implemented of ELO that takes into account multi-player games:

A player's ELO score on BGA is based on the ELO formula, which is one of the most popular ways to evaluate a player's level.

When you have never played a game, your ELO is zero.
When you finish a game, the number of points you gain/lose depends on the level of your opponents, and more precisely on the ELO difference between you and your opponents.
The easiest situation is a 2 player game. You will gain a number of ELO points equal to K x (W - p(D)) where:

W is the result of the game: 1 for a victory, 0 for a defeat, 0.5 for a tie.
D is the difference of ELO between you and your opponent.
p(D) is the probability of victory considering the previous difference (see Wikipedia for details).
K, the 'elasticity factor,' has a value that depends on the number of games you have played: 60 for your first 10 games, 40 between your 11th and 20th games, 20 for your 21st onwards.

Some more details and specific cases:

On your very first game, you always win at least 1 ELO point, even if you lose the game.
Until you reach 100 ELO (beginner), you can never lose ELO points. After that you can never go back below 100 ELO.
When you play with more than 1 opponent, we consider that you win against each opponent who scores lower than you during this game, and lose against each opponent who scores higher than you. For example, if you place 2nd in a 4 player game, you gain ELO points as if you won against the 3rd and 4th players, and lost against the 1st.

Like Cohensius, I will assume you are looking to create a player rating for your group's hearts games. I assume that an Elo based system is more complicated than you need/want.
Recommend the following:

Rate player based on game results, instead of hand results. The goal in hearts is to win the game and this greatly reduces your data entry.
Need a score to rate each players result in each game. The scoring method I chose for a tournament I ran was: [player's points] - [winner's points] + (constant between 0 and 100, if not the winner). For my elimination tournament I chose a fairly high constant, but point differential alone may be good enough for your group. It is easier to explain as "the average number of points the player looses by".
Player rating is the average of their game scores.

Unlike an Elo system, this system doesn't address the following issues:
A. Some players improving over time.
B. Stronger (or weaker) players playing each other more often.
This type of rating is likely good enough for a social group of under 15 players, especially if games are NOT arranged by skill level.
If you do want to account for a larger group with a wider range of skills, I recommend the following:

Instead of the constant referenced in item 2, calculate extra points given to non-winners as [Sum of ratings of players in game]/4.
New players should start with a rating at or above the group's average rating.

One additional scoring rule I recommend:

Any score above 100 is considered 100 when calculating point differential with winner.
This rule helps minimize the penalty for final desperate attempts to win via a run.

Any rating system that accounts for other than strict Win-Loss will be gamed. This system you propose punishes players who take a late hit in attempting to stop a Moon Shoot. Do you really want to introduce that dynamic into your games? I wouldn't.

@Forget Evaluating solely on game win% ignores information on the performance of the 2nd-4th place finishers. This is important if some players don't play many games. Win% should also be tracked with the same spreadsheet.
The hearts scoring model does punish a player who stops a run, so the dynamic you describe is already part of the game. An end-game stopper with a big lead still scores a 0 by stopping and winning. If winning is not possible, deciding to stop or not allows the player to pick the game winner. This is a situation common to most multiplayer games.

Don't be absurd. You seem to think the game is Diplomacy. It's not; it's Hearts. There is no second place in the game. Your ranking system makes it better to come second every game than to win half the games and come 4th in the other half. That's silly.

@Forget Hearts includes situations where a player without a shot of winning can determine who wins. So like other multiplayer games, there is an element of diplomacy.
Always 2nd player would have a below average rating compared to the group he plays with. Winning is the only way to score better than the group average.
Multiplayer Elo has the always-2nd beating 2/3 of his competition, while the 1st-4th player beats only 1/2 of his competition.
Do you have a better answer to the question?
Win % alone can be gamed by choosing weaker opponents.
This solution worked well enough for my group.


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AI effect on chess openings and variations
I'm writing an essay related to AI and chess. However I am not a chess player, but a Go player. There are many AI chess engines nowadays that significantly overwhelm the chess ability of human.
Go has many powerful AI engines. The one thing I think about the disadvantage of AI is that so many openings and variations are reduced. For example, there are many openings in Go (i.e. some of the 3-4 Point openings) that were evaluated to be not so good (maybe unconvincing for amateurs) by AI engines, so they become less involved in many Go games.
My question is, did Chess follow the similar trend?  Did AI chess engines really have an impact on the chess openings or variations? If so, it would be really interesting to show supporting data that quantify how much reduction has happened. Showing some examples would be nice to!

"The one thing I think about the disadvantage of AI is that so many openings and variations are reduced." << Regarding go, I've observed the exact opposite of what you describe. Before AI, we had joseki and opening sequences that people would follow blindly. Then AI came along and said "stop playing standard sequences, use strategy and imagination instead" and brought a lot of diversity to the opening.

In short, no. I can think of three possible reasons for this.
First, most of the advanced chess-level games are draws. While still important, opening is not the most crucial part of modern chess studies. As many have
already mastered opening skills ( there are some basic principles to follow, like developing pieces, pawn structures, etc.), endgames are the real battleground of Grand Masters. Magnus Carlsen, one of the best players of all time ( best of the current generation), is the best ( not one of ) endgame player of all time.
Second, most openings are being studied at least 30 to 40 steps into the game. When AI analyzed it, it was just all zeros ( indicating a draw), which is unhelpful at all.
While indeed some lines are discovered by AIs, those are often so-called "weird" openings that players rarely play in actual games. Moreover, when playing, we can always choose a different line that is more thoroughly studied.


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When someone can call out the bidder out rule?
I play dbl deck pinochle once a week with the same 3 friends and was introduced to the bidder out rule which I never played in all my 60 years of playing.
bidder out rule: if both teams go over the amount it takes to win (usually 500) in the same round, the bidder wins regardless of the opponents higher score.
When does one put the rule into effect? For example, if the score is 260 to 215, should someone be calling out that rule?

someone will call out this rule before either team has reached the winning score what do you mean by "call out"? Just remind people of a potentially relevant rule? Or try to (mis-) use the rule?

The rule is always in effect. It doesn't get put into effect at some point in the game. You don't need to call it to have it be in effect.

To be honest a lot of bidding games where one player/team wins the bid have a rule where the bidder wins if multiple people/team go over the winning score on the same hand. I also find it not uncommon that you need to have the bid (or set the bidder) in order to win and you can be above the winning score and not win.

The rule is always in effect for single or double deck. We generally say “bidder goes out” as a reminder but it isn’t required.

Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.


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Euchre question about ranking
Played online and saw a situation where the trump was Hearts, the led card was Spades, and the Queen of DIAMONDS won over the Ace of Spades (the led suit).  Which one is it?
I Used to play all the time… but its been a while, and I forgot some things. I’m now playing online and it seems weird. Always told: trump suit first, same color suit second, opposite color last. But the highest led card wins over everything but the trump suit.

I suspect it was the Jack of diamonds that won the trick.  With hearts as trump, the left bower is the Jack of diamonds, and the second highest card overall.

If a spade is led, then the highest trump played wins. If no trump is played, then the highest spade wins.
Card rank is normal, but with the Jack of trump highest and the same-colored Jack as the second-highest trump.
The off-suit, non-trump queen will not win the trick.
From Wiki:

The player who played the highest card of the suit led wins the trick unless a trump is played; then the highest trump card wins the trick.

Card rank (highest first) J (of trump suit) J (of same color) A K Q 10 9, sometimes 8 7


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Usefulness of Splendor rare moves
I'm writing a AI for the game of Splendor. While the following moves are allowed by the rules, I'm more curious if there is ever a use case to actually play them:

If you are buying a card, is there a benefit to use the Joker when you have the currency to afford it without the Joker?
If you can afford to buy a card, is there a reason to rather reserve the card?

A generative adversarial network could allow your AI to work out the answer by playing tons of games against itself to quickly improve.

sometimes you might want to take a card off the table simply to keep it out of somebody else's hands

A possible scenario in which you would want to reserve a card rather than buy it:

You have:

10 VPs
3 red development cards
3 green development cards
4 black gems

Your opponent has:

12 VPs
3 white development cards
4 blue development cards
3 black development cards

A noble is present which requires 4 white and 4 blue development cards to visit
The only white development card visible on the board costs 3 black and gives 0 VP
A development card is present which costs 5 black, 3 red and 3 green and gives 5 VP

You cannot purchase the 5 VP development card this turn, so you must block your opponent from taking the 0 VP development card, visiting the noble and winning. If you buy the 0 VP development card, this sets you back significantly in being able to purchase the 5 VP development card without really developing your position at all. If you instead reserve the 0 VP development card, the gold token you get means you threaten purchasing the 5 VP card on your next turn and winning yourself.
(I haven't actually checked if those specific development cards mentioned actually exist but they're pretty close to real cards, and in any case it will be easy to modify this example to cards which do exist)

I think this is a valid scenario. I don't think it needs quite as many conditions for reserving a card you could buy to be the optimal move. Reserving a card simultaneously provides you with a joker which you could use to buy the card you need to win next turn, and prevents the opponent from buying it. So it is a much more common scenario than this answer would imply.

@qdread I don't disagree; I just wanted to set up a situation where it was unambiguously the right thing to do rather than just probably the right thing to do.

So in brief, you might reserve a card just for the gold token and/or to block it from the opponent, not just because you want to play it. Even without blocking, you might be one token short from playing a winning card (from your hand, hopefully), while there are none of that color available to pick in the usual way.

@ilkkachu Yeah, that second case is probably easier to set up - you need (say) 1 white gem to be able to win but there are no white gems available, so just reserve a card for the gold token instead.

In games in general, any time there are more than two players, for any action, no matter how apparently self-defeating, it's usually possible to construct a scenario in which it is optimal. Your action might help another player, who then can block another player who is more of threat. Finding a reason for the move becomes even more of a possibility if you're engaging in collusion/trade with other players.
Even in a two-player game, there are edge cases where the scenarios you mention are optimal, especially your not buying a card case. If the reason you want the card is more to block the other player, rather than wanting the card for yourself, then reserving the card rather than buying it allows you to both block your opponent and save your gems for buying something that you actually do want.

Great point about helping another player as a means to block a third player who is more of a threat. That sort of logic works for even more contrived scenarios than the original question. Such as spending tokens on a card instead of using the bonus discount. This could restore an empty pile allowing another play to draw tokens and then do something on a subsequent turn that blocks a third player. A very contrived, long play but theoretically possible nonetheless.

Short answer: removing those possible actions, will probably not reduce the win-rate too much.
Second thought: explore those actions only close to the game-end, since the chance that this action will be optimal is higher and the size of the search-space is smaller.
Responsible answer: test it, let your bot play vs bot* where bot* do not consider those moves.  If the win-rate of bot* is no less than 50%, then it is safe to remove those options.
From theoretical point of view:

action #1 can be used in order to block an opponent: for example, assume a single color stuck is depleted, and the opponent needs that color + 2 other in order to buy something.  By using the joker you block that action from the opponent.
action #2 sound to me a waste of a move, but might be optimal in a 2 players game, reserving a card keeps the options open.  For example, assume 2 players game, our agent can buy one of 3 cards A,B,C while the opponent can buy A and, if takes {b,c} tokens can buy B or C respectively (depend on which tokens she collected).  Here the agent's optimal strategy might be to reserve A, and on the next turn, buy either B or C, depends on which card the opponent made the preparations to buy.

I disagree that these moves can be safely removed. The justification given by @Cohensius for action 1 is valid, but to me there is a more likely justification for action 1: if returning a colored token to the stack would result in 4 or more tokens being in the stack, allowing the opponent to take 2 of that color at once (which they might need to buy a key card next turn). So by using the joker instead of the colored token, you prevent the opponent from doing that.

You are assuming that OP will have programmed his bot to properly take advantage of these moves. It may be that the moves are valuable but the OP does not know how. That is the entire purpose of their question.

Possibly but the original question just asks whether there are "use cases" for either of the listed moves, and I think they aren't really that rare or esoteric of cases. In my experience, they don't occur every game, but probably every ten games or so.

@qdread, you right, so I edit my answer.


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Impossible bid at Pinochle
If a person bids 43, only has 11 meld, but claims they can take all the tricks is it allowed? There are only 25 tricks and we’ve assumed it would be a set.

I'm unclear what you’re asking. It sounds like they will go set, but are you asking if there’s a rule against making a bid that’s impossible to win?

Team bid 43 but only had 11 meld. They felt they should be able to play it because they could take all the tricks!

There is no rule stating that you cannot make a bid that's impossible to win, or that you cannot proceed to play the hand if your bid is impossible.
Some rule sources have a rule that a player can choose to throw in their hand and not play the trick-taking portion of the hand; others do not have this rule. But even when playing with this rule, it is an optional choice for the winner of the bid; never mandatory.
Now if you are playing with this rule, then a player who cannot make their bid but chooses to play it out anyway is only wasting your time, and I would consider it poor sportsmanship; something I would be annoyed about. They are also risking giving the opponents extra points if they do not manage to capture all 25 points. So the decision to play the hand is strictly worse than throwing in the hand at that point.
In your specific situation, there is not enough information to understand exactly what happened. Did the player explain why they wanted to play the hand? Was it just because they wanted to see if they could manage to capture all 25 points, even though they knew they would go set anyway? Or did they not understand something about the rules that made them think that they could avoid going set?
In a friendly setting, if it was a very relaxed game with everyone having plenty of extra free time to sit around and play the game, then I could see someone asking their opponents if they mind playing the impossible hand just for fun, to see if they are able to take every trick with their hand. But if a player objects and says that they don't have that extra time to spare, then it would be rude to insist on doing it anyway.
In summary, the play is legal, and according to some rule sources even mandatory.


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How can I identify the mechanics of Risk?
Today I learned about game mechanics and I'm trying to find some game mechanics in the board game Risk. It is pretty hard since it is a new lecture I learned. So far I found 4:

player elimination,
rolling the dice,
the Risk cards,
the armies.

Could someone help me please?
Thank you!

Good place to check is the BGG game page, the mechanics are stated under classification:

So from the sounds of it, you've just sat through a Game Design 101 course lecture, and part of the homework is to identify all the mechanics of the game. I had to do that too at one point.
The thing you're probably having trouble with is this: “mechanic” is kind of a broad concept! Essentially, a “mechanic” is every single thing the game does or every option it gives you. (Your lecture might give a slightly different definition.) Things that aren't mechanics are generally considered narrative elements (“this is a war”) or aesthetic elements (the map specifically being a world map, not just a plain diagram), since those aren't distinct things the game does.
Where it gets really broad is that you can look at mechanics from a big picture perspective:

Combat is a mechanic

Or from a more zoomed-in perspective:

Picking units to move is a mechanic
Moving those units is a mechanic
Designating combatants is a mechanic
Rolling for combat a mechanic
Choosing casualties is a mechanic
The continue/retreat choice is a mechanic
Retreat is a mechanic

And both of these lists are more or less true: these are all mechanics that can be considered sub-mechanics of the combat mechanic.
Risk does a lot of things. And all of those things it does almost certainly contain more specific, smaller units of things it does. This means the cutoff point for what you consider a mechanic and how zoomed in you want to go is kind of arbitrary and depends on what you personally are trying to get out of this analysis.
The mechanics you've identified are all accurate so far, but far from the end of the list. The risk cards are a mechanic. They also consist of further mechanics: drawing a risk card is a mechanic, playing it is a mechanic, the things the individual risk cards can do are mechanics. They might engage with other mechanics: it's conceivable a risk card can cause combat to happen, for example.
I suspect you're having some trouble because you're not sure what is and isn't a mechanic or how far to zoom in and break things down, and well, the mechanics are almost all of it. Almost every single thing that makes up the game is a mechanic somehow, aside from the aesthetics and narrative. Your homework assignment needs you to consider this, and you can drill down as far as you feel you need to meet what it's asking of you.

Thank you so much for this, you helped me out a lot. I really mean it :) Hope you have a nice day!

You're very welcome! You have a good day too! Good luck with your assignment! :)

Game mechanics are like TV Tropes - they can be extremely broad or exceptionally granular


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Memorizing the cards dealt in the game
So I've recently found this game 'Gin Rummy' on Playstore and it keeps me interesting. Its similiar to Rummy and its got this feature called 'knocking' and that is quite a different take from the usual game. I try to play almost every day on it. One aspect of it is it helps my mind alert.
In the game my method of trying to memorize the cards that are being dealt on the table is to club the cards together in my mind.
For example If a Jack of diamonds is dealt on the table, in my mind I say aloud J.
Then if a 7 of spades come I append that to the J in my mind so it becomes J7
Then if a 2 of clubs come the list in my mind becomes J72. Since that seems complicated to me I say Jay Seventy Two (J72)
ok, so after 10-15 cards come on the table the list in my mind becomes something like this
Example:
J72 Q96 564 KK2 798
since in my mind I cannot write down the list like the above I say it like this
Jay seventy two - Q ninety six - Five sixty four - Ksquare 2 - Seven Ninety eight
Ok. Uptill here it is okay with me. But when the list goes on and more than 20 cards have been dealt in the game I am not able to memorize the cards which have been dealt in the current game.
So, I was wondering - I am not the first person to whom this problem has happened, there would be loads of people who have had this problem. And that is why I was wondering if any of you guys have had this problem. And what strategy do you use to memorize the cards that come along in the game?

I am not familiar with gin rummy but one method used by memory experts to remember a whole deck of 52 cards is to create yourself a memory palace with  at least 18 rooms. You have to do this once and reuse the same palace forever.
Additionally, for every card in the deck you have to learn a person, an object and an action.
This is your setup.
When the cards are then dealt you start filling your palace.
Say the king of spades is George Washington, chopping and a hat.
The 3 of clubs is Britney spears, singing and a broomstick
And the 8 of diamonds is your mother, cleaning and a candle.
Let's assume the first room in your palace is the guests toilet.
Let's assume the sequence starts with K♠ 3♣ 8♦
You would then memorize George Washington singing with a candle in your guest toilet.
And so on.
The initial effort is pretty high though: you have to learn 52*3 references to cards and build your palace

Hey that is brilliant!

Aldinjo's answer is the best practice if you can find in you the mental power to build that great palace.  If for some reason you don't feel you can build the palace, here is an easy walkaround: write.

In order to be expert at Rummy-Gin, you need to memorize more than just  the cards that been dealt, each card is in one of the following states:

unseen (either deck or opponent)
my hand - seen/unseen by opponent
opponent's hand
discard by me/opponent/first card

Chapter 5 at the book How to win at Gin-Rummy:Playing for fun and Profit, is dedicated to figuring the opponent hand.  The author use 3 matrices: your hand, opponent hand and opponent likely hand.

Make those notes only at games that do not consider writing as cheating.

Thanks for the method and the book. I need to go check that out.


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Passing cards to prevent an opponent to shoot the moon
In the game of Hearts, when holding J432♥. Does passing a single low heart reduce the risk of someone shot the moon?

Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.

No, because the 2, 3 & 4 can be played to the A, K and Q leaving your J master.

@WeatherVane until you get finessed. OK, less likely in a game like Hearts than Bridge but still a possibility.

@PhilipKendall I did not say it was a certainty, just that you are giving away your 'cover'. If you had a 'spare' heart, then yes.

It would also help to know what the rest of your hand is like as that will influence what the pass impacts as well.

It is almost always better to get your own void instead of dropping 3 hearts

No it is not and in fact it might ensure that they do shoot the moon. IF they happen to have the AKQ♥ you have lost the ability to stop it by taking a trick with the J♥. If you pass one of your hearts they are still guaranteed the first 3 heart tricks which would include all 3 of your hearts. Depending on the card distribution that could also leave them with the only heart left to be played.
If you are worried about preventing someone from shooting it would be better to keep all 4 hearts so you have a better chance of taking a heart trick and preventing them from shooting.

Maybe.
One of the biggest liabilities when shooting the moon is low hearts (2, 3 and 4 in particular) because you have to save them until everyone else is out of hearts.  This is different from low cards in other suits, where you can try to play them early and bet on a no-trick hand.  If someone is sitting on only a few hearts (say just the ace) and mostly high cards in other suits, passing them the 2 of hearts will almost certainly ruin their plan.
On the other hand, one of the best ways to shoot the moon is with a fistful of high hearts that you can use to draw all of the other hearts.  If someone has A, K, Q, and 10 of hearts, passing them the 2 in this situation will actually reduce your ability to stop them, as you will only have three hearts left and they can pull all of your hearts with the A, K, and Q.  By comparison, if you had kept four hearts, you could have played low hearts to the A, K, and Q, and then had the J in reserve to beat their 10.

So if the user had a Q instead of a J, they would likely be able to cover the shoot even if they passed the low heart?

Probably.
The likelihood is low that a player holds the top three hearts. You can prevent a run by the person receiving your pass; unless they have this rare distribution.
However a hand with these four hearts would likely be better off passing other  cards. Holding these four hearts already makes it more difficult than usual for someone to run. Note that even if you retain 4 hearts, you still need to be careful about breaking hearts in order to defend against a run.


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Tournaments for the No-Forced-Jumps Checkers?
Are there any tournaments for the No Forced Jump version of the Checkers?
I grew up only playing the No Forced Jumps variant of Checkers. I see now that there are tournaments for the Forced Jumps version, and I see how that appears to be the more respected variant of the game generally.  Are there any organized groups that hold to this variant?

As per Sultan Ratrout's "A Guide to Checkers Families and Rules" there aren't any current officiated rules that do not include mandatory capture of one form or another.
While many people play without mandatory capture in casual settings it is strictly speaking a house rule, and so most likely will not be found in any serious tournament setting.

I would assume this is to prevent forced stalemates.

anecdotal evidence suggests it does reduce draws, but it's not 100% effective, as perfect play always results in a draw.


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Can I build a settlement on a "broken" road?
If I have a settlement with many roads connected, let’s say at least 6 roads deep, and my opponent cuts it off and builds a settlement between them, can I still build a settlement at the deep end even though my roads aren’t connected to my settlement anymore?

yes
From the rules:

You may only build a settlement at an intersection if all 3 of the
adjacent intersections are vacant.
Each of your settles must connect to at least one of your roads.

If you don't break either of those rules and you have the resources you may build a settlement.
You might be getting confused with how a player 'breaking' a road with their settlement can shorten the longest road. Another player building a settlement on your road doesn't prevent you building a settlement if it is not adjacent to where you want to build.


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Strategies in battleship
In the game of Battleship what are the best strategies to

Place the ships
Shoot other ships

Please also provide an explanation for your strategies.  TIA
The rules are:

Both players place their ships on a 10x10 grid.
Ships have to be placed so that adjacent to a ship is only water.
Opponent's feedback on each shot is one of three : HIT, MISS or SUNK.
Each player have the following ships:

1 ship of length 5
2 ships of length 4
3 ships of length 3
4 ships of length 2

Is that standard? The Milton Bradley version has five ships total - one 5, one 4, two 3s, and one 2

You are right, I changed my question

"The ships have to be placed so that adjacent to a ship is only water." Is this actually a rule in the paper version? That greatly limits the number of arrangements of a fleet. Or was it only that the ships couldn't overlap the same location?

From what I understand, variants of the game differ in two aspects: (1) either ships can or can not be adjacent to each other, and (2) the amount of ships from each length.

A strong algorithm for a slightly different set of rules:
Ships Can be placed next to each other.

DataGenetics wrote a fun piece about solving Battleship a few years ago. If their algorithm isn't optimal, it's at least extremely close. The author combined the concept of parity with probability density functions. That is, you only have to fire at every i'th square of the grid, where i depends on the size of the smallest ship. And as the number of shots increases, some spots are more likely to contain ships than others depending on how many rotation and translation-configurations of a certain ship is possible considering the space that is left.
I think it would be interesting to attempt to optimize fleet layout against their strategy. Maybe it's possible to lay out the ships in such a way that the probability density function gives the least amount of information for the maximum amount of rounds?
https://www.datagenetics.com/blog/december32011/
The paper compares 4 algorithms, running each algorithm 100M games.

Random is just a (bad) base line, see that it has a probability of 17/100 to shot all the 100 places.
No parity also called Hunt/Target plays random until it hits, then shoot next to hits.
Parity do the same as #2 but also use Parity (as in the answer of @Zags (N = 2 to start))
New algorithm is the winner and it shots in the following manner:

calculate the most probably location to fire at next based on a superposition of all possible locations the enemy ships could be in.

The following graph display number of turns distribution, we can see that in most games, the New algorithm sunk the opponent's ships in 30 to 60 turns.

Could you put more details of the strategies into your answer so users don't have to visit the site to understand it.  All answers should be self contained so if the link you use breaks the answer is still valid.

I independently found that article and didn't make reference to it because it has a number of flaws.  Most importantly, their implementation of the "parity" strategy doesn't take into account whether or not a ship is sunk, and therefore wastes an incredible number of moves surrounding sunk ships with hits (and consequently ranks very poorly given this).  Additionally, their proposed "new algorithm" requires a statistical analysis that cannot be reasonably performed by a human.

@Zags, the flaw you are talking about is a matter of different rule set: The paper uses: "Ships Can be placed next to each other" While the OP ask about: "adjacent to a ship is only water."

@Cohensius The article assumes ships can be placed adjacent.  If that rule changes the analysis substantially, then the article is even less relevant to this question.

@Zags, agreed, I think I should edit the answer to highlight the different set of rules.  Never the less, the algorithms that the paper use are still valid (with a minor fix).

The strategy for placing follows from the optimal strategy for shooting, so let's start with shooting.
To shoot, do the following:

Start in a random part of the board.  Go to step 2.

Check every N squares from where you started, where N is the smallest opponent ship remaining (N = 2 to start).  If you already have an established search grid in another part of the board, you should use the same search grid in this part of the board.  You should explore in a random direction each time you expand your search grid.  If you don't hit, stay on step 2.  If you do hit, go to step 3.

Check the squares adjacent to the one you hit.  Once you discover the direction of a ship, keep checking in that direction until you sink a ship.  Once you sink a ship, go back to step 1.  Note that there is a rare case where two ships can be parallel, so if you have two hits with misses on either side, check the other direction.

For example, with N = 3, you are trying to sweep a pattern like this:
X . . X . . X
. X . . X . .
. . X . . X .
X . . X . . X
. X . . X . .
. . X . . X .

This is the sparsest pattern (fewest number of total guesses) that is guaranteed to find all of their ships.
Given this, the best thing you can do when placing your ships is at random such that no two ships are touching (some variants of Battleship have this prohibited in the rules, but even if it is allowed, you shouldn't do it).  The problem with ships touching each other is that when the opponent hits one of your ships, they will be checking around that hit to find the rest of the ship, and thus may find your abutting ship by accident.
Other advice for ship placement is only helpful if the opponent is searching sub-optimally, but here it is nonetheless:

Place your ships far apart; in particular, make sure your three smallest ships are far apart.  The simpler version of the systematic search involves starting in one area of the board and sweeping from there without ever resetting (a player would go from step 3 back to step 2 rather than to step 1).  By placing your ships far apart you can nearly guarantee your opponent will have to search most of the board.  Having the small ships far apart is particularly important to exploiting this behavior because sinking the small ships are the biggest boon to a searcher (once you have sunk all the ships of a certain size, you can increase the N of your search grid).

Avoid the corner around 1A.  Humans are bad at picking at random, so the 1A corner is the most likely place people will start searching.

Put ships in a mixture of along the edges of the board and in the middle.  Again exploiting the fact that humans are bad at picking at random, and will likely be exploring in a particular direction, either towards the edge or towards the middle, but not both.

Put your ships in such a way that minimizes the number of diagonals that they share.  This way, you maximize your chances of the opponent missing one of your ships if they try to do a wide sweep (such as N = 4) to start, requiring them to go over the entire board again.  See below for an example, where the same ship placement of three small ships guarantees that at least one ship will be missed by an N = 4 sweep (@ = unhit ship, # = sunk ship, X = miss).
  1 2 3 4 5 6
 1 # # . . X .
 2 . X . . @ X
 3 . . X . @ .
 4 . @ @ X . .
 5 X . . . X .
 6 . X . . . X

   1 2 3 4 5 6
 1 # # . . . X
 2 . . X . @ .
 3 . . . X @ .
 4 X @ @ . X .
 5 . X . . . X
 6 . . X . . .

   1 2 3 4 5 6
 1 @ @ X . . .
 2 . . . X # .
 3 X . . . # .
 4 . # # . . X
 5 . . X . . .
 6 . . . X . .

The random walk feels correct to be as an answer, but it's not obvious why the step size should be the smallest ship remaining. It feels to me there's some value in going to a larger value because you could find a length-4 or length-5 ship quicker which then rules out a larger number of other potential squares, can you can always go back and "fill in the gaps" afterwards to find the length-2 ships.

Agree with @PhilipKendall, There is a chance that you will hit all the 2-size ships before shooting all the N=2 places. For example, you can start with N=4:
X . . . X
if after that you still did not find all the 2-size ships, then fill the gaps:
X . X . X

@Zags's strategy minimize the number of shoots in the worst case scenario.  However I think that there are better strategies to minimize the average case scenario.

@Zags, The ships have to be placed so that adjacent to a ship is only water. So this part is redundant: "the best thing you can do when placing your ships is at random such that no two ships are touching. The problem with ships touching each other is that when the opponent hits one of your ships, they will be checking around that hit to find the rest of the ship, and thus may find your abutting ship by accident."

@Cohensius I've played variants of battleship where ships can be placed adjacent

@PhilipKendall Battleship is fundamentally a game about finding the small ships.  Finding a large ship only removes 1 or possibly 2 (in the case of a 5-length ship that has it's end on your grid) places that you'd be checking in an N=2 grid.  Conversely, finding all 2-length ships removes 50% of your remaining spaces because you can go up to the N=3 grid.  Despite the game's famous catch phrase ("you sunk my battleship"), the primary goal of the game is to sink the patrol boat.

@PhilipKendall I think you would want to go with one of the larger ships as it allows you to cover more of the board rapidly and you can still find the small ships while doing this.

Sure your biggest battle will be in finding the small ships but if they are on the opposite side of the board from where you start you are going to have a lot of missed shots to find them. But if you target the larger ships first there is still the chance of finding the smaller ships much faster. You can always start looking for smaller ships as you take out the larger ones. But if you find the smaller ships while your search radius is still large you gain a decent advantage of not having to search large chunks of the board.

I'm almost interested enough in this problem to start writing some simulations, but I've also got a bunch of IRL stuff going on, so...

@JoeW Note that in my strategy, you restart the part of the board you are searching upon hitting a ship so that you aren't exploited by ships placed far apart

That doesn't help you if you are not hitting any ships to begin with.

@JoeW I added a fourth ship placement tip to my answer that is the countermeasure to your proposed strategy (starting with a search grid of N = 4)

@Zags Sure it isn't perfect but yours has its flaws as well. Mine is designed to cover as much of the board as possible while yours is designed to not need to go back to areas

I may be mistaken here, but in step one, is it better to use a random square which would have been a part of your previous search strategy if you have more of that size to find? e.g. if you were previously looking at A1, B2, C1 squares - i.e. odd squares on odd-rows, even on even, you should pick G1 or H2, rather than H1 or G2... In the worst case this would help avoid some edge-effects, I think.

@NeilTarrant That was implied in my search algorithm, but I tried to make it clearer

I would say the optimal strategy for shooting is aiming to destroy the largest ships first in order to cover as much as the board as fast as possible. I would suggest starting out with a gap of 4 and move down as you sink the larger ships.
Below is an example of starting out with a gap of 3 between shots and filling it in later with a gap of 1 between shots.
X . . . X . .
. X . . . X .
. . X . . . X
. . . X . . .
X . . . X . .
. X . . . X .

X . O . X . O
. X . O . X .
O . X . O . X
. O . X . O .
X . O . X . O
. X . O . X .

I suggest this for several reasons.

You still have the possibility of hitting and sinking the smaller ships
If you start on the opposite side of the board from their ships you will waste a lot of time
You will cover the board much faster.
Starting by blocks of 4 lets you cover the entire board quickly and then come back and finish the board by filling in the gaps to rule out 5 positions with a single hit

Note: I am not suggesting where to start on the board, just the pattern to follow.

This strategy is easily defeated by placing your ships on different diagonals, especially if you have four 2-length ships as is in the question.  Clever placement will guarantee that you will miss at least one small ship on your initial pass, requiring you to fill in all the rest of the board.  Conversely, trying to find all the 2-length ships initially gets you to the point where you can safely increase the size of your search grid faster.

@Zags sure it isn't perfect but yours has its flaws as well

How to Win at battleships
There are two repeating phases in the game: Hunt and Kill.
In the Hunt phase you are trying to find ships. Since all ships occupy at least two contiguous squares, you only need to fire at every other square. If it was a checkerboard, you'd only fire on the red squares and not black, for example. Once you score a hit, go to the kill phase.
Kill phase obviously results in trying to figure out which way the ship points and where the ends are. In this case you fire immediately adjacent to the hit location. The rest you can figure out.
You can save some time by knowing which ships are still out there. If you have found the destroyer, you don't need to sample every other square, but rather every third, as the smallest ship will span at least three adjacent squares.
I'd start randomly firing off shots, but don't hunt in adjacent squares. Then you can fill in holes later after sinking a few ships and knowing which ones are still out there.
TL,DR; Every other square to find ships, then sink them.

This answer repeat @o2h2o answer.  Also the link you provided is summarizing of the link provided by o2h2o answer. Both explain the work done by Nick Berry from DataGenetics.


text:
Identify this 10 Column Solitaire
A few days ago the person next to me on the plane was playing a solitaire game I had never seen, and I have been looking for the game name without success.
What I could figure out is:
Deal:

Two decks (104 cards).
10 columns, each with 5 face-down cards.

Movements:

The Draw action: draw from the deck a single card on ALL 10 columns (10 cards in total).
The Move action: you can move partial cards as usual between columns.
When no arrangement is possible, you draw the deck again.

Special rules:

You can combine same suit and when you have A-K sequence, that set goes away.

End game:

Win: completes all 8 sequence of A-K.
Lose: getting stuck and run out of cards in the deck.

Update: It looks like some kind of a Spider game.

By "blocked", you mean face-down?

By "naipe" you mean card?  in order to combine the two cards, they must be identical in both Suit and Rank?

@Cohensius I mean they cant be accessed b/c there are other cards on "top", but they are indeed face down

It sounds exactly like "Spider Solitaire" included in the games supplied with Windows 7. However, the initial deal is uneven: the first 4 columns are dealt with 6 cards, so there are 54 cards in the deal, leaving 50 cards in the deck – 5 whole rows of 10 cards. It can be played with 1 suit (easy), 2 suits or 4 suits (hard), but always with 104 cards. The next row cannot be dealt if there are any empty columns on the table.


text:
Do I get bonus points for undercut with gin?
Let’s say I get gin, but I don’t knock. Then my opponent knocks with deadwood of 8. Since I have gin, do I get the bonus points for both the gin and undercut, plus the difference of 8? If not, what bonus do I get?

Not a duplicate because the opponent did not have gin.

The issue is that the answer to both question are answered with the same rule text.

The situations are totally different though. One is asking about undercutting gin (you can't) and one is asking if gin applies to an undercut (it doesn't). That's two separate rules.

See also this meta on another site

right, two different questions with the same answer, should be reopened.

You only get the Undercut bonus + the 8 deadwood difference.
Gin can be made only by the active player. Source: pagat:Gin Rummy

Knocking with no unmatched cards at all is called going gin

The following sentence casually explains that the non-active player that has zero deadwood did not made gin.

Even if the other player has no unmatched cards at all, the person going gin gets the 20 point bonus the other player scores nothing.

@Styxsksu's answer is 100% correct, my answer cites pagat which is  better source for rules of cards games.

This seems like a comment (a correction to the terms being used) rather than an answer. It doesn't seem to address the question.

@L.ScottJohnson, I have edit the header to better answer the question.

I would go with only getting the underknock bonus since you didn't knock.  I would argue that the Gin bonus is only given to the player that knocks since it is given for getting rid of all dead wood through meld when knocking. If you are playing the second player gets both bonuses it changes how the game is played since there is an advantage to sitting on gin since you might be able to pick up both bonuses.
relevant text (bold added by me to show relevant text)
In standard gin, a player with 10 or fewer points of deadwood may knock, immediately ending the hand without giving the opponent a chance to play. Knocking with no deadwood is known as going Gin or having a Gin hand, while knocking with deadwood points is known as going down.[6]
After discarding to end a turn, a player who wishes to knock must clearly indicate their intent; this is generally shown by laying the discard face down, but can also be done through a verbal declaration or by tapping the playing surface. The player then lays out their hand, organized into melds and with any deadwood separated from them. The opponent, or "defending" player, shows their melds and is entitled to lay off any deadwood cards that fit into the knocking player's melds, provided that the knocking player does not have a gin hand.
For example, suppose that the knocking player has a meld of three Kings. If the defending player is holding the fourth King as deadwood, they may lay it off by adding it to the meld and thus reduce their deadwood count by 10.
The difference in the two players' deadwood counts determines the score for the hand as follows.
If the knocking player has the lower count, they score points equal to the difference.
The defending player can undercut the knocking player by having a lower or equal count. In this case, the defending player scores the difference plus a bonus (usually 15 points). An undercut may occur either before or after the defending player has laid off any deadwood.
The knocking player can never lay off their deadwood into the defending player's melds.
https://en.wikipedia.org/wiki/Gin_rummy

This matches the way I understand it.  It amounts to a minor penalty (depending on how an undercut is scored) for not paying attention.

Having the second player get both bonus basically makes it so it is an advantage not to knock with Gin unless you think they will get Gin before you.

Rather thah just linking to the game rules, it would be more helpful if you were to also quote the specific relevant rules. Otherwise this citation is more like "it's in there somewhere, promise".


text:
Name this variant of Rummy with mystery cards
Any idea what it is variant of Rummy?

2 decks
10 cards dealt per player
Mystery card can help to complete a set
Meld all 10 of your cards.

Example would be 8c,9c,Jc and the mystery card being 10 of clubs to form the Run.

By 11 of club you mean Jack of club?

My guess is a variant of Gin-Rummy with jokers
The 10 cards starting hand is matching.  There are variants of Gin-Rummy where players can not knock (melding most of the cards), but must finish a round with Gin (melding all 10 cards)
Rummy is a large group of games (see: pagat, wiki). If I understand you then the mystery card is a Joker.
Some details are missing to identify the exact Rummy game you are referring:

When a player laydown her cards, is it must be all her cards or she can have several cards that are not part of any meld?
Can players laydown Melds every turn and Add to melds of other (as in Contract-Rummy) or only at the round's end (Gin-Rummy)?


text:
Strategy for Movable Tic Tac Toe
Movable Tic Tac Toe is similar to the classic game as it uses 3 x 3 matrix and has the same goal of winning, which is to align 3 X's or O's marks horizontally, vertically or diagonally.  The difference is:

A player is limited to 3 X's or O's marks.
Once a player has all 3 marks placed on the grid, the player has to move a piece when it's his turn.

Play:

At the first phase, the players place their pieces one by one in a normal tic-tac-toe form.
At the second phase, after each player placed his 3 pieces, players can move any piece in the direction of the arrows presented. They can move up to two spaces in the same direction and can jump over their own and opponents pieces. Turning is allowed at the end of a turn but moving cannot happen afterward.

Q: What would be a strategy for this game?
Example game:

You might want to ask: what is the name of this variant? This will allow to search for strategy for this variant.

The game you are describing sounds much more like Three Men's Morris than Tic Tac Toe.

In order to solve the game, we need to know which arrows each tile has.

The arrows are just a two perpendicular lines. But it changes because players can rotate them 45 degrees. They can change between orthogonal and diagonal.

@Jonah, so when a player sets a tile she choose if the tile will be able to make orthogonal or diagonal moves?  And at the end of each move, she can choose again between orthogonal and diagonal?
If so, please add that to the rules

@Cohensius, to clarify, the pieces themselves have the arrows and define the direction of the piece. The square they are on has no effect.

The game you are describing is more similar to Three Men's Morris than to Tic Tac Toe.  Unlike Three Men's Morris, the extra movement options under the rules you cite mean the game is likely a draw under optimal play.  I'm assuming that this game has something akin to Chess's draw due to Threefold Repition; if not, the optimal result of the game is that you play forever, in which case the only winning move is not to play.
The classic Three Men's Morris was solved in the 1200's as a first player victory.  The Libro de los Juegos lists the following solutions (translation from here):

There are two possible victories, depending upon the second player's moves, the first being: 1. b2, a3; 2. b1, b3; 3. c3, a1; 4. b1-c1, any; 5. b2-c2. The second is 1. b2, b3; 2. a1, c3; 3. a3, a2; 4. a1-b1, any; 5. b1-c1.

Those solutions give a good starting point for this game.  I'm going to gloss over a lot of the piece orientations during setup; in general, the optimal piece orientation is implied by the subsequent moves a player wants to threaten.
As player 1, you want to start in the middle with your piece orthogonal (B2+).
Case 1: If player 2 responds in the middle of a side (say B3), player 1 can force a win by playing 2. a1, c3; 3. a3, a2.  This generates the following board, where player 1 can move a1-c1 to win:
  1 2 3
A X O X
B . X O
C . . O

If player 2 instead plays C1 on turn 3, player 1 can move b2-a2 to win.
Given that, player 2 should respond by playing in a corner (say A3).  Player 1 can then force either of the following boards:
Case 2 (1. b2, a3; 2. b1, b3; 3. c3, a1):
  1 2 3
A O . O
B X X O
C . . X

This seems to be a draw.  Unlike in Three Man's Morris, here Player 1 must move to a2 to prevent a loss (player 2 threatens b3-a2).  b1-a2 is the best move as it threatens a player 1 win, but player 2 just responds with b3-c2.  Player 1 would then move a2-b1, player 2 would move c2-b3, and the game would be a stalemate.
Case 3 (1. b2, a3; 2. a2, c2; 3. c3, a1):
  1 2 3
A O X O
B . X .
C . O X

I can't see any way player 1 can force a win here.  If player 1 moves c3-b3 to threaten a win, player 2 moves a1-b1 to block, and the players would then reverse those moves causing a stalemate.  Anything else isn't moving towards a victory.  I believe this case is a draw as well.

In this variation, the direction of the arrows presented matter. Sometimes a move won't be possible in the cases above. Also, pieces can be moved directly across corners (i.e. a2-b1, b1-c2, c2-b3, or b3-a2). So in Case 1, after X does b1-c1, O could directly move b3-a2 and win the game depending on the arrows direction.

@Jonah If the design of the board is relevant, please update the question to include a picture of the board.

The board is a normal tic tac toe shape. It is just a 3x3 square. Whereas in Three Men's Morris, the board has a 3x3 of spaces, but the connections/paths are not the same. Hope this helps.

@Jonah The Three Man's Morris Board is isomorphic to a Tic-Tac-Toe board (Tic-Tac-Toe is essentially a variant of Three Man's Morris where players have unlimited pieces and can't move a piece once it is played).  In the Google Play link, the board pictured had the Three Man's Morris Pattern overlaid on the 3x3 grid and did not include any arrows.  If the board you are describing is different from this (such as arrows that can be turned), please update the question to include a picture of the board, as well as the rules on how the arrows behave.

I edited the question to show the board and pieces, but I am not sure this will help. In Three Men's Morris, an edge can lead to a corner and the center, but not another edge. In this tic tac toe variant, a piece oriented diagonally can jump from edge to edge directly.

@Jonah You need to add substantially more detail to the question.  Please include a full description of how wraparound movement works as well as how the diagonal and orthogonal pieces work (what are their initial states, how they change, and how they interact with the rest of the game).  Adding several sample turns to your question could also help clarify the rules.


text:
How can a TCG player overcome "short term memory overload"?
Many complex decisions in trading cards games seem amenable to a three stage model.

The player must see as many potential lines of play as they can.
For each potential line of play they see, the player must deduce the resulting potential game state (often several, depending on possible interaction from the opponent).
The player must recognize which resulting potential game state is best for them.

My question is how to improve at #2 when there are many lines of play, the resulting potential game states involve many details, or some combination thereof.  This is the aspect of decision making I find to be the biggest bottleneck as I otherwise get better at a game through analysis and practice.  The problem is not that it's hard to mentally simulate any single potential line of play, but that capacity to keep several resulting potential game states in mind while still simulating other potential lines of play is limited.
For example, in Magic the Gathering, I may be considering several blocking formations, but also have the ability to flicker one of my potential blockers either before or after blocking, perhaps also triggering one of several ETB abilities which alter blocking decisions, and for each outcome, I would have to mentally track the resulting board state and life totals.  And that's a situation with only one relevant card in hand.  I could take notes to help, but would need to figure out a system to do so efficiently.  Sometimes the logic of situations allows many potential lines of play to be ruled out, but on other occasions, the tracking load feels like a bottleneck to making better plays.
It would be easy to shortcut #2 in software; just program a client to fork a game state into as many "sandbox" windows as desired, and during a game, execute each noticed potential line of play in a window, then pick the best resulting potential game state depicted among the windows.  However, this doesn't help much in paper games.  Are there any specific memory or notetaking techniques that trading card game players deploy to overcome difficulties in this aspect of decision making?

There's several things you can do to help memory and evaluation:
In the broadest cases, write things down. In Magic the Gathering, spells like Thoughtseize take a little longer at high level play, less because they don't know what card they want to pick, but because the player is writing down the cards they see in their opponent's hand. Having it written down makes it easier to manage without needing to remember that information, and helps with other points, it's easier to evaluate possibilities when there's less hidden information.
Know your deck. A lot of this comes down to knowing the cards you're playing and how they interact. You can also get a feel for what your opponent's deck is trying to do and how it runs through play. Knowing what is and isn't going to be valuable to your game plan, or in stopping your opponent's plans, simplifies some of the evaluations.
Don't try to remember everything. In your blocking example, you don't need to evaluate every possibility at all times, a lot can be rejected out of hand (don't risk the small creature who is vital to your strategy if you don't have to) others can be evaluated and discarded. You don't need to keep every possible option in mind at all times.
And accept that you will make mistakes, TCGs are games of imperfect information, but even if they weren't you're human and you won't always see or recognise the best options. Mistakes and misplays happen, they help players get better at the game when you learn from them.

First, particularly when you have to make such decisions many times over the course of a tournament, physical fitness is important, and so is eating and drinking the right thing before playing.
Second, this is something you can train.  Play chess, which demands this kind of decision making constantly.  (But keep in mind some people are innately better at this than others.)
Third, if you keep playing the same decks against a few other similar decks, you will end up making similar decisions which means you can rely on patterns you have observed and not have to think about everything from scratch.
If you're looking for mnemonics or mental shortcuts that help, there aren't any that work reliably, and they tend to get it wrong and blow up at the worst times.

I was expecting a Bridge reference rather than a Chess one; the advantage being that Bridge, like TCG, is a game of incomplete information while Chess is not. Notwithstanding that reference, and despite someone's early dislike of this answer: this is the correct answer. Practice and study, which will likely take years, are the remedy.

One big thing to develop is a set of heuristics. A heuristic is basically any simplification that will tend to steer you in the right direction. Some examples of heuristics for a TCG like Magic might be:

About 1/3 of your deck should be lands.

Drawing a card is worth 2 life.

One mana should deal about 1.5 damage.

Are the heuristics correct? Probably not, because I just made them up, but even if you could find the right numbers to put in there it ignores a whole lot of context. Your deck might need more lands if you're running WUBRG compared to mono-green, and there's no point paying your last two life points to draw a card if it's going to lose you the game. However, you can form your own heuristics and also build on their complexity as you gain experience. For example, the first heuristic could evolve into something like "Your deck should be 1/3 lands, plus 2 lands for every additional color, minus one land for every non-land mana ramp card".
The same thing can apply in combat - if you can assign some kind of basic value to each card on the field, and also to your life total, you can quickly identify whether it's "worth" chump blocking or trading creatures compared to letting the damage go through.
It's similar to how chess pieces have a standard point value that represents how good a particular trade is (pawn = 1, knight/bishop = 3, etc) but good chess players will learn to adjust those values to account for, e.g. where the piece is on the board.

Your numbers aren't that far off, though usually a card for one life is what people expect to pay, there are cards that occasionally see use and cost 2.

I feel like this answer is more geared toward improving at #3 than improving at #2.  Still valuable info of course.  As for drawing a card being worth 1 life, I'm pretty sure Necropotence is Banned/Restricted for instantiating this tradeoff.


text:
Can I discard a card in Sequence when I have a second similar one but only one empty space on the board?
If I have two A♥ in my hand and only one A♥ is empty on the sequence board, can I discard the second A♥ since there is no empty space for it?

No.  A card is not dead until both of it's spaces are covered by chips.

Dead Card
If you hold a card in your hand which does not have an open space on
the game board because both spaces representing that card are covered
by a marker chip, you are holding a DEAD CARD and you may turn it in
for a new card. When it is your turn, place the dead card on your
discard pile, announce that you are turning in a Dead Card and take a
replacement card (one card per turn). You then proceed to play your
normal turn.

According to the rules:
https://www.jaxgames.com/sequence-game-rules/


text:
How to print Card sizes (2.5" by 3.5")
I want to print cards with the size: 2.5" width by 3.5" height to test how they look.  I don't know what program to use, should I use Word, Google docs, or Medibang paint pro which is what I use to design the cards.
How can I print cards of the size: 3.5" height by 2.5" width?

So far every printer I used had a print preview page directly in the print options that could be displayed on the monitor. Worst case just have a physical card and place it on your screen, play with the settings until they match

Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.

Are you trying to print onto pre-creased cardstock, or just regular paper?

Software
I'm a big fan of google docs, but I havne't tried it for layouts like this.  I've had good luck with OpenOffice though.
I would design something like this in Google Drawings (available in Google Docs) or Inkscape, but feel free to keep using your existing design software if it has a usable export to SVG or PNG.
Export the design
You want to export the file from your design software into something you can load into the word processing software you choose to use.  Exporting as an SVG will give you a vector file that should print at the maximum resolution of your printer.  You could also export an PNG, but that will give you a bitmap that may be higher or lower resolution than the printer.  If the PNG gets rescaled at a factor that isn't a multiple of 2 you can end up with artifacts.  PNG files are also much bigger than an equivalent vector file.  Disk space is cheap, but larger files will be harder for many printers to receive and process.
Paper or Cardstock
If you really need this exact size of output I would layout a page with crop marks around each image and then use a paper cutter to trim them down to size.  I'd use a 28# paper or cardstock so they feel substantial.
It is interesting to me that your size is very close to US business cards size (3.5" x 2.0").  If you can live with that size you can easily get prescored sheets from Avery or their many competitors.  This will let you skip the paper cutter and also means that there are pre-defined layouts for these from Avery and preloaded in OpenOffice and presumably MS-Word as well.


text:
a board game with a pirate skull?
I remember playing it as a kid with my family (I’m 21 now)! It had a skull as the centerpiece & we remember there being plastic bones that would have either dots or numbers on them. You would maybe shake the bones in a cup and throw them out. I also remember there being eyeballs. There were different colored ones. I don’t really remember the object of the game.

Is there anything distinct about the game that has you recall it as a pirate skull? Was it a skull and crossbones for example? Did it have an eyepatch, or was the game otherwise somehow pirate themed?

Is the game possibly Tomb of Doom?

Although it doesn't appear pirate themed, it does have bones with dots and eyeballs.


text:
Trading Post version of Splendor
When playing the Trading Post version of Splendor, are you required to have the 3 black bonuses power to get the 5 prestige points for having the 5 green bonuses and 1 noble tile power?

The rules for the different powers and ways to get them can be viewed at ultra board games.

Requirement: You must have 3 black bonuses.
Power: 1 prestige point for each of your coats of arms on the board.

Requirement: You must have 5 green bonuses and 1 noble tile.
Power: 5 prestige points.
For the 5 prestige points the only thing you need is the 5 green bonuses and 1 noble tile. For the prestige point for your coats of arms you only need to have the 3 black bonuses.
The bonuses are independent from each other so you can get any of them at the time you have the requirements.


text:
Solitaire with cards triplets which sum to 9,19 or 29?
My Dad taught me the following solitaire game:

Deal: remove all face cards, putting down 5 rows.
Play: one card at a time, try to get 3 cards to a total of 9, 19, or 29. If they do, discard them and keep going through the deck, reusing the discard pile when needed, with out shuffling.
Game ends: when all cards are in the discard pile. The last card is always a 3.
Score: if you win, you take the discard pile, draw 5 cards at a time and that's where I forget how to score.

Does anyone know the name and how to score?