text:
What is the name of this Rummy variant?
It's called Devil's Delight by the people I know but I can't find any google results for it. Does any one know what people call this?
The game is played with two decks and everyone gets seven cards passed to them. Then the deck is put into the middle of the table with the first card placed up. The person after the dealer takes the first turn.
EDIT: At the start of a turn, a player is passed a card from the previous player. They can either take the card, or pass it to the next person who must pick it up along with another card. Then you must discard a card, and the next person can either pick it up or pass.
The goal of the game is to make sets and runs depending on the round. First round is three sets, next round is one run with two sets, the round after that is two runs etc. Twos are wild and can be played anywhere. After you get your required sets and runs you can put them on the table (go down). Once you do you can play on other players who are down and take their 2s that are down. Also, sets are three cards and runs are four cards of the same suit. One hand has a seven card run in it.
The round ends when someone has no cards in their hand. Then players add up their cards which turn into points. number cards (3 through 9) is 5 points, 10 and any face card is 10 points, an A is 15 points and a 2 is 30 points. The player with the lowest score at the end of seven rounds wins.

What actually happens on a players turn?  Does a 'set' have a minimum number or cards (if you only have 7 or do you acquire more).   What you're describing sounds like a variant of Rummy based on having a deck with one card face up and players collecting sets/runs.

It's just one of many forms of a class of games called Contract Rummy. (The various rounds' goals are called contracts).
The major variation here seems to be:
The discard (or rather lack of discard): I guess by your description (since one cannot make three sets with only seven cards) that players just draw a card each turn and are not required (or permitted) to discard, but rather can only play melds and lay off on other melds.
See more common versions at, for example, http://www.rummy-games.com/rules/contract-rummy.html

This sounds very much like frustration
Frustration involves 'going down' when you can meet the required hand for the round and the round ending as soon as the first person is out of cards.  If you are not 'down' when the first person gets rid of all their cards then you have to repeat the round while the rest move on to the next round


text:
In Euchre, can you call a misdeal with "No ace, no face, no trump"?
In the game of Euchre I have been dealt a hand of nines and tens, none of which are trump.  May I declare a misdeal?  I have seen some groups play that the hand is redealt by the same dealer while other groups pass the dealer.  Is this an official rule or just a house rule?

Are you saying that it called a misdeal after trump is called?

Yes only after trump is made therefore all nines and tens with no trump. Some people play  as a misdeal and no points awarded and goes to next dealer Yet others play as a redeal of the same dealer.

I edited the question and voted to re-open. While it's still not clear to me what exactly you're asking, I'm sure that you'll find an answer in this wikipedia article about FARMER'S HAND

This is a house rule.  I have seen it played in informal games, but never among serious players.  Once, I saw a person try to declare "ace, no face" in a $5 game.  Since this person shared information about their hand it was ruled that they should be bumped and forfeit 2 points even though no cards had been played.  All of the spectators and other players agreed with this decision, including the player's partner.  The person who declared "ace, no face" was told not to do that again.

No Ace, No Face makes 0 sense since you still are able to make individual plays. I've never heard of this, but people do crazy things with this game - when it's for fun that's fine... but other times they just invent stuff without taking the maths inherent in the game into account.
I haven't done the maths fully, but what's the probability of you ever helping to take a single trick in a 'No Ace, No Face, No Trump' case? The answer is technically 1 - if you have suits 1-4 (imagine suit 4 is trump), you can only ever have suits 1-3 with '10's & suits 1,2/1,3 with '9's. This leaves 1 '10' taking the final '9' as the only time you could assist in taking a trick. However, is this even doable given 3 other players & only 4 cards not in play - *Perhaps if someone makes it trump when 3/7 of them aren't in play & it is the same colour suit as the '10' beating the '9' & that 4th card not in play is part of this suit too.
Then you have player 1 (you), 2 & 4 (opponents) & 3 (your partner) each with 1 card of the '9' & '10's suit. Then players 2/4 & 3 throw their card of this suit away & you might then beat the '9' of player 2/4 iff [If & Only If] you or the '9'-holding opponent are playing first. EXCEPT you can't play first as you will never have priority & so only if they have priority & play this on turns 3-5 with no trump & both other same-suited cards (one of the opponents & your partner) have thrown theirs away already.
This situation is so obscure, that having a 'No Ace, No Face, No Trump + this situation above' is probably so unlikely that it might have happened once since the beginning of the universe with each star living 4 thousand-million years & having 1 habitable planet each that lasts just as long & are full of creatures that only play Euchre the entire time from start to finish of each solar system. That's obviously false, but you get where I'm going with this.
The more controversial question is can you 'MAKE IT' off of the left-bauer only? Again the maths needs to be done to create a final verdict here, I am for it - though I do think that it might be reasonable to not let that be the case.

This doesn't really answer the question asked, the question doesn't ask about the case where some of the 9s and 10s are trump, it asks about the 0.014% chance of having been dealt only 9s and 10s that are not trump after its made.

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What is the name of this questions asking with emotions card game?
A player draws a card from 2 different stacks.

First stack: a question that the player must ask another..."will you marry me?".
Second stack: an emotion or attitude...."Aloof".

The player must ask that question in that manner.
What is the name of this game?

Can you describe the cards in detail : comic book characters, or photographs, or text only? An image would help...

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text:
Where can I find a database of Go games with move times
I am looking for a database of 19x19 Go games (complete games) including the time spent on each move, or the global time in each move. Other aspect is that its need to be without bots or any artificial intelligence, just people Vs people.
I have found databases (such as gokifu) with everything I want except for the time per move.

I thought I remembered a duplicate of this question, but I cannot find it (any more) – could one have been deleted?

I agree that this could be interesting, and one gathers from numerous studies of games (case in point: The Meijins Retirement Game that they are recorded for professional games, but I think that the main problem with this will be that as far as I am aware the SGF format does not provide for it, at least not in the standard form.

SGFv4 allows time remaining (after the move was played).  "BL" is "Black time left" and "WL" is "White time left", in seconds.  (Couldn't use BR and WR, because those were already used for players' ranks/ratings.)  "OB" and "OW" are for byo-yomi / overtime.  See https://www.red-bean.com/sgf/properties.html#WT (scroll down a couple lines).  You can also see these in the SGFs from Go servers, if you view with a text editor.

An earlier question about database for 9x9 games contains a link to a database for 19x19 games:
http://ps.waltheri.net/


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Michigan Rummy? Incorrect Name?
I remember a rummy variant that I played as a child. I was taught it by older family members, who are all long dead. They called it "Michigan Rummy" but it was quite different from the game that I find online by that name on several different sites. Can anyone tell me the correct name of the game I knew, and point me to full rules?
The game was much like many rummy variants, in that the object is to form combinations or Melds. These were of two types: a "Set" composed of three or more cards of the same rank, and a "Run" or "Sequence" composed of four or more cards of adjacent ranks, such as 6, 7, 8, 9 or K, Q, J, 10. Ace could be high or low, but not both at once. I can't recall if a run had to be all of the same suit.
Each hand had a separate goal:

In the first hand, the goal was two sets.
The following hands were one run and one set,
two runs,
three sets,
two sets and one run,
two runs and one set,
and finally three runs.

A player could go out only by completing all of the required melds for that round. Extra melds were not allowed, but IIRC one was allowed to "lay-off" cards on the melds of other players.
I think two or three decks were shuffled together. Three players was the minimum, 4-6 more common.
On each turn a player drew or picked up a discard, optionally set down one or more melds, and ended with a face-up discard. Any other player could claim this discard, and picked it up along with the total discard pile. If no player wanted the discard, the player to the right of the previous player drew a card from the stack, and the discarded card remained face up until another discard was placed on top of it.
If more than one player wanted a discard, whoever called for it first got it, leading to fast and raucous play.
To start, each player was dealt a hand of 6 cards. Thus in each round but the first, a player would have to take the discard pile at least once to have enough cards to make the required melds. A player scored positively for cards in melds or laid off, and lost points for all other points. Spot cards were worth there face value two thru ten, face cards ten each, and aces fifteen.
When a player went out, other players were not allowed to  meld cards left in their hands -- these counted negatively. The player who went out could make a final discard, or not.
On the last round special rules applied -- no melds might be put down except by going out, and the player who went out had to make a final discard. This was summarized as "down and out with a discard".
All this is remembered from more than 40 years ago, and I may have some details incorrect. Can anyone identify this game and point to full rules?

This is a form of contract rummy called progressive rummy.
(I note that since the contracts you name include ever-increasing ones eventually leading to ones that cannot be met with only seven cards that each deal probably involves an additional card)

Progressive Rummy: Progressive Rummy is played very similarly to Contract Rummy. The main differences are in the number of cards dealt in each of the seven deals. The first deal starts with 6 cards dealt, the second deal 7 cards are dealt, and so on until the 7th deal where 12 cards are dealt. The initial meld requirements are the same as in standard contact rummy. The player generally completes the hand by playing all his cards to the table to meet the contract, as he will usually not have any additional cards in his hand (unless he opted, on another player's turn to take the current upcard, as described in the rules for Contract Rummy, above). If this is the case, the player may play cards to other melds on the table (if any) once they have made their initial meld. A player may also play their last card by discard, at which time they also win the deal. Scoring in progressive rummy is the same as in Contract Rummy, except that jokers are worth 25 points each.

Thia is not, or not quite, the game that I played. A particular point was that although the number of required cards increased in each round, the initial hand size did not increase, so that one had to take discards, thus increasing the size of the hand, and risking having too many cards.

That sounds like an unknown (to me) combination of 500 Rummy and Progressive Rummy, then.


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In Game of Thrones, is it possible to moving back units after winning a combat following March Order?
May I move back some of the units after winning a combat? I mean, if there is time for defeated troops to retreat there will definitely be time for winning troops to move back as well. Does that not make sense?
I couldn't find any mention in the rulebook specifying that the winning units all have to stay in the conquered territory, that some (or even all) cannot move back after winning. I don't see why you can move back if you lose but you can't move back if you win? It should be even easier for winners to move back as they should be in better shape.

The attacker does not have the opportunity to retreat if the attacker wins the combat.  The only allowance for retreating is for the losing army:

After suffering casualties, the losing army must retreat from the embattled area (supporting units do not retreat.)

There is no mention of what happens to the winning units after combat because nothing needs to happen to them.  Combat began by them moving to the territory they are trying to conquer.  Thus, all that needs to happen in cleanup following an attacker victory is the removal of order tokens:

After combat is completed, remove the attacking player’s March
  Order token from the game board.
If the combat was won by the attacker, remove any Order token the
  defender had assigned to the embattled area (if one remains) as well
  as any Power token in the area (which would exist if the defending
  player had previously established control there, see page 24)

One pseudo-exception to this is Loras Tyrell, who moves the march order with the attacking units if they are victorious.  You can use Loras to move attacking units back to their original territory after they win a battle, but doing so is not a retreat (these units will remain upright) and is not immediate (this cannot be done before your next turn in order resolution).

The short answer is No.  While it does makes sense to be able, it is not part of the rules.

see rules of Agot
One major effect for this rule: it will make siege towers super strong (not saying if it is good or bad).

The siege towers wouldn't be able to, since they cannot retreat following defeat either. Why is there no mention to what happens to the winning units after combat? I wish there was. It just discusses the losers. Anyway, I'll do as you say, thanks!

no mention to what happens to the winning units after combat? because nathing happens to them.  It would be too long to write all the things that do not accur...


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Was Backgammon played in ancient Rome?
In the film «Spartacus» (Kirk Douglas, 1960), during a bath scene at 2h07m,  one can see what clearly is a Backgammon set on a bench, right beside Caesar.
Considering that the scene probably represents a period around 50 B.C., is it known that Backgammon was played at that time in Rome?

While old, we can pretty conclusively say that Backgammon itself was never played by the Romans. Backgammon is a relatively recent iteration belonging to the Tables family of games, the oldest within the family that could be described as Backgammon is τάβλι (Tables, which is conveniently where the family gets it's name), dating from c. 476–491 CE [1].
We do have record of Romans playing another game within the family called XII scripta (12 marks)[2], or more formally Ludus duodecim scriptorum (The game of 12 writings). However, the earliest known mention of XII scripta was in Ovid's Ars Amatoria (The Art of Love), which dates to somewhere between 1 BCE and 2 CE, so it may not have been around ~50 years earlier.
XII scripta almost certainly developed out of the Egyptian game Senet, which existed at least as long ago as the Third Dynasty of Egypt (c. 2686–2613 BCE)[3], so there is plenty of potential for Caesar to have been playing a game within the same family as Backgammon.
All that said, while Spartacus is surprisingly accurate for what is essentially an action movie, they most likely spent very little time on what board game Caesar may have been playing.

[1]: Austin, R. (1934). Zeno's game of τάβλη (A.P. ix. 482). The Journal of Hellenic Studies, 54(2), 202-205. doi:10.2307/626864
[2]:
Austin, R. (1935). Roman Board Games. II. Greece and Rome, 4(11), 76-82. doi:10.1017/S0017383500003119
[3]: Finkel, Irving L. "Ancient board games in perspective." British Museum Colloquium. 2007

While it's less likely that modern-looking backgammon sets existed in that time frame, the game of backgammon has its origins much earlier -- it's believed to be as much as 5000 years old, likely the oldest game still played.
Like all widely played and long-lived games, backgammon has evolved a good bit over such a long life; other modern games are also derived from it, including pachisi (also pretty old).
Worth recalling, however, that Spartacus wasn't primarily intended as a historically accurate depiction of Rome, but as an action movie, a vehicle for Kirk Douglas, with the gladiatorial games of Rome as its setting -- and the grandeur of the film would not be diminished (IMO) even if a much newer game (like, say, modern chess) had been depicted instead of backgammon or a close ancestor.

A game with the same board and pieces, Tabula, was played in Rome in the fifth century. It derived from the "Game of Twelve Lines", played around year 0.
From Wikipedia:

Tάβλι (Tavli), i.e. tabula meaning 'table' or 'board' in Byzantine Greek, is the oldest game with rules known to be nearly identical to backgammon. It is described in an epigram of Byzantine Emperor Zeno (AD 476–491).[20]

The board was the same, with 24 points, 12 on each side. Like today, each player had 15 men and used cubical dice with sides numbered one to six. [20]

The τάβλι of Zeno's time is believed to be a direct descendant of the earlier Roman Ludus duodecim scriptorum ('Game of Twelve Lines') with the board's middle row of points removed, and only the two outer rows remaining.[21] Duodecim scriptorum used a board with three rows of 12 points each, with the 15 men being moved in opposing directions by the two players across three rows according to the roll of the three cubical dice.[20][21] Little specific text about the play of Duodecim scriptorum has survived;[24] it may have been related to the older Ancient Greek dice game Kubeia. The earliest known mention of the game is in Ovid's Ars Amatoria ('The Art of Love'), written between 1 BC and 8 AD. In Roman times, this game was also known as Alea, and a likely apocryphal Latin story linked this name, and the game, to a Trojan soldier named Alea.[25][26]

Wikipedia also includes more history of the evolution of tabula from other race games, but that is off topic for the question at hand.
Wikipedia's citations:
20: Austin, Roland G (1934). "Zeno's Game of τάβλη". The Journal of Hellenic Studies. 54 (2): 202–205. doi:10.2307/626864. JSTOR 626864.
21: Austin, Roland G. (February 1935). "Roman Board Games. II". Greece & Rome. 4 (11): 76–82. doi:10.1017/s0017383500003119.
24: Austin, Roland G. (October 1934). "Roman Board Games. I". Greece & Rome. 4 (10): 24–34. doi:10.1017/s0017383500002941.
25: Finkel, Irving L. "Ancient board games in perspective." British Museum Colloquium. 2007. p. 224
26: Jacoby, Oswald, and John R. Crawford. The backgammon book. Viking Pr, 1976.

Downvoter: please help improve this post by pointing out the error or the misinformation, thanks.

The Gloucester tabula set (c.1100 - 1120) is the oldest known to use shaped points, prior to that simple rectangular points were employed.

Interesting. If you have a citation, consider correcting the wiki entry.

Strange that wikipedia has an image of the Zeno's Tabula board, but then describes it as the same.


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scoring straight (or run) in Cribbage
In Cribbage, what is the scoring rule in this example?

Player 1 plays a 4.
Player 2 plays a 3.
Player 3 plays a 5. (claims 3 points for 4,3,5 run)
Player 4 plays a 6. (now 4 more points for 4,3,5,6 run)
Player 1 plays a second 4 (here the debate)

He claims that he should get another 4 points (for 3,5,6,4) indicating by pointing at each card in reverse of the sequence of play (counterclockwise) 6,3,5,4 ending with his second 4).
I claim that he can't count the second run of four cards because they were not in the sequence of play (clockwise).
Who is right?

I don't understand what you're asking here; why is "3564" problematic, but "435" and "4356" are acceptable? None of those are in order, so I don't see how "the sequence of play" comes into question.

From the American Cribbage Congress Rules of Cribbage:

straight (or run), single: Sequence of three or more consecutive cards in any order during the play of the cards; for example, 3-5-6-7-4 (counts three when the 7 is played and counts five when the 4 is played)

When the second 4 is played by Player 1 the last 4 cards played are:
3, 5, 6, 4
This set of 4 consecutive cards clearly meets the definition above of:

... Sequence of three or more consecutive cards in any order during the play of the cards ....

Player 1 is entitled to score 4 for this run.
In regards to your claim above that:

... he can't count the second run of four cards because they were not in the sequence of play (clockwise).

Nowhere in the Rules is there a necessity to identify the qualifying cards for a score in a specified order. Your claim otherwise is entirely bogus.
The sequence counts solely by virtue of the required cards, having been played, meeting the criterion of being "Sequence of three or more consecutive cards in any order".  Any such identification of qualifying cards is purely informative, and instructive, to assist beginners in learning the game.


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Backgammon stacking rule
When can we stack checkers one on top of other on a single point?
Is there a rule that stacking allowed only when a position has more than 5 checkers?  Can I stack the checker when a position have only 3 or 4 checkers?

Stacking pieces on the same point is not necessary unless it would otherwise be unclear where those pieces are meant to be. There are no rules about how you place pieces on a point; it is only common sense that mandates clarity on exactly which point a piece occupies.
You could stack every subsequent piece on the first one on the same point, if you really felt the need. However, this is strongly discouraged, because it may disguise the number of pieces on that point, especially if the point has only two pieces.
You gain nothing from stacking them before you need to, and risk an accusation of poor gamesmanship. Why bother?

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text:
Gust Rules Clarification
I'd just like to clear up the Gust rules in Dandelions by BoardGameTables, which I think is based on a Japanese game called Birth.
The rules say:

If you plant in a garden with other players' dice matching your value, move all the matching dice to one adjacent garden.

I want to be super clear that this means what I think it does.

You can never move your own dice
You have to move all matching opponents' dice
All moved dice must move to the same (adjacent) garden


text:
In Yaniv, is it possible to Discard the card you just Picked up?
I'm curious about the card game Yaniv (Wikipedia reference, Pagat reference). I've played this game a few times, but I learned it from a written description rather than in real life, so I've ended up with some house rules that are a weird mishmash of common Rummy rules and the actual rules.
Specifically, I am interested in the details of taking a card from the previous meld in Yaniv.
Yaniv rules summary:

You are only allowed to knock/call Yaniv at the beginning of your turn
and only if the point total is 5 or fewer. The game immediately ends
when you do this and a winner is determined. Let's call a turn without
a Yaniv call an "ordinary turn".
The structure of an ordinary turn is this:

Throw a single card, or a meld. A meld is a Rummy meld or a pair.
Take a card, either from the stock or from the ends of the previous meld.

Both Pagat and Wikipedia are very clear that drawing happens after discarding a meld. This is a large mechanical difference from Rummy, a game which is otherwise similar to Yaniv.
Anyway, I am interested in whether the card taken in step 2 can be used for the meld in step 1.
For example:

Suppose player B holds TS, JS in hand.
Player A discard a meld of 7S,8S,9S.
Player B would like to pickup the 9S in order to complete the meld 9S,TS,JS.

Is player B allowed to pick up the 9S and discard 9S,TS,JS as their turn?

Player B can not do that in one turn.
The reason is, like you said, pickup happens after discard.  Therefore, player B should discard something, pickup the 9S, and on the next turn discard the 9S,TS,JS meld.


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Which solitaire game is this?
This game may not actually be an actual solitaire, as it might have been something my grandmother had me do when I was wee to keep me out of her hair.  But if anyone DOES know it, I would dearly like to know if I am forgetting some of the rules or playing it wrong.
Play: using standard 52 card deck, deal 4 cards, one into each of 4 piles.  If some of the cards have the same rank then move the matching cards to the rightmost, repeating for all matches.  Then deal another 4 cards, one onto each stack, and repeat.  If all 4 on top of a stack are the same card (four of a kind) you withdraw them from the deck entirely. You repeat until you have no more cards.
For example, if you dealt A 2 3 4, nothing would move.  If you dealt 2 3 3 4 on top of that, the left 3 would move onto the right three.  This would reveal the 2 that it had covered, and the 2 on top of the leftmost stack would shift to the right.
Once all cards are dealt, you pick them back up in sequence (This is the part I remember the least.  I THINK that the leftmost pile ends up on the 'bottom' of the new stack, and the rightmost pile on the top) and then deal through again until you win.
Thanks guys!

This is very similar to a game called "Perpetual Motion" -- the rules from Wikipedia specify gathering same-ranked cards to the left, and only allow for eliminating groups of cards if the four of a rank are dealt out to the four piles as part of a single deal.  They seem similarly unclear as to which pile should end up on top of the new stack.

I don't get the impression that they are "unclear" as to which pile should end up on top.  I think they imply that it doesn't matter, as long as you are consistent.

see this analysis for the game  https://arxiv.org/ftp/arxiv/papers/0907/0907.1955.pdf


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Is it possible to postponed the Turn 7 reshuffle to Turn 8?
As a Twilight Struggle player, it's important to be aware of the Turn 3 and Turn 7 reshuffles, and you need to plan your card management strategy accordingly. For example, a US player holding De-Stalinization would normally try to space it on Turn 3 (and not Turn 1 or 2), as this keeps it out of the game for a long time. In a similar way, cards discarded on Turn 7 or later will not come back in the game via a reshuffle (although cards like Star Wars and SALT Negotiations can retrieve discarded cards).
My question is, is it possible to have a game without a Turn 7 reshuffle? While the Turn 3 reshuffle is unavoidable, I'm thinking that it might be possible to have a game without the Turn 7 reshuffle. This would lead for an interesting Late War, with very few scoring cards and a deck that's likely to favour the US player.
If possible, I imagine such a game would see heavy use of the China Card, but no use of cards that cut down on hand size (Five Year Plan, Grain Sales to Soviets), nor cards that mill the deck (Our Man in Tehran, Ask Not...).
If relevant, I have the Deluxe Edition and play with the optional cards.

I've had many games without a turn 7 reshuffle. It's totally possible if playing with the 7 optional cards. This depends on the following:

How many cards are removed from the game in Turns 1-2.
How many cards are held in Turns 3-6: players may hold:

Multiple cards by playing The China Card, Ussuri River Skirmish/Cultural Revolution (multiple China card plays), SALT Negotiations;
No cards through the plays of Blockade, Five Year Plan, Grain Sales to Soviets, UN Intervention.
The space track may also throw a wrench into that, but we won't investigate it as impractical.

Whether Ask not what your country can do for you... or Our man in Tehran have been played or not. This technically falls into #2, but I consider them different enough to deserve a mention on their own.

Here is a theoretical example, assuming: the 3 aforementioned factors work in the way of delaying the reshuffle:

No events are removed in Turns 1-2.
No China Card play in Turns 3-6.

Turns 1-2
There are 38 early war cards: 3 scoring, 6 neutral, 14 US, 15 USSR. For the sake of simplicity, let's also assume no China Card play or hand-size reductions in Turns 1-2, albeit you shall see that it does not affect our analysis. Thus, we assume that players hold a single card in both turns.

16 cards will be drawn on Turn 1, leaving the deck with 22 cards.
14 cards will be drawn on Turn 2, leaving the deck with 8 cards.
At the end of Turn 2, there will thus be at most 14+14=28 cards in the discard pile, assuming that no starred events were removed.

There is no way to trigger the first reshuffle earlier or later than turn 3. On the one hand, there are at most 3 hand-size reductions (Blockade, Five Year Plan, UN Intervention), which would leave the draw pile at the beginning of Turn 2 with 5 cards, if all were played on Turn 1. On the other hand, only 2 extra cards may be held, during Turns 1-2, still not enough to delay the Turn 3 reshuffle.
Turn 3
When dealing cards on Turn 3, there are:

8 cards in the draw pile
14 cards that have to be dealt
28 cards (at most) in the discard pile

Therefore:

The first 8 cards are dealt to both players.
The (max) 28 discarded cards are reshuffled to form a new draw pile.
Finally, 6 more cards are dealt to each player, leaving the deck with 22 cards.

Note that prior hand-size reductions or plays of the China Card in Turns 1-2 do not affect the aforementioned numbers. If players hold more or less cards, this will of course affect which cards are held through the reshuffle, but not the total number of them. For instance, if the US cannot hold a card on Turn 2 due to Blockade, then at the beginning of Turn 3 there are 15 cards to be dealt, but also 29 cards in the discard pile, thus not affecting our numbers at all.
Let's assume now that both players will now on hold exactly one card, thus holding 1 card at the end of Turn 3.
Turns 4-7
There are 48 mid war cards: 4 scoring, 11 neutral, 18 US, 15 USSR. On turn 4:

There are 22 cards remaining from the early war.
The 48 mid war cards are shuffled in the draw pile.
A new pile is formed of 70 cards in total.
We assume that players hold a single card and thus 16 cards are dealt each turn.

This would mean that at the beginning of Turn 7 there will be 70 - 16×4 = 6 cards in the draw pile, thus not triggering a reshuffle! This would lead to the 23 late war cards being added in Turn 8, leading to a delayed Turn 9 reshuffle. This would mean that all late war cards would be guaranteed to be drawn by the beginning of Turn 9.
Hastening the reshuffle
The aforementioned analysis suggests that 6 cards need to be "eliminated" to trigger a Turn 7 reshuffle. These could be:

Early war starred events eliminated in Turns 1-2, thus not entering the reshuffle.
Hand-size reductions during Turns 3-6, increasing the number of cards that need to be drawn.
Playing Ask not what your country can do for you... or Our man in Tehran, which either thin the draw pile or cycle faster through it, respectively. These may also be played on Turn 7, not just during Turns 4-6.

On the other hand, not removing many starred events in Turns 1-2 and successive plays of the China card in Turns 3-4 would result in not triggering the Turn 7 reshuffle. Playing SALT negotiations lets you hold multiple cards, thus delaying the reshuffle as well.
Fine notes: if the reshuffle has not been triggered by Turn 7 and the US player holds Our man in Tehran, then they have a huge control on what will enter the reshuffle or not, if there are at most 5 cards remaining in the draw pile. In this case, he should:

Play as many US cards or scoring cards he would like to enter the reshuffle again.
Play Our man in Tehran to trigger the reshuffle.
Play Ask not what your country can do for you... to discard the USSR or scoring cards they would like to miss the reshuffle (or just space the former).

Amazing! I don't have enough rep to upvote (yet). Under Hastening the reshuffle it says "...that that 6 cards..." (one "that" too many), but it's too few characters to edit.

@HenricF You are very much welcome. I fixed the typo, thanks for the heads up. :)


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Gin Rummy, incorrect knocking
What is the penalty for going down with a hand that has more than 10 points?
For example, a player may lay down a 4d,5d,6d but one of the cards is actually of the heart suit.

Here's one answer from http://ginrummytournaments.com/pdfs/Rules_2012.pdf. Tl;dr if you could have knocked then you can accept his knock and undercut; otherwise game continues, he plays an open hand, and he must knock at first opportunity.

IMPROPER KNOCK: If a player makes an IMPROPER KNOCK, with his count being
  higher than the knock card, his hand must then be PLAYED OPEN, ALL TEN
  CARDS FACE UP. He MUST KNOCK when his point count is at the value of the
  knock or below. HE CANNOT BE FORCED TO KNOCK BY HIS OPPONENT. When a
  player makes an illegal knock with more than the knock card count, the opponent
  may accept the knock as proper, provided his point count is the same as the knock
  card or lower.(example; the knocking point is 8 and a player knocks with 10 points,
  the opponent with 8 points or less may accept the knock and get credit for the
  undercut). The opponent may also lay off points to get under the knock. When a
  player announces he is ginning or knocking, or calls a number and starts to lay his
  meld down, he must continue to do so. If his hand is not a gin or his knock is not
  legal he must play an open hand. The opponent may ask that the cards be spread
  for proper viewing, but may not touch the cards himself.

For casual play however I would tend to let my opponent pick up his cards and play normally - he's the only one who's been hurt by showing them to me.

Agree with casual play. I'd only enforce this rule if I'd shown them my hand already because of their call, but if they often made mistakes I'd be more careful about checking their hand before showing mine.


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Is there a quantification of how much skill a game requires?
For example, if you play a round of cribbage mathematically perfectly, someone will win because they got better cards on average. But if that difference in scores comes down to 10 points, that could come down to imperfect play or even gambling on a card.
Is it possible to say that cribbage is only for example, 50% skill?

I can think of two mathematical measures that might be useful, both based around Elo ratings.

Is the correct Elo distribution function.  Let's suppose Player B beats Player A 64% of the time, and Player C beats Player B 64% of the time.  How often does Player C beat Player A?  Generally, speaking, the higher the number, the less of a role luck plays, though you should be suspicious of answers much above 83%.  (83% is what you would expect if all player's performance in a game (either because of luck or variance in performance) is normally distributed, all with the same variance)

Is the Elo difference, usually the difference between the top player and an average player.  Filtered through the answer to the previous paragraph, this basically means how often the top player beats an average player, except this is frequently hard to directly observe (either because top players never play average ones or because the answer is "always"), so you may need to measure this indirectly through Elo.

In many games, you want to think of a "game" as actually a sequence of games for this to make any sense (just like playing cribbage to 120, as usual, is in some sense a sequence of games).

If instead of just the Elo distribution, you have the history of all game results in the community: Measuring skill and chance in games
is a research paper by Duersch, Lambrecht & Oechssler from 2017. It is an attempt to rank games on a scale of luck vs. skill. The main idea is to look at how likely a stronger player is to win against a weaker player. In a pure-skill game, a stronger player should always win. In an luck-heavy game, the probability should be close to 50%.

An important thing to mention is that this approach to measuring "luck vs skill" depends on the community of players considered, not just on the rules of the game. For instance, if you look at the game played among professional chess players, you might conclude that chess is a high-skill, no luck game; but if you look at the games played between amateur players in bars, you might conclude that chess does have a fair amount of luck.

@Stef Which (properly) raises the question of what “luck” means. If you and your opponent are both capable of recognizing and capitalizing on 50% of all possible mistakes, is it “luck” if you win because more of the mistakes made by your opponent happened to fall in the category of those you can exploit than vice versa? And as we think about that, we have to remember that we have implicitly assumed that all mistakes are equal, both in how recognizable they are and in how impactful they are, which is clearly not the case. Goes a long way to showing why this question really is semantic.

(Not to say that this set of definitions and the resulting approach to estimating the answer under those definitions is in any way deficient—it’s a great answer and I have upvoted. I just appreciate the food for thought here even more than the actual answer itself.)

As a refinement of Point (2), one might consider "How long must a session of play be so that an average player loses more than 95% of the time to an expert player?" An average club bridge partnership can expect to get a couple of club wins a year; but will only get a couple of two session wins against the same opposition in a lifetime, and likely never get a 4 session win.

Chess doesn't involve any luck (other than metagaming), yet people beat people of higher Elo all the time. And if it were all luck and no skill, then everyone would beat everyone else 50% of the time (assuming no draws).

@Acccumulation The answer proposed in this answer would suggest that playing a game of chess, does, indeed, involve luck. Intuitively this can easily be explained: there is chaos in what mistakes we make, how focused or tired we are, what impact our mistakes have on the game, etc. We're not robots that always play at the top of our capacities. For comparison, the game "Who's older?", where two people say their age and the older player wins, has absolutely no luck at all: the older player will always win.

@Acccumulation: There is absolutely a game-theoretic min-max strategy at play whenever top experts meet - which is why different openings and defenses exist. As selection from this mixed strategy requires both players to make random selections that one's opponent cannot predict - There absolutely IS an element of luck in Chess played at the highest levels.

Compare the Expected value to the Standard Deviation.
The higher the luck factor in the game, the higher S.D(X) - E(X).

For example, lets look at a game of Poker with high and low amount of luck: Assume a player that have a small edge over a Poker table, meaning that her expected value is positive E[X]>0, now

In a single round of Poker, the result is very much luck driven. The Standard Deviation is much bigger than the Expected value S.D(X) > E(X).
In 1M rounds of Poker, the variance of the sum of results decreases due to the law of large numbers, and expected value is larger than the variance. E(1MX) > S.D(1MX)

Is this something you can look up somewhere?

Variance and expected value are not expressed in the same dimension. So a statement such as "the variance is larger than the expected value" doesn't quite make sense. Perhaps you meant "standard deviation" instead of "variance"?

I see what you're getting at, but this answer is pretty imprecise with statistical concepts. Playing more hands narrows the variance of the expected value (standard error of the mean), but does not at all change the variance of the value of a hand. You suggest comparing expected value vs. variance to compare skill vs. luck, but then also seem to suggest that you can lower the variance and therefore make a game less luck-dependent simply by playing it many times, which makes no sense.

@NuclearHoagie, you can lower the variance and therefore make a game less luck-dependent simply by playing a new game: "the sum of several games".  Tennis is good example.

@Cohensius In the long run, any game will have the more skilled player win more often, making every long series of non-random games effectively devoid of luck. That's not really a characteristic of the game being played, since it it true of every game. If you play enough times, only skill matters, regardless of what you're playing.

@NuclearHoagie, I think we moved a way from the original question, my answer is that you can measure Luck vs Skill in Games by comparing the Expected value Vs Standard Deviation.  Then I showed an example that you may did not like.

It would very difficult to come up with a metric that depends solely on the game itself, and not the population of players. It's much easier to answer the question "How large a role does luck play, in comparison to the skill difference of players?" than to answer the question "What is an absolute measure of how much of a role does luck play?"
If it's defined in terms of the players, then there are a variety of metrics. One would be to look at the variance of win rates among players; the higher the variance, the less important luck is. However, you'd have to adjust for the fact that players tend to play players of similar skill, which decreases the variance; if two players of exactly equal skill play, then the game will come down solely to luck. We could also look at how much Elo spread there is (different games use different parameters for their Elo assignments, but if you construct Elo scores using the same parameters across games, then comparing the Elo spreads should give some sense of the size of luck).


text:
What is the optimal strategy for deciding dice to reroll when trying to reach a target value?
Let's say that I have N dice (standard d6) and I'm trying to reach a value of x or higher.  I roll all of the dice once and I don't get my target value.  I can do one reroll and can freely choose which dice to reroll and which to keep as they are, but I have to accept whatever number I get with the reroll.
Is there a a statistically valid way of calculating which dice I should reroll?  So for example if I have 3 dice and have a target value of 18 I would want to reroll any die that wasn't a 6.  However, what if my target number is a 17 and I have 5's on all dice, I need to reroll one die, but how do I determine how many to reroll?
depending on how difficult it is to determine the optimal rolling strategy I'd also be interested in any shorthand strategy that would allow one to quickly come up with a close approximation to the ideal solution.
ps. I'm asking this here because this situation comes up in so many board games.  I know the Math board would likely be better able to give me a quick answer, but I figure the answer is more useful here, this is where other's wanting to know such a strategy are more likely to find it.

With the minimal details given here, there is no optimal strategy; the answer will depend on the relative penalties for failure and success - i.e. if rerolling can produce a worse result than your current one.

You want to go through each of your dice from lowest to highest and,  if your chance of success is at least as good if you re-roll that die than if you do not re-roll that die, add that die to your list of re-rolls.  As soon as you find a die that worsens your current chance of succeeding, stop, and re-roll all the previous dice in this procedure.  If you run out of dice, re-roll everything.
For example, if you roll [4, 5, 5] and are trying to beat a 17, here is what it would look like:

Base case, re-roll nothing: chance of success = 0.

Consider re-rolling [4]: chance of success = 0.  This is the same, so keep going

Consider re-rolling [4, 5]: chance of success = 1 / 36.  This is better than the previous proposition, so keep going.

Consider re-rolling [4, 5, 5]: chance of success 4 / 216.  This is worse than the previous proposition, so stop and re-roll the previous proposition, namely [4, 5].

Optimal result: re-roll [4, 5].
The reason that this works is that if re-rolling a given die is not helpful, you won't want to re-roll any die with a higher result as it will be even less beneficial.  Similarly, if re-rolling a given die is helpful, you will want to re-roll any die lower than it at least as much, because re-rolling that will be even more beneficial.  This assumes all of your dice are the same size (ex. D6s).  The analysis is much more complicated with dice of different sizes.
Here's a more formal (i.e. Python) statement of the algorithm:
def find_rerolls(dice, target):
    if sum(dice) >= target:
        # If you are already over the target, don't re-roll anything
        return []

    rerolls = []  # This is the list of dice to be re-rolled, which starts empty
    p = 0  # This is the probability that your current rerolls will be greater than the target value
    for die in sorted(dice):  # for each die, starting with the lowest
        new_rerolls = rerolls + [die]
        # This is the total we would need to beat given the dice we are re-rolling
        reroll_target = target - sum(dice) + sum(new_rerolls)
        new_p = probability_greater_than_target(len(new_rerolls), reroll_target)
        if new_p >= p:
            # re-rolling this die improves your chance of success (or is at least break-even), so do it
            p = new_p
            rerolls = new_rerolls
        else:
            # Re-rolling that die hurts.  Given all other dice are at least as high, stop trying
            return rerolls
    # Re-roll everything
    return rerolls

The only thing missing from this is the implementation of probability_greater_than_target(number_of_dice, target) (i.e. what is the probability that a set of dice will be higher than a target without re-rolls), which is then a well-formed question for math stack exchange.

Great answer! One nit: it's not strictly true that "if re-rolling a given die is helpful, you will want to re-roll all dice lower than it." For example, suppose you rolled 5 on one die and 4s on the rest, and you're 1 short of the target. If you reroll the 5, you have a 1/6 chance of rolling a 6 and reaching the target. However, if we let the number of dice go to infinity, rerolling all the 4s as well will guarantee failure since the mean of a d6 is only 3.5.

Fortunately, this is simple to repair: observe that, given the choice of rerolling one of two dice, you would never prefer to reroll the lower one. Thus for any potential selection of dice to reroll, you could repeatedly swap dice until the lowest dice are selected for the reroll while improving the solution (or at least breaking even). So in the above example, you would reroll a 4 instead of (rather than in addition to) the 5.

@HighDiceRoller edited to "you will want to re-roll any die lower than it".  It's the all dice that's problematic

Expected Value
Expected value is the statistically 'average' result of a random event.  That is to say, if you did the randomization action a million times, what would be the average value of your results.
It's calculated as P(R1)*V(R1) + P(R2)*V(R2) + .. + P(Rn)*V(Rn), where P(Ri) is the Probability of Result i, and V(Ri) is the Value of Result i.
For a single die roll this amounts to 1/6 * 1 + 1/6 * 2 + 1/6 * 3 + 1/6 * 4 + 1/6 * 5 + 1/6*6 = 3.5  Notably, you can't actually roll 3.5 on a 6-sided die, but that's the expected value anyways.
For an event with an symmetric distribution like a die roll (or any number of die rolls), the odds of getting the expected value or higher is >= 50%.  (Specifically it's 50% + half the probability of rolling exactly the expected value)
If you're looking for a rule of thumb, reroll any dice below the die's expected value.  Note that this only is a good rule of thumb for symmetric distributions.  If you're playing a lottery where your winnings are 75% $0, 24% 10$ and 1% $1,000,000 then your expected value is $10,002.4, and this rule would indicate that you should reroll for anything under the jackpot - but if you're only playing the game once you're actually probably better off keeping a $10 win rather than gambling for the 1% chance.
There's an old saying that a bird in the hand is worth two in the bush.  There's no rule of thumb to help you decide whether you should risk existing results for ones that are statistically better, but not guaranteed to be better.  That will always depend on the game state.
The reverse is also possible, where the statistics aren't in your favor, but your current rewards aren't valuable enough to be worth keeping, so there is incentive to stretch into long odds.

Expected value of each die is the way to go to maximize expected total.  But it breaks down when trying to evaluate beating a target.  For example, if you want to roll at least 17 with three D6s, and have rolled [5, 5, 5], expected value says "don't re-roll any because they're all over 3.5".  But that's clearly wrong, since re-rolling some gives you a chance of winning whereas keeping all your current dice does not.

@Zags yeah, that was what I was talking about in my last paragraph, although admittedly from the other direction, where you're statistically likely to gain, but the thresholds fall against it.  I've added a bit for the reverse.


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Rules for solitaire card games
I know of pagat for games with multiple players, but is there anything similar for solitaire?  I prefers to play with real cards so I am only looking for the sets of rules.

Wikipedia has quite a collection, and the site you mention also has a page with further links. You might find more online if you also search for "patience", the more common name for "solitaire" outside North America.

You can find rules of 499 solitaire games at BVS Solitaire Collection.


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Othello - Most number of legal moves in a given turn
What is the maximal number of legal moves for a given turn in Othello/Reversi?
For example,

On the first turn, there are 4 possible legal moves,
On the second turn, there are 3 possible legal moves,
On the third turn, there are 4 or 5 legal moves, depend on the move taken on the second turn.

That seems like it will be very complex to work out. You might be better off asking it on Puzzling.SE or even Mathematics.SE.

The maximum number of legal moves in reachable positions is 33, as proven by Hiroki Takizawa in his 2023 paper.  The paper presents two such positions with 33 legal moves.
He also proves that the maximal number of legal moves from unreachable positions is 34.

It is very hard to say it without browsing all possible combinations. Another question is are you asking about moves in game that make sense or any random game.
I was playing this game many years and usually one consider move choosing out of 3 maximally 5 possibilities for good move. However in mid-game there are 10-20 legal moves frequently.
You can try some maths to estimate max number of legal moves. Board is 64 fields. You can move only on adjacent. So in my opinion max number possible moves is when you have filled center 6x6, lets say white are on boarder of 6x6 and black are in center. Black have a move so he can move on any field left on board. It gives 28 possibilities. I would say it is maximal estimate.
If you still need to analyze, have a look on WZebra which does in-depth analysis. It is used by most good players. There is also big openings book.

It's easy to come up with a board position for which there are 32 possible moves, though it's not a position that's actually reachable through legal play.

Here's a position with 32 legal moves

Nice, but is it reachable in a game?

No, because F7 and G7 are stable once played. So white has to play them. But F7 would turn F6 white and there's no angle of attack for black to win it back.


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A game with no luck nor skill?
Is there a game that does not use luck or skill in any of it's game mechanics?

If it doesn't use luck, and it doesn't use skill, I question whether it could even be called a "game" at all at that point.

What is the motivation for this question?

I am only aware of a few such games.  One player deals out cards the other pretends to look at them, throws any at random to the table, and then declares "I win".  You had out some more cards so he can declare "I win" again. Obviously this is more entertaining with a small child. Two player spin the bottle works too... but then you might end up with a  small child.  Finally pay to win games could count but these are usually mobile games, not board games.

@kaine I think spin the bottle would be luck based. However, your other two suggestions to me are indeed answers to this question. Too bad it was closed. +1 to you

@El Bromista. Spin the bottle... with only two players!  If it points back at you, you just respin.

@kaine yeah, if it lands on you, you're unlucky. It might land on you every time! I would say a game of flip the coin, "Heads I win, tails you lose" would work here as well.

The Game. You just lost it.

@Matti, funny but it requires luck and skill to avoid jerks like you who make me lose.

If you take away luck and skill, then there is still something left: pure game mechanics. An example of such a purely mechanical game is the card game war. The winner is predetermined, but it is non-trivial to find out who that winner is, so it can still be fun to play, and you can play with as many people as you like.

@hkBst, War is defined as luck based.

In mobile games, there are games that the "best" player is the one that invested the most amount of playing time and/or money.

There could be games just trying to tell a story. Story could be one time story created by game or created by players. If there would be no win condition then this would fit nicely.

This is a "shopping question" which is off topic. A similar question might be on topic on GameDesign stack exchange.

How do you figure out who wins if there's no randomness (no luck) and no player decisions that can affect the game (no skill)?
If there's no skill, then that means players can't make meaningful decisions, i.e. ones where a better decision increases chances of winning. If there's no luck, they can't make meaningless ones either, like picking heads or tails on a coin flip.
That leaves games where the winner is pre-determined. For example, in Candyland, shuffling the cards determines the entire game. But then there's still luck, it's just that the entire game is one big coin flip.
So unless you believe in some concept of "fate", so that you can base the winner on who was "fated" to win, and declare that to not actually be luck, there can't be such a game. The player with the alphabetically first name wins? Use the players' names as seeds for a (deterministic) pseudo-random number generator, and use that to shuffle the deck in Candyland? Those still sound like luck to me; even though there's no luck in the actual "playing" of the game, one player was lucky enough to have been given the name that caused them to win.
Bottom line, anything where someone wins, there has to be a way they were determined to be the winner, and the common notions of "luck" and "skill" are such that one or both will always be involved.

Example: player who's name comes first in alphabetical order wins. No luck, no skill, still someone wins.

@Deo I addressed that. It's not luck within the game, but it's still luck who wins.

It depends on how you define luck, but I see your point.

@Deo Yeah, I think most people if they really thought about it would think of it as luck. If you got a job because your name came first and you got interviewed first, that's luck, right? It's like flipping a coin before the game starts, except it's a very complicated coin and it was flipped years ago.

It can also be referenced as "fate", though trying to define and distinquish these two goes way beyond scope of this question.

I think the fourth paragraph of my answer addresses that pretty clearly.


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in Klondike-Solitaire, how likely is a deal with no legal moves?
In Klondike solitaire with standard rules (Draw 3 cards, Re-Deal infinite), a 'null' hand is a hand where you cannot play any card.
Statistically, is it more common to win the game, or have a null game?

Are you saying that a "null game" is the same as losing a game, since you can't play any cards and are left with only "null hands"?

See also https://math.stackexchange.com/questions/121305/what-is-the-probability-that-a-solitaire-game-be-winnable#:~:text=For%20a%20%22standard%22%20game%20of,is%20between%208.5%2D18%25.

Does this answer your question? Can every game of Klondike-Solitaire be solved?

@Cohensius This does not appear to be a duplicate of that question as it is asking if it is possible to win every game while this one is asking what is the chance of not having a valid play at all.

@JoeW right, both of those questions are close not the same, retract my vote.

In Klondike Solitaire there are 7 cards face up on the table, 21 face down on the table, leaving (out of the 52 card pack) 24 cards in the deck. If you're dealing 3 cards at a time, only 24/3 = 8 of these cards are available. So only 15 cards are available at the start of the game.
In order for there not to be any valid moves at the start, you would need:

No aces
No adjacently numbered cards

This is easily achievable with 15 cards. For example:

4 Kings
4 Jacks
4 Nines
3 Sevens

According to Wikipedia, which answers the probabilities:

About 79% of the games are theoretically winnable
The number of games a player can probabilistically expect to win is at least 43%
In addition, some games are "unplayable" in which no cards can be moved to the foundations even at the start of the game; these occur in only 0.025% of hands dealt

You are therefore far more likely to win the game (even if your decisions are far from perfect) than get an unplayable/"null" hand.


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Strategy for Ultimate Tic Tac Toe
Ultimate Tic Tac Toe is played on nine tic-tac-toe boards arranged in a 3 × 3 grid.
Rules:  Playing on a spot inside a board, determines the next board in which the opponent must play their next move. The goal is to win a three in a row boards. You can play your next move at any board if you are directed to play in a full board or a board that has been won.
Example:

If the last rule is excluded then the game has been solved and has a winning strategy for the first player (paper, implementation).  That is to say, if a player is directed to play at a board that has been won but is not full yet, she does not get a wildcard move, instead she must play at that already-won board.
With the rule that directing to a won board allows the opponent to play at any board, the game is currently unsolved. This was mentioned on the site some years ago.
I known of computer implementations of the game that use Monte Carlo or similar methods.  Are there known strategies that a human can apply and use? Something like favorable or recommended openings for 1st player, and responses for 2nd player?

Super-Human agent (AlphaZero-like) at https://www.uttt.ai/

The following ai-agents evaluate game-states using the following features.  It is a reasonable assumption that an expert human player should consider those features as well.
AI Approaches to Ultimate Tic-Tac-Toe [paper]

heuristic#2 takes into consideration the following features:

Small board wins add 5 points,
Winning the center board adds 10,
Winning a corner board adds 3,
Getting a center square in any small board is worth 3,
Getting a square in the center board is worth 3.
Two board wins which can be continued for a winning
sequence (i.e. they are in a row, column or diagonal without an
interfering win for the other player in the third board of the
sequence) are worth 4 points,
And a similar sequence inside a
small board is worth 2 points.
A symmetric negative score is
given if the other player has these features

heuristic#4 builds upon the previous heuristic, but adds:

if you are sent to a small
board that is full or won you can play anywhere, so that add 2 points
to the heuristic (and -2 for the other player)

ULTIMATE TIC-TAC-TOE by Powell & Merrill [paper]

Winning the game is worth infinity points. Losing the game is worth negative
infinity points.
Winning or losing a board results in a gain or loss of 100 points.
If a board is won and it results in two won boards in a row (i.e. winning one more
board would result in a won game), then an additional 200 points are added (this may occur multiple times if there are multiple paths to victory).
Winning a board that results in blocking three in a row for the opponent results in
150 points.
Winning a board that is already blocked by the opponent’s boards results in -150
points.
Making two marks in a row on a small board adds 5 points
Blocking an opponent win on a small board adds 20 points
Making a move in a board that has no benefit to the player subtracts 20 points

They report that alpha-beta pruning that explores 7 moves a head and evaluates states with using this heuristic won 100% of the games vs a random agent and vs a greedy agent.

Why would you care about winning the center board when it isn't that critical of a square in normal tick tack toe?

The middle board is the strongest since it involves in the most "winning lines".  The middle square is part of 4 winning possibilities, Corners are part of 3, and edges are only part of 2.

But it is also one of the easiest to block a corner spot gives your opponent more opportunity to make a mistake.

Honestly when you play in a corner there is only 1 out of the 8 possible moves that will prevent you from controlling the board and winning. This also applies to a game of ultimate tick tack toe as well.

I would treat the larger board like a single game of tic-tac-toe and play like you are trying to win a single game.
https://www.wikihow.com/Win-at-Tic-Tac-Toe

Most experienced tic tac toe players put the first "X" in a corner when they get to play first. This gives the opponent the most opportunities to make a mistake. If your opponent responds by putting an O anywhere besides the center, you can guarantee a win.[1]

For me I would start by trying to win one of the corners and after that react based on what my opponent does as if you win a corner you should at worst be able to force a draw.

Doesn't that ignore the rule that the position your opponent played in the smaller board determines which of the smaller boards you have to play with your next move? So if you play in the top right corner of the top right board as X, your opponent plays in the centre of that board (since you just forced them to play top right board), forcing you to play your next move on the centre board. Your opponent needs to let you move back to the top right board by playing top right on a sub-board.

@Andrew I am not saying to completely ignore the smaller boards but you if you get a corner and your opponent gets the center you are still better off as you will have more options at getting a win overall if you have a corner than if you have the center. In truth if that situation happens the game should end in a draw.

This is very weak strategy.  Have you got much experience in this game?

@Cohensius Please explain why you think this is a weak strategy, I have not had any bad experience with this as that.

@JoeW, please try to play few games using your advice, you will see it is a losing strategy.  Can try it here:  https://ultimate-t3.herokuapp.com/

Please, explain to me why you think it is such a bad strategy instead of just telling me it is one.

You also haven't explained why the center is better than the corner when the corner only has 1 of 8 possible responses that won't lead you to winning the game.

"The corner only has 1 of 8 possible responses" - this would be meaningful if you play Vs a player that makes random moves. Assume strong opponent, if there is a single good response, she will play it.

This doesn't explain why the middle is as good as you claim it is. If you are playing against a strong player you are likely to get a draw every game anyway.

@JoeW, are you talking about regular TTT? Ultimate-TTT is unsolved yet.  My conjunction is that the game is a first-player win, not a draw.

@Cohensius So you are making a guess about it being a first player win? You don't have any evidence that supports my advice being wrong?

@JoeW, an educated guess. from https://www.cs.huji.ac.il/~ai/projects/2013/UlitmateTic-Tac-Toe/files/report.pdf
"We ran two identical alpha-beta time-bounded agents (0.1 seconds), and tested which player has a better chance of winning. The first player won 56.17% of games (n=300, p-value<0.05), meaning he has a statistically significant advantage.

Your still making guesses and not explaining what you think is wrong with my answer. It sounds like you think it is wrong but lack evidence to prove it.

@JoeW, Hey Joe, I really love to read your answers and comments on this site! Except maybe on this question :) .  The thing is you are right, I am lucking of evidence to prove you are wrong.  It's not trivial to prove you are wrong, however, it is easy for you to play few games and see that you are wrong (without proving it).   I will be happy to try proving it after you said you played 10 games and still thinks that the center square isn't better than the corner.

@JoeW, I found a strong evidence (not a proof) that might convince you: the strong ai-agent of www.uttt.ai always start with first move at middle of the middle board.

Found several tips that @Arkadiusz Nowaczyński learned from playing vs his super-human AI agent  that he wrote:

Start in the center square of the center subgame.

The 'O' response is to push to the corner subgame, so then let the next 8 moves be played in the corner subgames.

When the 'O' breaks out of the corner subgames, jump between the side subgames (these are the least useful to take, but still, one has to be careful not to mess up here).

Maintain the overall balance on the board and wait for the opponent's mistake (the game is a marathon, not a sprint).

Think twice before sending your opponent to the finished subgame (being able to choose any move from the unfinished subgames is very powerful).

My less important tips:

don't let your opponent play in the middle board.  Do it by completing 3-in-a-row without the middle in the non-middle boards.

focus on the boards that matter: it is common to see a player that won 5 mini-boards losing the game.


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Is there a term for games that use kinetics?
Is there a particular name for categorizing board games that have some kinetics?
Some of the examples are Fireball Island (monster throwing fireballs), Monopoly Jackpot (push button spinner) etc.

Almost all games involve moving something around, which we could call "kinetics". Where are you drawing the line between those examples and games that involve rolling dice or moving pieces?

I think OP is referring to games in which fine motor skills are purposefully required as an integral part of game play, for example, striking objects by flicking components toward them (Flick 'em Up!). These would be called Dexterity games.
However, Monopoly Jackpot, I would posit, isn't a Dexterity game, but rather just includes a spinner as a game component.
I don't believe there's a catch-all term that combines the concept of a true Dexterity game and spinners.

@Manath This certainly answers my question. Thank you so much!!

https://boardgamegeek.com/boardgamefamily/5552/finger-flicking-games is also relevant

@Manath Right, it's not a dexterity game because you're just meant to give the spinner a shove.

These are commonly called "dexterity" games.
https://en.wikipedia.org/wiki/Board_game#Categories

See the comments on the question. Notably the point that the question includes spinners in the group under discussion, and spinners by themselves don't make a game a dexterity game. The OP agrees that this term (dexterity game) does not fit the group.

As far as I can tell, the "push button spinner" in Monopoly Jackpot is only meant to be a randomization device, and its implementation is therefore just not interesting for the purpose of classifying a game. I don't think "uses kinetics" is a natural category if it includes games like that but excludes games that use dice.

Flicking mechanism and Action / Dexterity category.

The mechanism your referring is called: Flicking

Description: A Physical Action needs to be performed by one or more players to determine the outcome of the action.

The highest rated board game that use kinetics is Crokinole.
A second option to group those games is Category: Action / Dexterity.

Description: players compete in physical reflexes and co-ordination


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Klondike Solitaire - less than 3 cards in the stock?
In standard Klondike solitaire (deal-3 Klondike), you deal 3 cards at a time from the stock to the waste.  What if only 1 or 2 cards are left in the stock?

Pretty sure you just deal the last 1/2 cards as normal and that is how it is handled on the computer.

That just means you have lost the game.

@Chenmunka If you only manage to play 1 or 2 cards from the deck on the first cycle of the draw deck you would get in this situation and that does not mean you lose.

you deal out the cards up to three. If there are less than three you just deal out those cards. Use what you can. And then put them in the discard pile and start over.
If those are the only cards you have left including the rest of the discard pile then you might be in a lose scenario.

The stock/waste rules of deal-3 Klondike are as follows:

You can play the topmost waste card to the tableau or foundation if there is a legal place to move it.
If there are 3 or more cards in the stock, you can deal 3 cards from the stock to the waste, maintaining their order.
If there are less than 3 cards in the stock, you can only deal all of the remaining cards to the waste, maintaining their order.
If there are no cards left in the stock, you can return the waste cards to the stock maintaining their order ("normal" deal-3 klondike lets you do this as many times as you like).

Edit: As suggested, here are some links to various papers which describe the rules of Klondike:

The Winnability of Klondike Solitaire and Many Other
Patience Games: Blake & Gent 2019 - specifically Section 2 on page 2-3
Constraint Models for Relaxed Klondike Variants: Dang et al 2024 - Specifically Section 2 Stock Relaxations bullet 1 on page 3
Solitaire: Man Versus Machine: Yan et al, 2004: Specifically Section 2 on page 3. Note that the variant of Klondike presented in this paper is different to that presented in most other literature (as quoted by Bjarnason, Tadepalli & Fern 2007 Searching Solitaire in Real Time), as partial tableau moves are disallowed. Yan et al. doesn't specifically name the "stock" ("the pile" in bullet 4 of page 3), and what I have called "waste", they name "talon" (bullet 5 of page 3).

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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Name of a trick-taking-game where the hand size decreases each round?
I play a game where the game play is much like hearts/spades/etc. Standard 52-card deck. Players play one card each "trick" and the highest card gets the trick. (Highest based on lead suit vs trump)
In this variant each player starts with 7 cards, and before the round begins, players must bid on the exact number of tricks the expect to take.
The next round you start with 6 cards, etc. down to 1 card.
I have played this game for a while and would like to look up the official scoring/rules, but cant remember the name of it.
Anyone know the name of this game?

This sounds very similar to "Wizard", in which you bid on the exact number of trickts you expect to take, but you start at 1 card hands and work your way up to dealing out the entire deck

What you describe, is a game that I've always called spades, except it was played with an arbitrary number of people (10 people got a bit silly).  Number of cards / hand went from Max Possible, down to 1, then up to max possible.  Which is very different from how Wikipedia describes spades.

When I was a child it was known as German Whist and had rules for being 'on a dog' or 'on a blind' if you won't no tricks in a round.

Oh Hell!
The games goes by many names but Oh Hell! is its most famous name. See rules at pagat.

Its original name Oh Hell! evidently offended some people and has been bowdlerised in many books to Oh Pshaw! or Oh Well!, while others have preferred more robust alternatives such as Oh Shit! Some call it Blob or Blackout... has given rise to the names Elevator (l'Ascenseur in France), Up and Down the River (in Australia and New Zealand) and 10 op en neer in the Netherlands. In Britain it is often known as Nomination Whist... Other names include Bust (in Australia and New Zealand), Boerenbridge (in the Netherlands), Kachuful (in India) and German Bridge (in Hong Kong)

Note that this is also called "Up and Down the River."

Quote from the link:
Its original name Oh Hell! evidently offended some people and has been bowdlerised in many books to Oh Pshaw! or Oh Well!, while others have preferred more robust alternatives such as Oh Shit! Some call it Blob or Blackout... has given rise to the names Elevator (l'Ascenseur in France), Up and Down the River (in Australia and New Zealand) and 10 op en neer in the Netherlands. In Britain it is often known as Nomination Whist... Other names include Bust (in Australia and New Zealand), Boerenbridge (in the Netherlands), Kachuful (in India) and German Bridge (in Hong Kong).

When being polite, we call it "Prediction". We go from maximum cards down to one, then back up to the maximum. We do "simultaneous bidding" as explained at Pagat. However if the total is the same as the number of cards dealt, then the dealer must change their bid by one.

Same here... The idea being that at least a player must be wrong...

The game you are referring to is called DIMINISHING BRIDGE. You start with seven cards for the first round and you bid to see how many tricks you can make. Second round is six cards dealt to everybody, third round is five cards and so on until you get to having one final card left for the last round. OH HELL has 13 rounds and it starts with dealing one card to each player for the first round to see who can win the first trick. Second round everybody gets two cards dealt, third round is three cards and so on up to seven and then you go backwards from 6 cards to 1 card again.

The accepted answer posted a link to rules for oh hell that disagrees with what you say.


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Wingspan - Player out of eggs
In Wingspan there are certain actions which require the payment of eggs which have been previously acquired.  If a player reaches the point where any action on their part requires at least one egg and the player has none, what happens? I can't find the anything in the rules, but I would think the options are:

That player defaults their turn and play continues with other players.
The game is over.
The player automatically gets one egg to use for their turn (least likely event).

A player cannot choose to take an action that requires them to spend eggs they don't have.
This means that a player with no eggs cannot chose to place a bird in anything but the first column, they cannot choose to spend an egg to get an extra card, and they cannot take any bird actions that require spending eggs.
But bird actions and spending a resource for a bonus resource are both optional, so the only full action that is outright prevented is adding new birds.  A player will always have an option to take an action that does not require spending eggs.

I was playing the game incorrectly! I/we were adding egg costs to any of the actions (gain food, lay eggs, pick a bird card), and that's wrong.  It made for some interesting strategy dilemmas, but I believe my wife and I will enjoy the proper way to play!. Your last paragraph fixes the problem!

@BillN That must have meant that players were spending most of their time on the lay eggs action.

@Acccumulation Yes, I did think that was strange. Not many bird cards were played.


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When you take a trick, you *take* a trick
I played a hand of Hearts with someone who had not played cards in a while. When she took her first trick, she started to put the cards in her hand before remembering to put them down.  That gave me an idea.
Suppose, when you win a trick, the winning card goes out but the others go into your hand.  The goal is perhaps to be either the first or the last to run out of cards.
Is this an existing mechanism?

You've described something similar to Top Trumps and its many different versions.
When a player wins a trick however they add it to their deck rather than hand but the principle is similar to what you have described.


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Whist Variant with points suit
This variant played as a normal Whist, with the last card dealt face-up to determine the trump suit.  the other suit with the same color as the trump suit is now the point suit.  For example, if hearts is trump, then diamonds is point.
There are there new rules:

You get points by how many point-suited cards your partnership has taken (same as in Hearts).
The "breaking hearts" rule - A player can not lead with a point suit until a point suit has been discarded. This rule to prevent the partners with high point suits from dominating the game early.
Point cards are anti-trump - If a player leads with a point suit, then any other suit can trump it. (Trump will trump non-trump trumps, obviously).

(Personal Note: This variation also makes use of the fact that there are four suits but only two colors in a traditional deck, which always bothered me a little.)
Questions:

Are there any problems with this variation which make it unplayable, or unbalanced?

Is there a way to exploit the rules, or a way to play where understanding the rules more deeply conveys an advantage?

Does this variation add to the complexity and fun of the game, or is it merely a complication which adds nothing unique or interesting to standard whist?

Would the game play better with only one of the rules rather than both?

I voted to close because it's not a Q & A so much as a discussion, but I personally prefer these opinion questions to remain if possible, so maybe a nice middle zone is, for these types, to do a large amount of diligence analyzing the pros and cons or the ways in which the variant changes the dynamics, then post the question as asking whether the game is balanced or how lopsided it becomes or something more pointed? Just a thought.

@Joey Thanks for your thoughts.  I've taken your recommendations and modified the question accordingly for your review.

To me it looks like only play-testing with big enough group of play testers can answer these questions.

If you are looking to distinguish the four suits more clearly, why not try Auction Bridge (simpler than Contract Bridge) or Bid Whist. Check out links here: http://boardgames.stackexchange.com/questions/25644/bridge-guide-for-experienced-spades-player

After some play-testing with friends, the complexity was intimidating, and so we settled on these rules:

The last card is dealt face up, and it is the point suit.
There is no trump suit.
You cannot lead with a point suit until a point suited card has been discarded.
When a point suit is led, any other card can trump it.

The results were interesting: Once players caught on to the game, they would discard points often rather than hording them, hoping their partners can pick them back up.  Teamwork seemed more vital in this variation than any trick taking game I've played.
It turned out that having a both trump suit AND an anti-trump suit was an unnecessary complication. The goal was to acquire point-cards which could be trumped by any card, and so having a trump suit felt superfluous.
Alternatively, we played the following variation:

The trump suit is the last card dealt, the point suit is the other
  suit of the same color as the trump suit.
The point suit cannot be led until a point suited card has been
  discarded.
The point suit is a normal suit, and is not trumped by  any suit
  except the Trump suit.

This variation worked well, and it satisfied my requirement that the game make use of the fact that there are four suits but only two colors.
However the first variation in this answer seemed more fun.  I'm not sure why.

"Teamwork seemed more vital in this variation than any trick taking game I've played." Have you played contract or duplicate bridge? Teamwork in play is utterly essential there. If it is even more so in this whist variant, I would be surprised.


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Castling when in check
Chess has a rule that forbids castling when in check. What is the practical value of this rule? How would chess without this rule compare to chess with this rule?

I have removed the "opinion based" part of the question and suggest that it NOT be closed. What's left can be answered by reference to the chess literature.

@TomAu I don't think it should be closed but to me this is pretty much the same question. It's not asking "why/when was this rule added". To answer the question as asked, it's still effectively going to be a comparison of chess now to what modern chess might look like without the rule.

However I feel that this question is suitable as a subjective question.

One important reason to check a king is to prevent him from castling later by forcing him to move. The reason is that a king that has already moved (and remains in the center) cannot later "castle" his way into relative safety on the side. Nor can a king castle while in check, so this prevents him from castling for at least that move.
There are two other ways to defend a king in check without moving him. One is to capture the checking piece, and the other is to "interpose" another piece between the checking piece and the king. If the king can then be prevented from moving, he can castle later. But these remedies expose the defending side to other risks, which are probably included in the reasons to check the king.

Answer doesn't address the question, just states the circumstances in which Castling can be prevented.

I think this does somewhat explain what was intended even if it does not fully explain it.

So if I am reading you correctly, you're saying that the prohibition on the king castling out of check, makes it possible to attack the a king that is ready to castle, possibly preventing the castling move. If this prohibition were to be dropped, it would be harder to prevent castling and thus the prospects for a player going on the attack would be reduced. So what I am really wondering about is whether there is some evidence of this in chess openings or tournament play.

@hkBst: You're reading my answer correctly. From what I understand, the "law" was established a long time (over 100 years) ago. So it may or may not be supported by recent results or tournament play.

By chance I ran into this game of Rybka (Computer) vs Deep Sjeng (Computer)
17th World Computer Chess Championship (2009)  ·  Slav Defense: Chameleon Variation (D15)  ·  1-0 where 15 O-O is illegal due to being in check.

Per the wikipedia page for castling, it appears that castling arose in response to the growth in the power of the bishop and queen move sets. The line that is most interesting is a reference to the Gottingen Manuscript:

In the Göttingen manuscript (c. 1500) and a game published by Luis Ramírez de Lucena in 1498, castling consisted of two moves: first the rook and then the king.

If this is correct, than 'casting' while in check would entail moving the rook first, and then 'leaping' the rook with the king. If the king is in check when you attempt to castle, you would be moving the rook with the king still in check.


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What are the chances of winning Accordion Solitaire?
I would like to know what are the chances of winning in both versions:

laying out the cards one by one
laying out the entire deck at the game start

What are you considering to be a win condition?

I mean getting all the cards in a single pile.

Are you looking for if you have prefect play or just how often player win?

Accordion
According to one of the biggest player on the solitaire market (SolSuite), the game of Accordion (one card at a time version) has a chance of winning in about 1 of 200 games, i.e. 0,5%

But I would actually say that there is no difference in the winning percentage (if played right) between the two versions you are talking about, since (in the one card at a time version) you could always lay out the entire deck first one card at a time before starting to play...

There is probably a difference in the win percentage. If you lay out the entire deck first, you have perfect information about which moves are most beneficial. By flipping cards one at a time and making decisions as you go, you may make a choice that in hindsight was worse (i.e.: your piles could have been more appropriately condensed).

According to the latest publication that compute the solvability of 45 solitaire games, Accordion is almost always solvable.

Freecell, Spider, and Accordion...are all very close to 100% solvable.

Source: https://arxiv.org/pdf/1906.12314.pdf

I suspect that there some difference in the rules between this Accordion and the one in the answer that state only 0.5% winnability.

At least one of each three games can be won in the version where you lay out the entire deck. Just follow these strategy tips:
You should select four cards of the same rank, clustered near each other and near the end of the layout. The strategy is to try to get all four selected cards to the end of the layout and never cover them with anything else until the very end of the game.

Is the link you provided pointing to a site you control or take part of?

I have changed my answer according to your remarks.

Are you estimating a 1/3 solution rate based on personal experience?  Or some database?

My estimation is based on my personal experience while playing Accordion in BVS Solitaire Collection.


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Twilight Imperium without the Agenda phase
The agenda phase in Twilight Imperium 4th edition feels a little "bolted on", and adds a lot of time to an already long game for not that much impact.  I'm considering a house rule to remove the agenda phase.
I hope this can happen relatively straight forwardly for two reasons.  First, the agenda phase doesn't even happen in the first several rounds of the game, so the round structure already supports this.
Second, in a substantial change from 3rd edition, your planets refresh both before and after the agenda phase, so there's no need to budget influence for voting and that the only impacts this phase has on the rest of the game is the effects from agendas and riders.
However, there are other components and abilities that depend on this phase.  So far, I have identified the following:

There are several action cards that interact with agendas (such as riders) that would need to be removed from the deck.  This is pretty straight forward.
There is no longer a time when non-neighbors can trade, which would make the Hacan slightly more powerful.  If this turns out to be a problem, it's pretty easy to add this back in (allow cross-galaxy trading as a step during the status phase once Mecatol Rex has been conquered).
The Xxcha "Quash" ability wouldn't work and would need a replacement.
The Xxcha "Political Favor" promissory note wouldn't work and would need a replacement.
The Nekro Virus "Galactic Threat" ability wouldn't work and would need a replacement.

Are there any other parts of the game that need the agenda phase to work, either mechanically or for game balance?
I'm also open to suggestions for how to patch the pieces of the game that currently depend on the agenda phase; in particular, I'd love ideas for how to replace the Nekro Virus "Galactic Threat" ability since that seems important to their pace of technological acquisition.

Honestly, I think it would be pretty straight-forward to remove The Agenda Phase from the game. Not too many components actually rely on it. With that being said, none of the below suggestions have been play-tested and there may be things that I have overlooked in terms of gameplay. I've played this game quite a few times but am by no means an expert.
Here's a list of things I found, some of which are also noted in your question:
Factions
The Nekro Virus

Faction Ability: Galactic Threat

The problem with the Nekro Virus is that they cannot research technologies. When you would research technology you instead gain 3 command tokens. This can be super advantageous in the early game. You could instead allow the Nekro Virus to research technology as normal whilst keeping their combat-centric technology thievery intact. This faction has good starting units but not getting early command tokens may be slow their early game expansion. Their late game would depend on how they balance neighbor relations and stealing technology. Removing Galactic Threat and allowing Nekro to research technology makes The Nekro Virus marginally weaker but not terribly weaker.
The Xxcha Kingdom

Faction Ability: Quash
Faction Promissory: Political Favor

I feel like the main fun of Xxcha is being able to play around with the Agenda Phase and being able to sell off your faction promissory. Without these abilities I'm not sure Xxcha would ever be a better choice over any of the other factions. I would recommend removing them from selection if there is no Agenda Phase.
Action Cards
These action cards could be removed entirely from the action deck. My only concern is now the action deck is less saturated with "later phase" cards. What I mean is that you'll now have a better chance of getting things like Sabotage and Direct Hit cards that will directly effect the main Strategy Phase. Common action cards may need to be slimmed down.
15/80 (18.75%) of all Action Cards directly relate to the Agenda Phase. These cards include:

Ancient Burial Sites
Assassinate Representative
Bribery
Confusing Legal Text
Distinguished Councilor
Repel Law
Veto

All Riders:

Construction Rider
Diplomacy Rider
Leadership Rider
Imperial Rider
Politics Rider
Trade Rider
Technology Rider
Warfare Rider

There are no Objectives (public or secret) which directly rely on The Agenda Phase.

While I understand not enjoying the Agenda Phase it can provide a breather from a normally strategic and tense game. It also allows you to build relations with players who are not your neighbor. In my opinion, it's all part of the overall strategy of the game as half is playing the players and the other is playing the pieces.