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Should I trash Copper or Silver with Mine?

Assuming I've got both Copper and Silver in my hand, which is better to trash in general and why?

I'm going to have to disagree with Pat; I hate having Copper in my deck, and rather have a consistent deck of Silvers.  Yes, it's nice if you get Gold - Copper - Copper in your hand, but Silver - Silver - Copper will buy the same amount.  Once you start running out of Coppers (or if you only have a Silver in your hand along with the mine), then you can start upgrading to Golds.
It's kind of hard to answer this question in vacuum, because there are so many different possibilities that could make one answer better than the other; for example:

If you're running an early Moneylender, upgrade the Silver to Gold, and use Moneylender on the Coppers to really ramp up.
If someone is playing multiple Thiefs, I may not even bother with the Mine.  Or if I do get a mine, I'll upgrade Copper to Silver since losing a Silver isn't as bad as losing a Gold.

I think you're right to point out that other opportunities to trash Copper make the Silver->Gold strategy more appealing, and ultimately the best option is determined by context.

With thief in play, if you upgrade copper -> silver, you throw away a rare opportunity for your opponent to help your deck (by trashing your coppper).

I would like to add that upgrading silvers to gold can put you in a situation where you have a mine+gold in your hand instead of having mine+silver leading to mine being a dead card more often.

Hating copper isn't a good justification for a strategy. I understand the copper-hate, but this answer doesn't give any objective reasons to prefer one strategy to another.

Another argument in favor of mining copper to silver first is that you will be less likely to see a hand where the mine is useless due to gold being the only treasure(s) in the hand.

In general, my preference is to favor upgrading the silver to gold.
My rationale is that I am trying to scale the value pyramid to get to the useful values of coins (5,6,8 typically).  With one gold I am likely to reach a good total coin value when the gold is drawn.  With the two silver, I'm more likely to have two mediocre hands instead of one good one (if the two silver come in the same hand).

This is my preference as well, and if there happens to be Platinum in the supply, all the better.

+1: I think your answer essentially describes the flaw in LittleBobbyTables' answer, even though it was posted first.

However, if you draw your mine again and you have only gold, you can't upgrade. Draw the mine again and have a silver, you can use it. This is why I generally choose to upgrade the lowest value.

@Konerak if you are stuck with "only" gold, you're doing pretty good :-)

@PatLudwig, true! But I meant, in the current hand. Your next hand will contain the copper you didn't upgrade ;]

If you have Platinum cards in play, your best bet is to mine Gold ($3) to Platinum ($5).  This also applies to mining Silver to Gold so you have the Golds to mine to Platinums.
However, with Prosperity, you may also have other options, such as Silver to Royal Seal or Hoard. Like Gold, Hoard can be mined directly to Platinum, but it also gives you the opportunity to get golds by buying Victory cards.
For the others, most of the time you'll want to mine Silvers to Golds first.  Here are just a few cards this applies to:
Trash Coppers:

Moneylender
Trading Post
Mint (to purchase)
Spice Merchant

Give Coppers to other players:

Masquerade
Ambassador

Play specific actions related to Coppers:

Coppersmith
Apothecary
Counting House

Silver/Gold work better with:

Mint (to play)
Herbalist

You'll want to mine Copper to Silver first if these cards are in play:

Saboteur (Silvers prevent other cards from being trashed)
Swindler (avoid gaining Curses)
Cutpurse (only discards Copper)
Forge (Copper is worth 0 for Forging)
Jester (Enemy gains a Silver instead of you gaining a Copper)

Don't bother with a Mine at all and concentrate more on action cards that give you money if one of these is in play with no defense cards:

Thief (Trashes up to 1 treasure, opponent has option to gain)
Pirate Ship (Trashes up to 1 treasure)
Noble Brigand (Trashes up to 1 Silver or Gold, opponent gains)

Noble Brigand can only steal Silvers and Golds, so mining to non-standard treasures or Platinums is OK.

Even if you don't have the opportunity to Mine a Gold into a Platinum, you want to Mine Silvers into Gold rather than Copper into Silver any time Platinums are in the Supply. The Gold->Platinum leap is the equivalent of getting to play your Mine twice on other cards.

Right. The counting house does make the Chancellor a little less useless :)

Updated this with a few new cards from Cornucopia and Hinterlands.

@shujaa Way back when I first posted this, there were only 6 cards listed... but it kinda ballooned since then.  That and it was the current rage back then to post images of the Dominion cards.

This answer is a "go-to" for copper FAQ! Upvoted long ago.

Stables should be under its own category since it doesn't trash the treasure but rather discard it. Of course it's still better to use it with a copper instead of a silver, but not as it would have been had it trashed it.
Other than that, good answer and a great list.

Exactly the right answer: depending on the kingdom. You might also add for the Jester that it's better for the opponent to hit a silver, instead of hitting either a copper or gold . Furthermore, there are situations where deck homogeneity is more desirable: Duke/Duchy games, as you need to consistently reach $5, games where Advisor is used to draw (much better to reveal Estate-Silver-Silver than Estate-Copper-Gold); on the contrary, if going for diversity (Menagerie, Horn of Plenty, Fairgrounds) or an Engine (a few strong treasures are more desirable) then it's the other way around.

Statistically, the difference is in the variance of how much money will be in your hand. Assuming no other cards swaying you one way or another (and no Platinum), as other answers have pointed out, regardless of whether you upgrade Copper to Silver or Silver to Gold

the total money in your deck is increased by 1
the number of treasure cards in your deck is unchanged
therefore the average amount of money you'll have in your hand is the same in both cases.

However, the variance of your hands will be different. If you upgrade all your coppers to silvers, the money you draw in hand will be much more consistent than if you upgrade all the way to gold when possible. Keeping some coppers in your deck increases the chances that you won't draw any higher-value treasures -- and increases the chances that you'll draw 2 or 3 golds at once. If all your treasures are silvers, you'll only draw silvers.
It boils down to what distribution of hand values you want. If you want consistent 3-4-5 hands, do copper to silver first, but if you're okay with some 2 hands to also get more 5-6-7-8 hands, go all the way to gold. I'm sure we can all imagine card pools where you'd want to go one way or the other. If you're trying to get a Province or other expensive card (Witch, Goons...) ASAP, go for Golds. If there's 4-cost cards you want to buy several of (maybe Caravan, Bridge, etc.), go for Silvers.
In the realm of unlikely but possible, if you go to Gold first, you run a risk of drawing your Mine with a Gold or two, but no Copper or Silver to trash, but this is a pretty small risk, and you probably won't be unhappy with nothing but Gold in hand anyway.

In Dominion, you almost always want a more varied money distribution.  The desire for a 5-2 split, a before second shuffle gold, and the steep utility increase from 4 to 5, and from 5 to 6 are more evidence.  Further, the Tactician card even gains from this idea.

@RobRenaud Why do you want a 5-2 split?

@Pureferret you don't always want a 5-2 split, but a lot of 5-cost actions are quite a bit better than 4-cost actions (what Rob calls the steep utility increase from 4 to 5), and especially with some of the stronger attacks you want one ASAP.

If there's the Swindler around, then getting rid of the coppers is of first priority!

Not really. Trashing coppers will often help you by thinning your deck

@Casebash: This is exactly what I wrote. It is even more useful to thrash the coppers when there's a Swindler.

Actually, you are right. They can change your copper into curses

A swindler has problems with the police?  I never would have guessed...

The decision boils down to a few things, at least for me...

extant gold, silver and copper ratio
number of remodels in the deck

If I have a lot of copper, I mine the copper into silver.
If I have a lot of silver, I mine the silver into gold.
If I have a remodel, and am near the top of the VP race, having the gold to remodel into a province trumps having more silver.
Another consideration is whether or not there's platinum in play. If platinum is available, moving the silver to gold is more valuable in that it gives me gold to mine into platinum.

In a vacuum, I will always mine Copper to Silver before Silver to Gold. My reasoning is simple: if I have Mines, Silvers can be further Mined and Golds cannot. Since the short-term gain is one coin for that turn either way, I'd rather not dead-end myself by having a Mine with no actionable treasures later on.
Needless to say, the preference is so slight as to be a tie-breaker. Many other circumstances may change my strategy. E.g.:

I'll always Mine Gold to Platinum if the option is available, since the two-coin gain can have very useful short- and long-term benefits
Money Lender benefits from having Coppers linger a bit, so if I'm using them, I'll favour Silvers for Mining
Various other circumstances which other people have already commented on, and which there's no point me rehashing here

I like to trade my coppers to silvers early in the game so I have a more consistent set of resources.  Later in the game, I prefer exchanging my silver for gold.

I'd do copper to silver, but I also don't usually buy mine if there aren't any other treasure cards available.

I would argue copper to silver before silver to gold.  The copper to silver trade doubles the value of that card, while silver to gold is only a 50% increase.

I think your math might be statistically misleading. Either operation increases your total money in deck by the same amount. It could further argued that when you draw them later the copper will be a 100% increase in value whilst the gold 150%, meaning you break even if you redraw the mined card only once, but profit if you draw it twice. Of course my math there is just as spurious as yours.

Perhaps more directly, thinking in terms of ratios leads to the conclusion that copper to silver (x2) is better than gold to platinum (x1.67). But I think everyone here can agree that if you draw Copper Gold Mine, trashing Gold for Platinum is the only reasonable choice (it it's available).

I'm with aslum on this. Here's why: ignoring all other cards in the deck, I end up either with (A) a mine, a copper, and a gold, or (B) a mine and two silvers. So I have the same amount to spend, total, when I next draw those cards.


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Risk Legacy: Is it better to roll 1 or 2 defense dice when defending a bunkered location?
In Risk Legacy, there is a Bunker that always adds (+1 to the highest defense die, except when the high die is a 6).
Is it better to roll 1 or 2 defense dice when defending a bunkered location.

I ran a script to calculate probabilities of attacker losing two troops (D wins), defender losing two troops (A wins) and each losing one troop (Tie).  The following table shows these probabilities, along with the difference from standard play in brackets.  The final column shows the troop loss ratio per die.
Number of  | Win Probabilities (Difference due to bunker)            | Troop loss ratio
 Dice      |                                                         | (A loss : D loss)
-----------+---------------------------------------------------------+------------------
D: 1, A: 1 | D: 0.722 (+0.139), T: 0.000 (+0.000), A: 0.278 (-0.139) | 0.722 : 0.278
D: 2, A: 1 | D: 0.861 (+0.116), T: 0.000 (+0.000), A: 0.139 (-0.116) | 0.861 : 0.139
D: 1, A: 2 | D: 0.583 (+0.162), T: 0.000 (+0.000), A: 0.417 (-0.162) | 0.583 : 0.417
D: 2, A: 2 | D: 0.533 (+0.085), T: 0.320 (-0.004), A: 0.147 (-0.081) | 0.693 : 0.307
D: 1, A: 3 | D: 0.506 (+0.166), T: 0.000 (+0.000), A: 0.494 (-0.166) | 0.506 : 0.494
D: 2, A: 3 | D: 0.352 (+0.060), T: 0.408 (+0.073), A: 0.239 (-0.132) | 0.556 : 0.443

If you look at each pair of rows then you can compare the defender rolling one or two dice.  In each case the defender's troop loss per die roll is decreased by rolling two dice, so it is always theoretically better to roll two dice.

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sort: votes


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Dominion: when playing the Big Money strategy, when should you switch from buying Gold to Duchy?
When there are how many Provinces left (if that is the way the game will most likely end), should you switch from buying Gold to Duchy (when you don't have 8 money)? Does this amount change for 3, 4 player? Is there a good rule of thumb based upon the number of players/potential buys before your next turn?

For 2 player, the generally accepted tipping point is when there are 5 Provinces left, buy Duchies (and Estates when there are 2 Provinces left). This has been shown as optimal according to simulator testing for BM-based strategies (e.g., BM only or BM + any given card, e.g., Smithy). For race games (e.g., Gardens or IGG), the tipping point is much earlier, although it depends on the set in question. The answer will also change if you or your opponent is playing a mega-turn engine deck.
For multiplayer, the key is to remember that 3 player games have 4 Provinces/player, just like 2 player, but 4 player games only have 3 Provinces/player. So, the Duchy-buying should occur earlier in a 4-player game.

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How can I mitigate some of the downtime between player's turns?
For games in which it is not possible to take simultaneous turns, as the number of players increases, so does the wait time between a player's turn and their turn again. It becomes a balancing issue with the game's design to keep the game the same or introduce elements that help speed up game-play.

What is the maximum downtime between turns that I can expect players to be ok with?
What steps can be taken to mitigate downtime between turns (examples from games, and your opinion of their effectiveness, are appreciated).

For example, Settlers of Catan, when expanded to 5-6 players, allows all players to make purchases during any player's turn. This is done to mitigate having too many cards if the robber comes up between your turns, but it also increased engagement on other people's turns. MtG and other CCGs have instants that can affect your opponent's turns.  Even games like Monopoly allow trading between players to keep them engaged.
What other design approaches can be used for larger numbers of players if simultaneous play (like Roll Through the Ages) isn't possible?

There is actually a tradeoff in design space here.  Games where there nothing that a player can do between other players' turns (like Chess, Risk, Scrabble, or Carcassonne) can work really well played asynchronously (especially over a digital medium).  Correspondence chess and Words With Friends are two popular examples of turning the lag between turns into a feature.

I think the main points have mostly been hit. A few strategies:

Direct interaction during other players' turns. For example, if there is a combat element, if the defending player has interesting choices such as playing cards from hand to gain advantage. As mentioned, Magic is a good example as the defending player has plenty of decisions to make and cards to play. Counterpoint is Risk, where defender just rolls dice doesn't work as well for keeping interest.
Indirect interaction during other players' turns. In a recent game Eminent Domain, player gets to piggyback on the decision the current player makes. Or in a game like Battlestar Galatica, there is so much meta-game discussion that regardless of whose turn it is, all players are engaged and invested even if the game mechanism doesn't allow them to interact with the "game" at that moment.
Pre-planning while avoiding Analysis Paralysis. Player can more or less make all decisions about their turn while other players are doing their own. A key part of this is avoiding adding new information during current player's turn. For example, if the player must draw a card, have them draw at end of turn rather than beginning of turn. This will give them more time to internalize their choices.
If there really is no way to do any of the above, then you need to find a balance in length of turn. Perhaps make really short turns, but if the player only has a few actions each turn they may be all the more frustrated because they feel like they can't get anything done on their turn. If you instead give them lots of actions, you can make the player's turn feel really beefy, but that's going to make the wait for next go-around that much worse.

I don't think there's a golden rule for amount of downtime. Instead, it's all about perceived downtime. My "turn" may only come up every 15 minutes, but as long as I am thoroughly engaged in what my opponents are doing during their turns, and I have true decisions and actions to take during their turns... it doesn't matter.

By the way, this is all a matter of preference. Check out Andrew Looney (Fluxx, Chrononauts) in his principles of game design -- he actually prefers no engagement when it's not his turn. I don't think most people are like that, but for some casual/conversational games (think light card games like Spades, or even drinking games) it may not be appropriate to have lots of engagement outside of a player's turn. http://www.wunderland.com/WTS/Andy/Games/DesignPrinciples.html

The maximum acceptable downtime will depend primarily on how much analysis is required (and possible) for a player's turn. For example, downtime in Power Grid can get quite high during the final few turns. I've had to wait as long as 20 minutes in one 6-player game. Yet, that didn't bother me, because the game state wasn't going to change dramatically before it got to me (that is, options will not open up for me, they will only be taken away) and there's a good amount of mental arithmetic involved in figuring out the optimal placement. To contrast that with, say, Carcassonne, I once had to wait close to 5 minutes for a turn due to one analysis paralysis prone player, and that was torturous. Even though we draw our tiles at the end of a turn to speed play, there just weren't that many options, so it was extremely boring. This would also be true for games where the board state will change dramatically between turns, so foreplanning is not worthwhile (Fluxx is a good example of this - any downtime that's not measured in seconds feels long for that game, because there's not anything worthwhile you can do when it's not your turn).
Along those lines, my personal experience is that the best way to mitigate downtime in a game with indirect interaction is to give players enough to think about when it's not their turn, either about the current turn or planning ahead for the future. Recognize, however, that not every game is (or should be) a deep, brain-burning game, so this is not to say that the answer is to add complexity; perhaps a better way to state this point is to ensure that the downtime is proportional to the depth of the game. You don't want people to run out of game-related things to think about, because you lose them once their minds start to wander.
If your game has any kind of direct interaction (e.g. negotiation, trading), then there's really no such thing as downtime, since all players are involved at all times. If downtime is a concern and your design would lend itself well to a direct interaction mechanic, that would probably be the way to go. Even something like a bluffing component can go a long way toward helping keep players engaged; for example, in hidden money games like Power Grid or Imperial, I greatly enjoy trying to project more (or less) wealth than I actually have, getting inside my opponents' heads to try to get them to do what I'd like.

Good comparison between Power Grid, Carcassonne and Fluxx.  The nature of the game really does matter as to how much down time can be tolerated.

An excellent analysis.  Especially that last paragraph; Settlers is an example of an almost-no-downtime game for that reason.

You've already hinted at the most successful method, at least in my experience.
I'll relate it by an example.
In Supremacy, the original was "On your turn, do steps 1 and 2, then any three of steps 3-8" (I might have the numbers wrong; I sold my Supremacy set years ago)
The revised sequence of play in the revised and expanded game is everyone does steps 1 & 2 simultaneously, then in each of the other steps, those doing that step roll for initiative, and act in rolled order.
This sequential play of each step reduces the wait between players, and preserves a sense of simultaneity, without actually having simultaneous play.
Star Fleet Battles, and the Impulse chart is another variation on this mode, as is Civilization/Advanced Civilization.
The other common ways include limiting which steps can be taken on one's turn, and some form of timing mechanic.
In Galaxy Trucker, you have only a couple minutes to finish building your ship after the first person declares theirs done; first one done flips the egg-timer... and calls stop when it runs out.
In chess, it's often played with a chess clock, and the game is lost if one is in check or one has run out of time on the chess clock.
In the original Supremacy rules, you don't get to do all the steps. This limited your turn time by reducing how long it took to resolve your turns.
One other useful tool for reducing down time is useful rules summary cards with the most common information on them. The biggest factor in slowing down many a game is rulebook referencing; by elimination of the need to go to the rulebook by an effective and clear summary card, one reduces the tendency to look in the rules.
One other item you hinted at in the question is the "reaction" effect. By having something that you get to do during the opponent turn, one tends to be more attentive to the opponent's turn, and not notice the downtime as much, despite not actually reducing the downtime.

+1 nice answer.  As you've mentioned Supremacy and SFB, I'd also point out the Puerto Rico / San Juan solution somewhere between the two - players do bookkeeping steps at the start and end of turn and then rotate taking single actions rather than entire turns.

Another game that takes the phase approach is 7 Ages.  All players secretly decide which two or three actions they'll take, and then the actions are run in order -- everybody who's doing maneuver does so, everyone who's buying units does so, etc.  Especially for longer games this frequent intaraction is important.  (I actually get bored with SFB, though I'm not very good, because every step takes what seems like forever to resolve and if it's not mine I'm not engaged.)

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 Should you play a Bunker Scar if you aren't likely to win the first game?
Since the Winner of a game is able to place their Major City anywhere on the board, even on nice defensive bunker scars...
Should you place a bunker on the board if you don't believe you are likely to win the first game?
Does this answer change if you are playing a 3, 4, or 5 player game?
Does this answer change if one or more scars have already been played?
(please only take into account staring scars, faction powers, number of players, and starting rules. No spoilers please, and no taking into consideration spoiler packets)
Starting Scars (3 Ammo Shortage (-1 defending high die), 3 Bunker (+1 defending high die))
Major City - +2 population, you may start here if no enemy HQ is adjacent.

It depends
If by playing your Bunker scar, the Bunker will be located in a nice defensive position or choke point (i.e. Central America, Brazil, Southeast Asia), you open up the possibility that the winner of the first game might place a Major City reward on top of your Bunker. This will give them a pretty major advantage in the early games, because unless someone places their HQ first (and adjacent) to the Major City that player will get to start there and their HQ will get the +1 defensive bonus. Additionally, if the opponent doesn't start there, you or another player will have to sacrifice troops to move into (or to the other side of) the city.
If the Bunker will be located on a less high value territory (Middle of Asia, Europe, or North America), then it wouldn't be as helpful to an opponent who wins before you. It will make those continents more valuable (which is probably a good thing).
Does this answer change with different numbers of players or scars that have been played?
The only difference between the number of players, and the scars that have already been played is whether you will get a new scar next game. There are 6 starting scars, so if by playing the Bunker you will make it so that there will not be enough scars to pass out the next game, you might want to hold off on using it. This is especially true if the majority of scars played so far have been Ammo Shortages. You will have a a better chance to win next turn, and if their are more Bunkers than Ammo Shortage scars, you have a higher probability of getting a Bunker and being able to place it in a good location if you expect to win for your own Major City.


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Is there an optimal swing die value for Changeling VS Iago?
Button Men is played until one player wins 3 rounds. For the first round, Swing Dice selection is done in secret. On following rounds, only the player that lost the round is allowed to change it's value.
Changeling: dX, dX, dX, dX, dX
Iago: d20, d20, d20,dX
Swing Dice (dX): Values for X may be any number between 4 to 20 inclusive, including nonregular dice like 13 or 7 sided dice. If a character has multiple dX dice, the value of X must be the same for all dX dice.
Is there an optimal swing die value for Changeling, and if so what is it?

If you believe in basic Swing Die strategy, then '6' is the appropriate value for X for Changeling.
The formula for Swing Die selection is:

(A-B)*2/3 = (Sides the Bigger Character must keep)
Where 'A'/'B' are character's dice side totals.

The general theory is
1) If you can force your bigger opponent to have to keep two or more dice, then you will have a distinct advantage. You are more likely to go first as a smaller character (smaller characters usually have dice more dice with fewer sides, and are therefore more likely to have the lowest die).
2) Select the biggest die possible, that condition 1) will hold true.
Until Changeling has won has won 2 matches, a swing die value dX='6' requires that Iagomust keep 2 dice to not lose by points. If you read down column '6', Iago must keep between 22.7 and 33.3 sides to not lose, even if they take all Changelings dice. Iago cannot select a Swing Die value that allows them to only keep a single die and still win.
Once Changeling has won 2 rounds, then their best Swing Die value of dX should probably be '20' unless Iago has selected dX=4 or 5. With 2 wins for Changeling, the only way Iago could switch swing die values is by losing and giving you your 3rd round win for the match. If Changeling doesn't have 2 wins yet, dX='18' is your next best swing die value. It gives you the biggest die possible, without requiring that you keep more than a single die. The best that Iago can do is select dX='4' for their next swing die, which only requires you to keep 17.3 sides. Even if they do happen to win an Iago'4' vs Changeling'18' round, you can switch back to Changeling dX='6' with your swing Die and require Iago keeps 2 dice again.
Changeling|'4' |'5' |'6' |'7' |'8' |'9' |'10'|'11'|'12'|'13'|'14'|'15'| '16'| '17'| '18'| '19'| '20'|
    +--+  +----+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+
    |60|  | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |  80 |  85 |  90 |  95 | 100 |
    +--+--+----+----+----+----+----+----+----+----+----+----+----+----+-----+-----+-----+-----+-----+
Iago| 4|64|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7|-4.0|-7.3|-10.7|-14.0|-17.3|-20.7|-24.0|
Iago| 5|65|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0|-3.3|-6.7|-10.0|-13.3|-16.7|-20.0|-23.3|
Iago| 6|66|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7|-2.7|-6.0| -9.3|-12.7|-16.0|-19.3|-22.7|
Iago| 7|67|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3|-2.0|-5.3| -8.7|-12.0|-15.3|-18.7|-22.0|
Iago| 8|68|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0|-1.3|-4.7| -8.0|-11.3|-14.7|-18.0|-21.3|
Iago| 9|69|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7|-4.0| -7.3|-10.7|-14.0|-17.3|-20.7|
Iago|10|70|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0|-3.3| -6.7|-10.0|-13.3|-16.7|-20.0|
Iago|11|71|34.0|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7|-2.7| -6.0| -9.3|-12.7|-16.0|-19.3|
Iago|12|72|34.7|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3|-2.0| -5.3| -8.7|-12.0|-15.3|-18.7|
Iago|13|73|35.3|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0|-1.3| -4.7| -8.0|-11.3|-14.7|-18.0|
Iago|14|74|36.0|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7|-0.7| -4.0| -7.3|-10.7|-14.0|-17.3|
Iago|15|75|36.7|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3| 0.0| -3.3| -6.7|-10.0|-13.3|-16.7|
Iago|16|76|37.3|34.0|30.7|27.3|24.0|20.7|17.3|14.0|10.7| 7.3| 4.0| 0.7| -2.7| -6.0| -9.3|-12.7|-16.0|
Iago|17|77|38.0|34.7|31.3|28.0|24.7|21.3|18.0|14.7|11.3| 8.0| 4.7| 1.3| -2.0| -5.3| -8.7|-12.0|-15.3|
Iago|18|78|38.7|35.3|32.0|28.7|25.3|22.0|18.7|15.3|12.0| 8.7| 5.3| 2.0| -1.3| -4.7| -8.0|-11.3|-14.7|
Iago|19|79|39.3|36.0|32.7|29.3|26.0|22.7|19.3|16.0|12.7| 9.3| 6.0| 2.7| -0.7| -4.0| -7.3|-10.7|-14.0|
Iago|20|80|40.0|36.7|33.3|30.0|26.7|23.3|20.0|16.7|13.3|10.0| 6.7| 3.3|  0.0| -3.3| -6.7|-10.0|-13.3|


text:
Is it better to try to reveal a Traitor early, or wait until later in the game?
Since a Traitor might help you, to avoid making it obvious they are a Traitor, is it better to wait to reveal them? The advantage of accusing early, is that if no White Swords are on the board, you don't get a Black Sword if you make a false accusation. You also prevent Special Cards being played by the Traitor (if they decide to reveal themselves) that can hurt everyone.
Does the strategy of when to Accuse change with the number of players? Why?

My experience is that a known but unrevealed traitor is less damaging than a revealed traitor. Moreover, an unrevealed traitor who doesn't know for certain he's been ID'd may be of some minor benefit, especially if the solo-quests are not his to lose.
An unrevealed traitor, however, can truly sabotage the single-time solo quests something fierce...
If the game is close to 12 swords, say 9+, and a quest is close it's time to gank the traitor to prevent 2 swords from flipping.

But, there is the rub. If you wait until you start getting White Swords on the board, if you aren't 100% certain who the traitor is, you flip a White Sword to a Black Sword. In a 4P game, that might result in 2 Black Swords (the Traitor can accuse on purpose incorrectly). If the Traitor has been helping, how do you know who he is? There is also the issue of allowing the traitor to gain Lancelot's Armor. If you allow that, you are in serious trouble. If you don't get your Siege Engine count up, how can you remove the Traitor from the board before he claims the armor?

Most traitor players tend to be "ineffective" in play, rather than outright saboteurs. We always shuffle with an extra loyal card, so we don't even know if we have a traitor in play. And the traitor can only accuse each player once... if he's accused everyone but himself and you, go ahead and ding him, because he's in a hurry to grab swords...

Actually, every player can only make an accusation once, period. If there is no traitor in the game (50% in 4P), since you shuffle all 8 loyalty cards and only use 4, you could end up having a net -4 Black Swords (if you wait till the end of game, and you have 4 White Swords), that is a pretty difficult deficit to overcome. If you happen to be right, and a Traitor is in the game, you can still have a net -2 Black Swords (I forget if it is flip a Black Sword if one is available, or just gain a White Sword). If you accuse early, you get to gain a White Sword even if no swords are on the board.

We generally wait until latter in the game for 2 reasons. First is the unrevealed traitor seems to be less damaging as aramis points out.
The second reason is because we normally don't meet the requirement of 6 siege engines or 6 swords until a good portion into the game.
I don't think I've ever played in a game where there were 6 siege engines and no swords on the table to answer that particular part.

It only requires 6 turns (1.5 round in 4 player), if everyone chooses to put out a siege engine. Quite easy to accomplish if you intend to accuse early.

It's fun when you know someone's a traitor, and they want to kill siege engines to keep you from pointing them out. Just keep on adding them right at the edge so they keep on it while you do useful stuff ;)


text:
Can an optimal strategy for Roll Through the Ages be created for two player games on modern hardware?
Yahtzee has been weakly solved* for single player, and uses about the same dice on average. The game is probably only slightly more complex than Yahtzee.
Can an optimal strategy for Roll Through the Ages for two players be implemented on modern hardware?
A couple of things worry me about the two player game. The two player game could technically never end, as neither player is forced to build monuments or buy developments. I am not certain that this is a problem for discovering an optimum strategy, but it could be. Another troublesome point, is that in RTtA even though you only start out rolling 3 dice, you can have you rolling as many as 7 dice per turn (as early as turn 3) instead of Yahtzee's 5 dice. This has already tripled the number of outcomes (using the bag-model described below) for the first roll of a turn.
(*Note: Given any roll of the dice, has an optimal strategy for "rerolling which dice/building which monument/buying which tech" be calculated that will maximizes your points while minimizing your losses such that you have the greatest chance of winning a game? (on current hardware))
The more I think about this problem, the less I think this community has the expertise to answer it. It is probably better suited for Math.SE, or StackOverflow.

Roll Through the Ages - (Solitaire Play)
1) Roll X Dice (x = Cities, x = 3-7)
1a) Choose dice to keep or re-roll, (skulls must be kept in the multiplayer game).
1b) Choose dice to keep or re-roll, (skulls must be kept in multiplayer game)
2) Feed Cities and resolve disasters.
3) Build Cities and/or Monuments.
4) You may buy up to 1 development.
5) Discard Goods in excess of 6.
Game ends at the end of the round when one player has 5 developments, or all monuments have been completed by at least one player. (solitaire play ends only on the 10th round).

Game Complexity
You can look at the complexity of a game it two different ways.
All possible games (game tree size), or all possible game states (state-space complexity).
From this paper about Optimizing Solitaire Yahtzee scores. You can see one of the generalizations about the game tree. The completely specified game tree is very complex.

(game tree size) = (permutations rolling 5 six sided dice) (ways of rerolling)^(2 times) (ways of choosing score line)
(game tree size) = (6^5) * (7^5)^(2) * (13!)
(game tree size) = (approx) 1.725 10^170

Trying to solve Yahtzee using this model is not feasible using modern desktop hardware. This isn't a problem, because the previous model made some assumptions that aren't true. For one, it assumes that you can distinguish between the different dice. This of course isn't the case. A roll of { 1, 1, 1, 1, 2} is exactly the same as { 2, 1, 1, 1, 1} (as well as 3 other rolls).
|Value    |Lists|Bag|Lists|
+---------+-----+---+-----+
|a,a,a,a,a|    1|  6|    6|
|a,a,a,a,b|    5| 30|  150|
|a,a,a,b,b|   10| 30|  300|
|a,a,a,b,c|   20| 60| 1200|
|a,a,b,b,c|   30| 60| 1800|
|a,a,b,c,d|   60| 60| 3600|
|a,b,c,d,e|  120|  6|  720|
+---------+-----+---+-----+
 Total          |252| 7776|
                +---+-----+

The bag model versus the list model gives us a reduction in possible dice states (from 7776 to 252) (Note: For RTtA, if you are rolling 7 dice, the bag model only has 792 (instead of 279936) initial outcomes on the first roll). Using this model does make it more difficult to calculate all the possibilities of what you can reroll. I won't go into the details (read the linked white paper if you are interested), but it reduces the game-tree size to 2.806*10^119 (51 fold decrease). This is a model of the entire game-tree, and it could be used to determine the optimal strategy from any point in a game.  A similar bag-deterministic model can be used for RTtA to reduce complexity, but this isn't really what we are trying to solve. What we are really interested in, is the state-space complexity. Jakub Pawlewicz's paper has done even more optimization to remove the number of edges (transitions) from one state (node) to another, and mentions that what would have taken 10 minutes without edge optimization only takes 30 seconds on modern hardware.

More research.

The start of the Yahtzee paper talks about prior work detailing how to maximize the score for a single player.  Do you know of any similar results for single player RttA?  It seems (from playing the games) like RttA is far more complex than Yahtzee.

@tttppp, game complexity is measured in a different way with respect to computer algorithms trying to determine an optimal strategy than the way that humans view complexity.

Yep, I can believe that.  I still think there's a correlation between the two measures of complexity though.

As an example of a game that seems more complex to humans, see "There is a game that is isomorphic to tic-tac-toe" on the wiki page for tic tac toe: http://en.wikipedia.org/wiki/Tic-tac-toe#Variations

I agree with you on two counts: I don't think weakly-solved is accurate (because the randomness can prevent a player with optimal strategy from winning), and I think your question requires probability and logic experience more than game knowledge to answer fully. (There was a question here on a different topic a while back, but with similar requirements; I'm not sure where it is now, or I'd suggest asking on that meta site to find out if your question would be a good fit there.) You might get a good answer here, but perhaps a better collection of answers elsewhere.

Are you willing to accept probabilistic pruning of subtrees?  (e.g. not exploring a subtree if you know within a certain high probability that it isn't optimal) If so, you can reduce the strategies to goal-based ones, and solve it much more quickly.

@DaveDuPlantis, for a probabilistic game, the game is "solved" if an optimal policy can be found: what move to make in every possible circumstance, to maximize your final score. Blackjack is "solved" in this way; you don't know if you'll win, but you'll know that you took the best possible choice given that you don't know what card comes next.  (Also, as a side note, the Wikipedia page is for deterministic games; Yahtzee is not deterministic.)

Are you still interested in the answer to this game?  I've computed state space complexity for many games, but am unfamiliar with this one.  If the answer is "it's small enough" are you interested in solving it?

I think you would need to know an idle strategy for single player as a baseline (potentially using a variant where you have to keep skulls) since most building games allow you to ignore the other player if you are playing well enough. This makes solo play a great baseline for how to play multiplayer.
If you don't have a good algorithm to figure that out, deciding how to handle the other player becomes much more complex.
Finally having the solo strategy solved allows you to create significantly better baselines for determining when an action would be bad. Since you would know that in single player that move would never be beneficial, you could more quickly put together heuristics for multiplayer.


text:
What are effective strategies for playing control against aggro-control?
In Magic, there's a style of deck known as "aggro-control", which plays a mixture of cheap threats and disruption (especially counterspells). Against a pure control deck, aggro-control seeks to set up quickly in the early turns and then protect its board position from sweepers and spot removal using countermagic, long enough to get an opponent to 0 life.
From a control player's perspective, this can be a difficult situation because you're on a pretty fast clock, but your normal tricks against aggro decks (like Day of Judgment on turn 4) just don't work with any degree of consistency.
What are some strategies that you can employ, either during deckbuilding or in play, to improve a control deck's performance against aggro-control?

You could try playing more spot removal (such as Condemn or Path to Exile) instead of mass removal. Typically aggro-control decks have problems if you succesfully remove their first threats. This way the control deck won't die in the early turns and will be in a good position to win the game, because it has a better late game.
The reason behind spot removal being better than mass removal in this kind of match-up is that it demands more answers: they only need a single counterspell to deal with your Day of Judgment, but they will need two if you play two Condemn. However, they'll need two answers if you play a second Day of Judgment, but usually you wont survive to your next turn if they counter the first one.

This depends greatly on what deck you are playing and in what format. One of the best ways to stop (or more like delay) a Tarmogoyf is play one of your own. It's cheap, stops his goyf, is probably bigger than his other guys and beats very well if you want him to.
A good way to get around his disruption with mass removal is cards like Pernicious Deed or Engineered Explosives which you can play any turn you think it's safe.
Since most of the aggro-control decks rely on tempo and you'll probably win in the long run, siding in cards like Daze or other cheap counterspells/removal might help you get through the tough early game and still have enough power for the late game.
Maybe you want to disrupt his hand before he gets the chance to cast what he wants (Thoughtseize and the likes)?
It all depends on your deck and what you're up against. If you want to give a more specified question we'll be able to give a better answer.

I often had good luck with cheap creature removers or delayers that are often underestimated, like unsummon, twiddle, swords to plowshares or similar.
Another card that usually makes people laugh but that can serve you well in this situation is force spike and sometimes mana short cast on the opponent at the beginning of their turn.
At times I used with some success island sanctuaries and even stasis and maybe kismets, but you need to build quite a complicate deck around them, and requires some luck to have a good combination of cards in your first draw...
What really made my aggro-control decks struggle where the quick discard+control decks. If you are forced to discard your creatures before you can put them in play on the first few turns, then you're probably doomed...

Return to Ravnica provided some new answers to this: Supreme Verdict and Abrupt Decay.


text:
Who's first in a battle in Sid Meier's Civilization: The Board Game (from 2010)?
There is a unit with 5 strength and 2 wounds. The attacker wants to use the resource ability of mathematics to finish the unit, the defender the healing effect of animal husbandry. Which effect is resolved first? According to the rules, there is no stack, so is it really just the one who cries loudest or fastest?

Question needs clarification - there are several board games named "Civilization"... "Civilization", "Advanced Civilization", and "Sid Meiers' Civilization: the Boardgame". I presume it's SMC:TB, as the referenced mechanics don't match, but there are a number of other games that people might reference as just "Civilization"... search on BGG

@aramis The civilization-board-game tag refers specifically to the FFG 2010 version

Whoever played the most recent unit has priority.
This is clarified in the Errata section of the FAQ 2.0

Battle Turns
During the “Engaging in Battle” step of combat, players
alternate taking battle turns, starting with the defender. Only the
player currently taking his battle turn can use abilities (such as
those found on tech cards or culture event cards) or play units. A
player’s battle turn consists of:

Opportunity to use an ability
Play a unit
Opportunity to use an ability
Battle turn ends

After a player plays his last unit, he does not take any more battle turns.

For the sake of the example in your question, let's call player A the player who controls the 5 strength unit and wants to use animal husbandry, and call player B the player who wants to use mathematics.
In the situation where a player A played the 5 strength unit against a 2 strength unit, killing the 2 strength unit and taking two damage, player A would be able to then use animal husbandry first, preventing the unit from dying.
Conversely, in the situation where the 5 strength unit is already out and player B plays a 2 strength unit against it which dies but deals 2 damage, player B would be able to use Mathematics first, killing the unit.

Cards with Battle abilities can only be played before or after an attack on an enemy front (or starting a new front), not during the battle.
Animal husbandry can therefore only remove wound tokens from units who've survived with some damage.  Likewise, Mathematics can only add wound tokens to units already in fronts.  All these cards are resolved before the next card is played (which will kill any units who've suffered wounds equal to their strength) or also at the 'end of the battle' which in the rules, explicitly checks again for dead/surviving units.
In the case you listed, therefore, a wound token is removed then added or added then removed, then the unit is only 'checked' later after all cards have been resolved.
This means that if you initiate the mathematics, you might put more than a unit's strength in wound markers on an enemy if you want to guard against the use of animal husbandry.
Since this particular case doesn't matter, the more general answer is this, though there is no stack, the rules say that you take turns playing cards (defender first) and also that battle abilities are played immediately before or after playing a card.  This implies that you take turns playing battle abilities, just like cards.  After your opponent plays a card and the attack is resolved, you can ask him or her to explicitly give up control to you to play a card (asking them if they are going to use any battle abilities before you declare your action).  Once you declare, it's too late to use an ability on you, since it's your control now.

So with attacker and defender switched, the unit would still survive because the death check occurs at the end of the battle?

Death check is when a card is played to a battle-front and at the end of the battle (see in the rules where it talks about putting the card under the unit stack).

This answer is incorrect given clarifications in FFG's official FAQ.  See https://boardgames.stackexchange.com/a/35430/9999


text:
Can starbases be pinned?
Typical situation: you fly into an enemy sector and pin some ships there with your ships. Now the enemy builds some starbases to pin your ship and let them be pinned so he can move his ships out of the sector (and into yours). Is this legal?

Starbases are classified as "Ships" (see page 6 of the manual), and despite their lack of a drive they work exactly like any other Ship as far as the game mechanics are concerned.  This would include being able to pin, or be pinned by, opposing Ships. (see also this response by one of the game designers to a related question)
As per page 14, the relevant rules for pinning are,

If your Ships move into a hex, or out from a hex, containing other players' or Ancient Ships, at least one Ship per each opposing Ship must stay (the Ship is said to be "pinned")...
  ...
  If you later on move or build more Ships to the hex, you may change which Ships are pinned.  The original Ships may move, as long as one Ship per each opposing Ship stays pinned.

As the rules clearly specify "Ship" without qualifying it further, they would apply to Starbases as they would any other Ship.  So yes, the move was legal.


text:
How early should I move my king in Hnefatafl?
In Hnefatafl (with these rules) the aim of the white player is to move their king to one of the corner squares. How do I know when it's safe to move the king? Are there 'signs', for example, the other player not having many pieces, or those pieces to mostly be on one side of the board?

To my knowledge, there are several reconstructions of Hnefatafl, with rules differences that impact this specific question (differing rules for king capture, differing rules for capturing against the "throne", &c.) -- could you provide a link to the particular ruleset you're using?

These are the ones that came with my board: http://www.bowdoin.edu/~dfrancis/viking/vikingApp/

In my experience (albeit with a slightly different tafl variant), a key part of white's strategy is maintaining the ability to play towards any of the corner squares.
The throne square isn't intrinsically all that much safer than any other square on the board. Initially, keeping your king near the center makes it easier to take advantage of momentary gaps in unexpected places. Moving your king is mostly about maintaining this sort of flexibility -- if there are a lot of enmeshed pieces near the center, for instance, running your king off to one side might open up the ability to both play towards the two nearest corners and cut around the jam to get to one of the far ones.


text:
In multiplayer, what happens if a player you're attacking dies before combat damage is dealt?
I can't work this one out. For example:
I declare a creature attacking one of my opponents (who's on 5 life). Before he/she declares blockers another player casts Beacon of Destruction (or similar), reducing his/her life to 0. They would then leave the game, correct?
What happens to my attacking creature, does it still attack the player who is no longer there,  or is it no longer attacking?
In a similar situation, if my opponent has a planeswalker and I attack it, if that planeswalker is destroyed or exiled before it gets to combat damage what happens with the attacking creatures?
My guess is the damage is still dealt to the player/planeswalker no longer there and therefore doesn't do anything except tap the creature, but I'm not sure about this.

Welcome to the site! I changed Lava Axe in your example to a similar Instant spell, just because Sorceries normally can't be cast at all except during your own main phase.

There are two questions already about all the details of what happens when someone dies: http://boardgames.stackexchange.com/questions/4749/in-mtg-what-happens-when-a-player-loses-in-multiplayer and http://boardgames.stackexchange.com/questions/5463/in-magic-free-for-all-multiplayer-what-happens-when-someone-dies

Players leave the game as a state based effect, the next time any player would receive priority if their life total is zero or less.

104.3b If a player’s life total is 0 or less, he or she loses the game the next time a player would receive priority. (This is a state-based action. See rule 704.)

In the above example, after you declared your creatures as attackers (and made all necessary costs associated with declaring them as attackers...usually this is is just tapping the creatures), there is a chance for all players to cast instants or use activated abilities, and one of the other players cast BoD. Everyone once again has a chance to react to BoD, but if no one does, BoD resolves, and then the active player (you) receive priority. At this point, the opponent leaves the game.
Your attacking creature remains an attacking creature until the end of your combat phase.
In a non MP game, there would be no difference. Attacking creatures remain attacking creatures until the end of the combat phase.

508.1j Each chosen creature still controlled by the active player becomes an attacking creature. It remains an attacking creature until it’s removed from combat or the combat phase ends, whichever comes first. See rule 506.4.

Damage is never dealt to nonexistent players/creatures/planeswalkers.

800.4d If combat damage would be assigned to a player who has left the game, that damage simply isn’t assigned.
510.1b An unblocked creature assigns its combat damage to the player or planeswalker it’s attacking. If it isn’t currently attacking anything (if, for example, it was attacking a planeswalker that has left the battlefield), it assigns no combat damage.
510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage.


text:
Munchkin as a two player game
Has anyone had any experience with playing Munchkin with 2 players?  If so, what variant/house rules do you play with, and how do you feel the experience compares to 3+ player Munchkin?

As well just look at the cards without playing, it's going to be much more fun.

As Matt Sheppard notes, the main problem with two-player Munchkin is that it eliminates the automatic balancing effect present with three or more players, where the weaker players can band together to pull the stronger ones down.  In normal play, this is the main effect that counteracts the otherwise fundamental unfairness of Munchkin — without it, it's quite possible for the game to quickly get so unbalanced that one of the players is almost sure to win no matter what the other does.
This can be a problem especially if one of the players is new to the game: if the experienced player plays for keeps, they're likely to leave the newbie feeling like they didn't even have a chance, whereas if they pull their punches, the game is likely to get boring because there won't any of the scheming and backstabbing that makes normal Munchkin interesting.
That said, I do think that Munchkin with two players can potentially be fun, provided that both players are a) about equally skilled, b) reasonably familiar with the game and how it's typically played, and c) aware that they're playing the game in a way it was not designed for.  In particular, it's probably a good idea for both players to be experienced enough to tell when they're in a hopeless situation, so that they can either concede the game or just play it out quickly and get on with the next round.
As for house rules, I have no real experience to share.  However, one possibility I'd strongly suggest would be going over the deck and picking out some of the most egregiously unbalanced cards like the Kneepads of Allure.  Basically, if it feels unbalanced in a multiplayer game, it's likely to be even more so with only two players.  Also, if the players are not quite perfectly matched, some kind of handicap system, such as extra starting levels, might be useful to compensate for the lack of automatic balancing.

Ps. From a game theoretical perspective, two-player Munchkin ought to be pretty dull: it's a two-player zero sum game, where the success of one player (measured as expected probability of eventually winning) is exactly the complement of that of the other.  Thus, in optimal play, there really shouldn't be any (unforced) helping or trading, or anything else that requires the consent of both players.
The reason it can still work out in practice is that real humans are not the perfectly rational, risk-neutral and infinitely patient and foresightful agents assumed in classical game theory.  Thus, in a real game it can happen that, say, both players find that trading certain items puts them both in more comfortable positions, or that one player is willing to accept a reward for helping that the other is willing to offer.
Also, the strategic elements of Munchkin are not entirely based on cooperation and trading: besides the simple process of optimizing your character build, there's quite a bit of strategy involved in deciding when to spend your one-shot cards and when to save them.  That still applies even in a two-player game.

A two-player version that my son and I came up with was pretty fun. Here are the altered rules:
OBJECTIVE: Be the first player to retire your four heroes at level 6.
SETUP: Start by separating out all the Class and Race cards. In the standard Munchkin game you will find 21. Shuffle these cards together. Next, deal 4 cards to each player. Each player places these character cards in front of him/herself on the table. These cards represent your Adventuring Troop of Heroes trudging through the Dungeons of Munchkingdom. Next, place a single D6 (six-sided) die on top of each character to represent their current level. Each hero starts at level 1. Lastly in Setup, reshuffle the remaining Class and Race cards in the Door deck, and draw 4 door cards, and 4 treasure cards per Player (not per character). Each player may distribute their 'loot' amongst their 4 heroes.
GAME PLAY: Roll the die to see who goes first, highest die wins. The first player may lay down any treasures or items below any of his 4 heroes. Note: Once a treasure has been laid to the table from your hand, it must remain with THAT hero to which it has been placed. Furthermore, a thief cannot steal a card from any allied hero pertaining to the same Adventuring Troop. A Thief can only steal from the opponent's Troop of Heroes.
Each Hero can later on be one Class and one Race as per normal rules. Furthermore, if Class or Race are lost as a result of a curse or some other reason, simply flip the card over...that hero still can be played as normal, just without the Bonuses/Penalties of the previous Race/Class.
Once the first player is ready to begin, he chooses ONE hero from his Troop (moving the Class/Race card forward slightly to show election to other player) to open the door, then flips over TWO Door cards. Both Door cards have active effects if they are monsters or curses. This means that they are resolved simultaneously. If they are two monster cards it is like the results of a Wandering Monster card as per the original rules (Running Away must be resolved from each monster by EACH hero involved in combat).
If they are both curses, they affect that single hero who busted down the door. A Wishing Ring or other item that prevents a Curse will deflect ONE of the Curses (active player chooses which Curse to be removed). The player may still 'Loot the Room' (drawing a face down Door card into your hand) or play a Monster by 'Looking for Trouble' from his hand as per normal rules, unless the Curse card specifically states the turn has ended.
If one card is beneficial (i.e. Class/Race card, Cheat card, etc.), the player may place this directly into his hand. The non-beneficial card is then resolved (i.e. fighting the monster).
If BOTH cards are both non-threatening, the player places both into his hand, and then may choose to either 'Loot the Room' or 'Look for Trouble' per normal rules.
Note: Monster Altering cards (i.e. Humungous +5) are non-threatening if drawn with a non-Monster card, and may be placed in the player's hand. But, IF drawn with a Monster, it alters THAT monster during that combat.
Also: The actual Wandering Monster card if drawn Face Up, invites your opponent to lay down ANY held Monster card in their hand!
After resolving combat with monsters per the rules below, or after 'Looting the Room', the player ends his turn by either laying down Item cards to individual heroes in his Troop (Treasure cards aquired from defeating Monsters can only be equipped directly after combat to the two heroes involved in combat...see combat rules below), or discarding them so that only 5 cards remain in his hand at the end of his turn. Every Dwarf character in his Troop allows the player to hold +1 card above the normal 5! If cards were discarded in this manner (at the end of the turn), the opponent if he has a hero with a current level less than or equal to the lowest level of all the heroes on the table, he may select ONE of the discarded cards and place it to the table below that lowest level hero (if its an item) or to his hand (if its NOT an item).
Note: Items that are unusable be a hero may still be equipped to that hero. The bonus is just not added unless conditionary requirements are met. But, heroes that are NOT a Dwarf can only equip ONE Big item, used or unused.
COMBAT: When fighting a monster, add up all the bonuses of all the Monsters and Monster Altering cards involved in combat. Unless one of the heroes involved in combat is a Warrior, the player must beat the Monster's bonuses by 1. This number is derived by adding the hero's current level, plus any bonuses (or subtracting any Penalties). If the first hero who 'Busted Down the Door' does not have sufficient Attack Points (Level + Bonuses), then he/she can ask for help. This is done by selecting ONE of his current heroes (those NOT Retired). The Opponent may even offer to help for some bargained price, with any ONE of his heroes. If someone helps in combat, their bonuses and levels are added to the first hero's. Once a hero agrees to join combat, he/she cannot back out. If for any reason the hero(s) cannot defeat a Monster(s) then each hero involved in combat must attempt to Run Away separately from EACH Monster in the combat. If a hero is unsuccessful from Running Away from any Monster, that hero must face the consequences of the Bad Stuff of THAT Monster.
The only Hero that gains Levels after defeating a Monster is the one who 'Busted Down the Door'. If for some reason another hero jumps into battle to help, then the first hero leaves. The second hero must face the Monster(s). That second hero does not get any levels if the Monster(s) are defeated, but does get all the treasures. Furthermore, a third hero cannot be asked to help.
Note: The Kneepads of Allure, or other similar Items may be used to force someone into help the wearer of the Item, OR it can be used to PREVENT your opponent from using ONE of his heroes as a helper! In either way, the hero being manipulated by the item gets a saving throw to resist. That player must roll higher than a 6, by rolling a D6 and adding THAT hero's current Level.
RETIRING: Once a hero reaches Level 6, he/she is Retired from play. Take all his Class/Race cards, and Item cards and discard them. Leave just the D6 to represent one Retired hero. Player who Retires All four Heroes in their Troop wins.
DEATH: When a hero(es) suffer Death from Bad Stuff, they lose all their stuff. The player of the dead hero(es) lays down all their cards in ther hand next to all the dead hero's items he/she had in play. All of these cards will be discarded. Prior to being discarded, the opponent gets to select ONE item to add to EACH of his active (non-Retired) heroes. These items must first be given to the lowest level heroes.
Note: this means that if both players have heroes that die in the same combat for whatever reason, one player's opponent will Loot his hero's body, while his own heroes will Loot his Opponent's dead hero's body. Dead heroes do not participate in Looting the Body.
The dead heroe's Level die (D6) remains at the same level.
SELLING ITEMS: Only ONE Level can be bought each turn by each hero in your Troop. Furthermore, Level 6 can only be attained as per normal Munchkin Rules regarding Level Ten.

this is a pretty neat adaptation to the game, I might have to try this

My friend experimented with this, but he ultimately determined it to be too much effort;

Two players are each dealt two player's worth of treasure and door cards.
Going back and forth, they take the role of each of their players, back and forth.
No trading between your own two characters

note: stealing as a Theif over-rides this

No helping in fights between your own two characters

note: the Kneepads of Allure over-rides this

No wandering monsters from your side in your fight.

The reason for the last rule is that its tempting to beef up one character, and have the other intentionally go out of their way to serve as the other players stepping stool. An interesting case that led to rule #5 was the use of a Potted Plant with a Wandering Monster card during his other character's level 8 fight.
If you try this, please leave a comment with your thoughts, and any additional rules you added.

Honestly there isn't that big a change, other than there's a lot less people trying to screw you over.  You can play Munchkin with 2 players just fine, it's just not quite as much fun.

That seems odd. Isn't the ability to ask for help important in playing (and winning) a game of Munchkin?

Jadasc: You can ask for help in a two-player game too.  You may have to bribe the other player to do it, but then, that's not exactly unusual in multiplayer games either.

My wife and I have played a lot of 2 player Munchkin rounds, and the asking for help is much rarer, and involves much higher bribes than in games with larger numbers of players, but it still happens.

My husband and I made our own rules up, with a third npc.
The npc is a co-op player that has their own turn and only helps a human player with a dice roll.

if you're asking for help in a battle (from npc) you must roll 4+ and be the lowest  level character.
if you're asking for help in a battle (from npc) and need them to play cards in hand to aid your battle (in addition to their strength with their armor, wepons etc..) you must be the lowest level character. You must also still roll and get 4+ to receive this help. (You can decide before each game if this needs just one, or individual dice rolls.)
ALL help from npc gives (at random) one treasure to npc, or 2 for 4 treasure monsters.
to gain help (from npc) to aid for adding to the monster(s) strength to defeat opponents you must be = or the lowest level character and have a dice roll of 1 or 2.
All other rules are the same, the two players cooperatively control npc and which cards are discarded/rewarded to lowest player (as the rules suggest for hand limit.)
all cards drawn and played in front of npc must be to the maximum benefits of npc as they would be by a third player.

We had a great time playing by these rules. Enjoy.

Welcome to Board an Card games. Nice first answer.

All good answers. I'd add that Munchkin Cthulu's additional rules for Cultists don't work at all in a two-player game, so skip that set if you decide to try two-player munchkin.

They can work if you go with @Droogans' suggestion to give each player two characters to play.

In my experience it's a lot less fun simply because it eliminates the "alliance" aspect of a game with lots of players. There's also the deception element of the game (tricking other players into using up all their curse/bonus cards before your turn) which doesn't happen in a two player game.
If someone has good house rules for it though, I'd love to hear them.

Surely this is a game that is just generically better for more players, rather than being mechanically unplayable for two people.
In a game with lots of random factors, it can be easy for a player to gain a quick lead through no real strategic fault of his opponent's.  This "problem" is almost completely mitigated in multi-player settings, where if one player is doing rather two well the others can gang up to keep any power imbalance contained.
If you're both of a basically cooperative mindset, then I can't think of any real reason for not playing Munchkin 2-player.  If you're more competitive, then you might want to play something with a bit less randomness involved, or where the games end quickly enough that if one player gets unbeatably far ahead, you know you'll be shuffling up and redealing quite soon.
Also, Munchkin is a kind of sort of D&D simulator - how many D&D groups have you heard of with just 2 people?  Part of the fun is getting a whole bunch of your friends over to play!

My biggest rule in two-player is: allow the players to trade levels that come from  defeating a monster, if they need help killing it. This helps with a lot of the stronger monsters in that you either try to run, or give a level to the other player for help. The level is worth a whole lot more then a shot at some treasure, so it can add a lot of incentive.

Deal in a 'phantom' 3rd player.
Play them as a normal player with the following exceptions:

Roll d6. (1-3) they are player 2.  (4-6) they are player 3.
This may make a big difference when resolving cards that specifically affect
  the player to their immediate left or right.
Determine the method to offer help or interfere with other players during the game.
Option 1:  Roll d6 at the beginning of each current players turn.
             On (1-3) offer help, on (4-6) interfere.
Option 2:  If the current player is Lvl 1-5, always offer help.
             If the current player is Lvl 6-9, always interfere.

On their turn, the phantom player must always:

Carry any items they have in hand, if possible.
Must change race and/or class each time one of these cards are drawn by them.
Never goes "looking for trouble".
Only sell items in their hand to go up a level.
Never trades with, bribes, or extorts, other players.
Never asks for help.

Out of turn, the phantom player must always:

Offer help or interfere with the current player.
Play minimal cards necessary to affect victory or defeat of the current player.

I play this with my son (7) regularly.  We play with a 'variable' rule set that includes bumping the hand to 7 cards (8) for dwarves, and allowing for slaughters by playing 'best of' games.  We also often shorten to level 6 wins.  This truly is a game where 'house rules' are encouraged.

I found these house rules.  Haven't played yet, but my wife and I are wanting to give it a try.
After shuffling the decks go through the doors and pick the first race and class and set them aside in a 3rd player’s spot.
Optional: You can also set aside the first 5 monsters from the door deck which can be added to combat if the other physical player has a wandering monster card or a rule allows legal use of the monsters and meets the 3rd player condition.
This could also be done with + to either side in combat cards.
Reshuffle the Doors and go through the treasures take out the first headgear, armor, footgear and legal hand weapons (one 2 hand or two 1 hand whichever comes first.) and set them into the 3rd player spot. reshuffle the treasure deck.
This player will be at level 3 to start the game and if elf will go up a level every time they assist in combat. Otherwise they can only go up a level by go up a level cards so the 3rd player cannot win the game.
To use the 3rd player to help yourself in combat or to hinder your opponent you must roll a munchkin D6 and achieve a roll of 4 or greater. If you use the 3rd player to defeat a monster you must roll a Munchkin D6 again and on a roll of 5 or greater you keep all the treasure, if you roll 4 or below the treasure is cut in half randomly and upgrades are added to the 3rd player anything else is discarded. (Better items, go up a level, etc)
As many 3rd players are you want can be used in the game. Or it can be determined by a random D6 roll for the total number of players in the game at the start.

That sounds interesting. Where did you find these rules?

@ConMan Looks like he found these rules here: http://majorspoilers.com/2015/01/20/munchkin-land-112-two-player-house-rules-redux/


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Playing Risk in an arbitrary graph
A Risk board represents the map of the world, or of Europe. Thus, it implies some constraints for example on the connectedness of a territory.
I would like to explore how graph theory could help your strategies, and on which measure would a change of the node number and degree change them.  Are there any variants of this game that are played on an arbitrary graph?  (Yes, I realize that it wouldn't be in the spirit of a war game at that point.)

The computer game Lux is Risk, but with a huge number of custom maps and themes.  You can also create your own maps using their map editor.
Many of the maps include additional rules, such as time-based continent values or starting positions.
If you're interested in Risk played on arbitrary graphs (nb. including directed graphs!) then I think this would be a great place to start investigating.

Here's an example of a non-planar graph, with negative re-enforcements for one of the 'continents': http://sillysoft.net/lux/maps/Nevada%20-%20Alien%20Assault

There are additional maps available for Risk. The most obvious is "Castle Risk" using just Europe. They don't substantially alter the play that much; sufficiently little that the other themed variants need other special rules to make them worth playing apart from the original world map.
That said, I've not seen any with a pure-grid topography. Not that it would be terribly hard to play it that way...
There is a variant with a regular pattern, but it's not a grid: Fleets. Fleets uses sectios of rings, in a clear pattern. It also uses a stacking limit of 1, so it has a very different feel.
I have played Fleets without the stacking limit; it turns out to be very much worse that way. Whomever gets the most territory early (a luck driven factor) wins the game as production is tightly linked to territory.


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In Ticket to Ride USA, does obtaining longest continuous path of routes highly correlate with winning?
It has in the first 15 (mostly 2-3 player) games I've played so far but I'm wondering if this is true in general. Are we missing strategies? Is this less true in 4-5 player games?
Another way of asking the question is whether certain game winning ways (which are perhaps the majority of game winning strategies/tactics) tend to produce longest continuous path (and using up all of your cars) as a by-product. These ways include:

having many 4-6 car routes (requires fewer turns to deploy cars and earns more points)
achieving long path mid game (increases chance for new tickets to mostly overlap)
avoiding a hub-and-spoke network (which traverses less territory)

Yes, obtaining longest continuous path of routes certainly does highly correlate with winning.  It's pretty simple to see why:

Multiple routes that "cooperate" by overlapping are obviously more efficient than short routes in different parts of the board that have nothing to do with each other.
Longer routes are vastly more cost-effective than short routes. A 6-length route takes you one turn to put down and earns 15 points. 6 1-length routes would take you 6 turns to put down and earn a measly 6 points.
As if the inherent advantage of playing long, complementary routes wasn't obvious enough, you even get an additional endgame bonus for having the longest continuous path!

As I suggested in my comment though, you don't have to roll over and let other players build long, efficient routes at their leisure. In my group, sabotage tactics are very common, and if someone  obviously has designs on a long, efficient chain of routes, then building obstructively, or just picking up the colours they have telegraphed they will be needing to collect, can really ruin their day.
I also mentioned what is possibly the strongest deterrent to building long, leisurely routes: the capacity for a player to speed up the end of the game by going out quickly.  The lucrative Los-Angeles-to-New-York mega-route in your hand becomes a huge liability if your opponents block a few key connections in the midwest and then play to run themselves out of trains as quickly as possible.
As such, it's not always good to have a hand of long, valuable, complementary routes at the start of the game: a couple of seemingly unambitious short routes may be enough to win the game, if you play to go out as fast as possible and are the only one to have completed all the routes in your hand.  Lumbering your opponents with big negative points can be just as good as working hard to score those points yourself: all's fair in love and trains...

I'm inclined to disagree. I'm Yet to decide whether it's worth the effort to calculate this. I'd need a sample of about 200 games assuming we're working out the correlation based on two variables. But then I'm tempted to include other variables such as number of players and number of tickets, perhaps tickets completed. Then there is the question of the board. I don't know if I could stomach 200 games of the US board. Stay tuned. I would need about 9 months to a year.

@Mohamad Quality of players would also make a difference.  A players with a strong grasp of the mechanics of the game may not need the bonus (though they'll take it if it doesn't hurt them to do so).  Weaker players may go for longest route when it's actually against their interests to do so.  I maintain that, as longest route is basically an additional reward for doing all the things you want to do anyway in Ticket to Ride USA, I'd be amazed if there wasn't some significant correlation between getting it and doing well.

What you say makes sense, but my gut instinct tells me the correlation is not as high as we think. This strategy may be self-propagating; in that, most players choose their routes to win the longest route, whereas there exists other, more efficient routes to reach destinations. I started to think about this yesterday. This week I managed to win 8 games with having the longest route only once (different opponents, on the iPad). I usually calculate the shortest number of required steps and follow that pattern, making changes as they become necessary. I'm tempted to make this a side project.

@Mohamad You could be right. It rather depends on the definition of "highly correlate" I expect!  It would certainly be fascinating to discover if Longest Route is in fact a red herring, and usually prioritising completing shorter routes is a surer route to victory. My intuition is just that the best possible path to cashing in multiple shorter routes is to have a big central backbone that takes you efficiently to lots of places... i.e. a longest route.

As the accepted answer explains in detail, "Yes" for the basic set. However, with the 1910 expansion using the "Mega" variant, the ticket mix and incentives change so much that the answer is not so obvious.
The biggest change is the 15 point bonus card for completing the largest number of tickets. Many of the additional tickets are short and overlapping East Coast routes. And the initial ticket draw is keeping at least 3 of 5, with subsequent draws keeping at least 1 of 4. So drawing tickets is a much better bet.
In the dozen or so games I've played since acquiring 1910, no one strategy has emerged as dominant, though we've seen some very impressive victories by obtaining and completing over a dozen tickets on the East Coast.


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What are some good tactics for Khet 2.0?
I recently bought Khet 2.0 and I've played it a couple of times (we used the "Classic" starting position both times). I didn't really feel like I knew what I was doing as regards tactics / strategy, mostly I seemed to be waiting for my opponent to make a mistake.
What tactics or strategy can I use to help me win?

I feel there really two things that need to focus on in Khet:

The first is overall board position. You want to create a situation where you have multiple pieces capable of attacking at any given moment, but haven't actually lined up the shot on the main pharaoh. For example, keeping two mirrors positioned on opposite sides of a target, so that when you're able to move an intermediate piece, you have a better chance at an opportunity.
The other thing I really look at is misdirection. Playing in such a way that an opponent can't determine what direction an attack is coming from is perhaps the easiest approach to this strategy, such as mixing your moves between defense, attack and a few "nonsense" moves (moving pieces that aren't part of your actually strategy in vaguely threatening positions).

There are a few articles on BoardGameGeek regarding this topic as well:

Beginning, Middle and Endame Thoughts
Opening Moves for Classic Setup

+1 for multiple attacks.  As in chess, keys to success are often forked attacks or multiple-avenue attacks that force the opponent to choose.  Keep options available.  Misdirection is nice, but note that a "nonsense" move should still accomplish something, or it's an empty threat.

(Also, in the article on Opening Moves, note that threatening the obelisk was a much stronger opening in Khet 1, as it erodes the opponent's defence.  In 2.0 this isn't the case, so concentrate more on mirrors.  It's a good article though.)


text:
What edition of Empire Builder do I have?
My family has an old edition of Empire Builder by Mayfair games, and the box I have isn't listed on Boardgame Geek's edition list.
I found an image of the box on that site. It is pre-fourth edition, as it doesn't have Mexico in it, and very little of Canada. The rulebook lists a copyright of 1982. It comes with a bunch of metal trains, the rule book is black and white, and the cards are black and white front with red 'M's on the back.

The linked picture is the first edition
The 1982 copyright suggests it may be a later printing of that edition (2nd edition was 1984)

Thank you very much! I've been curious about this for a while, and no one was answering. 50 reputation well spent.


text:
Erasable yet bold crayon for Empire Builder Games (e.g. Eurorails)?
We have kids, so we have lots of types of crayons in the house.  Everything from airline freebie to crayola.  None of them are very satisfactory for Eurorails (and related games).  Either they are too light to see or they won't erase easily.  The original factory crayons are long since gone/lost.
What crayon do people recommend for Eurorails?

Your best bet is to take the map to a map or printing shop, laminate it properly, and use overhead pens. Or to use clear laminate purchased in rolls at a home-decorating or home improvement shop.
Now, I used china markers on a couple crayon maps in the past, and even they don't erase completely cleanly from all "factory laminated" boards.
Another good option is a sheet of plexiglass or sheet vinyl and overhead pens over the map. Plexiglass sheets are available in many home repair shops. Rolled clear vinyl is available in many fabric stores (for making covers for furniture and for covering lace tablecloths). These have the advantage of being able to be washed in the sink.

Overhead pens... that would work.  I'd need to wet remove them.

On factory laminate, you use a damp sponge, in several passes. If you use a hot-application laminate, you leave the 1-2mm edge on the map, and can just rinse it in the shower. For an adhesive laminate, you need to either over-shoot the edges 2-3mm, or tape the edges, in order to assure water-resistance.

I don't think you will get a definitive answer, but probably just lots of suggestions. There has been.discussion about this question before on BGG. You are going to get a range of answers:

Crayola Washable Crayons.
China Markers.
Dry Erase Markers
Wet Erase Markers.
Standard Crayola Crayons

I found Crayola brand washable crayons to work the best. For the lack of boldness I subbed brown for yellow, purple for orange. I bought both Empire Builder and Empire Express straight from Mayfair but got different crayons with each. Express came with no-name crayons that leave a slight stain on the board.

Highly recommend China markers (Like these).  Just be sure to test them first.  I had a yellow one once that wouldn't entirely erase.

From BGG, one user reports that Crayola Washable Markers work well.


text:
A game for two. Should I make it playable by more?
I am developing a strategy game for two players. It is something
somehow in the line of 1960: The Making of the
President
(but less complicated and with a quicker gaming rhythm…) Both the theme
and the mechanics I have thought are optimised for two players.
Adapting the theme should not be very difficult ; it would mostly be a
matter of choosing another contestant. Adapting the rules would
require substantially more work and I fear that it might lessen
playability.
Do you think that it is worth doing it that restricting
the number of players to exactly two is not too restrictive?

Both TimothyAWiseman and thesunneverset anwser are relevantand raise more or less the same argument. They were posted aproximately at the same time.
I had to select one and chose Tim's because he presently has a much smaller reputation. Thanks to you both.

It depends, probably not at first.  Most truly enduring games (Chess, Go, Reversi, even Magic: The gathering, etc) were originally for two players.  But also most of them have variants that arose later that allow 4 players.
In short, if adapting for more than 2 players is non-obvious, then it is probably not worth the initial effort.  But if the game becomes popular and there is a demand for a multiplayer version, then it is likely worth doing at that point.  The changes could be fairly small, or they could be substantial (Magic required only small tweaks to produce multiple multiplayer variants, but most multiplayer versions of chess require a different board and rules tweaks.)

A lot of people WANT a game for two players, and I can see a game that is obviously optimised for two as having a valuable USP all of its own.
As an example of a popular existing game for two, I offer to you Reiner Knizia's "Lost Cities" (though he did in fact create another game later using a similar central mechanic for larger numbers of players).  With a bit of work you can adapt this for 3-4, but you have to buy an extra set to do so!  Even so, it's a really popular game for couples and people without regular access to large gaming groups.  I'm sure your game could be successful on similar terms too - if it's any good of course!


text:
Is there an official way to speed up Elixir?
We've been playing a bit of the excellent (and silly) Elixir, but we often end up with long periods of inactivity. When players are unable to cast spells, we have several rounds where all players draw their card and then pass, since they don't have the right ingredients. This can go on for some time.
We've tried doubling the draw rate so players pick up more ingredients - this seems to work, but might unbalance some of the "draw X cards" magic items.
Is this a problem others have encountered? Are there any official or well-tested solutions - do any of the expansions (which we haven't tried) address this problem?

Yes, others have encountered this problem. At least one poster on BGG (Tim, it isn't you, is it?), posted that the game drags and proposed a Draw 2 Variant.
No, there is no official variant to my knowledge. No variants are listed in the rule books for Elixir or any of it's three expansions. No variants are listed on the designers websites.
I am not sure precisely how your Draw 2 cards/finds is a better solution to just drawing 1 card and passing. You only pass half as often (since you are drawing 2), but how long does it take to Draw 1 and Pass in the first place? How much time are you actually saving?

Heh, no, it's not me. But I did think about registering to reply to that post ;)

The purpose of draw-two isn't necessarily to speed up the game time, it's to speed up the time between any player actions (to prevent players getting bored with the constant passing)- if players pick more cards each turn, they are be more likely to be able to cast a spell, or will be able to participate in (or start) transactions more often. However, even draw-two still has long pauses.


text:
Do you need spare actions available to play Throne Room?
The rule book explains Throne Room's effect as follows:

You pick another Action card in your hand, play it, and play it again. The second use of the Action card doesn't use up any extra Actions you have.

My question is:
If I played Witch with Throne Room, according to the rules, the second use of Witch doesn't use up another action, doesn't that mean the first use of Witch cost an action?
So in essence, whenever you play Throne Room, wouldn't you need to first play cards that give you additional actions?

Throne Room costs an Action to play; the card you play twice is part of the effect of Throne Room, and neither play of it consumes an Action.
My speculation is that that particular wording was in answer to a complaint encountered during development, something like: "Village gave you two actions, but you just played that Witch two times with Throne Room, so you have no actions left." That's a mistaken understanding of the way Actions work, of course, but everyone was a novice back then.
Other cards that include allowing you to play other Actions as part of the effect include King's Court (from Prosperity), Cultist, and Procession (both from Dark Ages).

I really don't know why the rules emphasize the second play of the other action; it really reads to me like it's implying that the first one does cost you an action. Seems like they could've just said something like "Playing the chosen Action does not cost actions; it's part of playing the Throne Room."

I agree. Notice that when the rulebook writers had a second chance in writing the similar card King's Court, they did it better: "This does not use up any extra Actions you were allowed to play due to cards like Worker's Village - King's Court itself uses up one Action and that is it."

Note that because Throne Room is all one single action, playing Throne Room on anything giving +Actions will net you more Actions than simply playing that card twice would. So playing TR on a Village would leave you with +2 cards and +4 actions, while merely playing 2 Villages from your hand would leave you with only +2 cards and +3 actions. And TR on a +1 Card/+1 Action cantrip might be the only way to pull off a +2 Action effect in some Kingdoms...

None of them cost an action, the only action cost here is playing the Throne Room itself.


text:
Correlation between a destination ticket's point value and the leastnumber of train cars it would take to fulfill it
I've been making my own new destination ticket for Ticket to Ride America. I noticed that for most of the destination tickets that come with the game, the point value is equal to the least number of train cards you would need to fulfill it (basically the distance between them). But then I found 2 tickets in the game that don't follow this rule:

Sault Ste. Marie - Oklahoma City 9 points
Sault Ste. Marie - Nashville 8 points

If this rule were followed, those point values should be flipped.

Is this an 'error' in the destination tickets, or was it done purposefully? I've looked at the difficultly to fulfill them and haven't found any significant reason for this.
When creating my own destination tickets, how should I set the point value? Should it always be the shortest distance between them, or should I account other factors, like availability of routes needed to complete them? If so, what other factors should I look for and how should I react to them when deciding the point value?

I understand that this is a really specific and nit-picky question that no one who actually had a life would care about, but I'm still very curious as to your opinions. :D

You should treat each possible route between two cities as wire with resistance equal to its weight. Then calculate the effective resistance between the two cities on the destination ticket. Simple! Although you should also introduce a factor reducing the resistance for gray routes.

Was it a misprint?
It appears that the minimum number of trains required to complete a destination ticket was only the starting point for assigning each ticket a point value. The claim is made  (in this post by Days of Wonder Forums user "Caboose")  that Alan Moon (the game's designer) said the ticket values were not supposed to be the shortest route between two cities. Lacking the context that this may have been said in, I believe the intent was to put to rest worries that some ticket values were mistakes or misprints, rather than to deny all connection between tickets' values and their minimum lengths. (This post by Caboose from several years earlier shows (s)he had previously believed the issue was due to a misprint.)
Additionally, if the changes made in the 1910 expansion were to "fix" the tickets to match their minimum lengths, they didn't fix all of them. It's been pointed out  (in this post by Days of Wonder Forums user "DiscJet")  that the Los Angeles to Chicago ticket and the 1910 expansion's Las Vegas to Miami ticket are each worth more than their shortest length.
Most likely, Mr. Moon increased values for certain tickets to give a slight additional incentive to choose them (especially given the different mix of tickets that would be used in 1910). Was it to balance out a disadvantage of these tickets, or to slightly change gameplay with a small advantage to certain routes? I wouldn't have a clue. However, I doubt it was a misprint.
How should custom tickets be valued?
The majority of tickets should be valued at the minimum number of trains required to complete them. Then think through what your goal is for adding those tickets. Do you want to create more competition for certain cities? encourage more cross-country routes? discourage the use of 5- and 6-train sections? Once you've clarified that goal, you might adjust a few custom tickets' value up by one point (maybe two) based on play-testing or your anticipation of the results.
In general, adding a small number of destination tickets, even with tweaked
values, isn't going to have a very large effect. If you've played with the Mystery Train routes (but still without the other cards available in the 1910 expansion), that would probably give you a good idea of how much of an effect your changes would have on the game.
Attribution Note: The first section is partially an adaptation from my answer to the question "TTR: Destination ticket value changes in the America 1910 expansion". I don't have access to my copy of Ticket to Ride and the 1910 expansion at the moment, so I can't verify the route lengths or values myself.

Sault Ste. Marie to Nashville is right.  You can get there in 8.
Sault Ste. Marie - Oklahoma City 9 points is probably an error.  The value for this ticket is 8 in the 1910 expansion.

I'd say stick with the shortest distance when setting the value for your own tickets.


text:
Is there a site to solve tsumego online?
I'd like to solve tsumego online, not having to install a program or app locally. Are there any sites that allow this? How about for smartphones?

GoProblems
http://www.goproblems.com/
The traditional problem site. Has many user contributed problems. Personally I'm not too fond of it, since the problems often vary in style getting me out of the problem solving flow.

+1 - Goproblems is a useful site with a large number of problems, also it allows you to both filter problems by type, or follow paths of related problem sets if you want to work only tesuji, only ladder problems, etc.

There is no app for android, is there?

There's SmartGo for the iPad/iPhone, but none that I know of for Android.  If there is enough demand SmartGo might be willing to do a port there.

I would love to see SmartGo ported to Android.  But in the meantime there is a good set of go problems on the Android market called "Magic Baduk Go".

While I do appreciate the efforts and concept of the website. The way problems are selected and presented is too chaotic for me. When solving problems in books there is a consistency in the problems that lacks on this website. For me this ruins it.

GoChild
http://gochild2009.appspot.com/
Currently my favorite. Has several large collections of problems. I like it for mass solving relatively simple problem.
First you need to login with a google account. Then choose a collection on the right. And finally you need to switch to the Question or Progress tab on the right to solve problems.

maybe better split it in 2 answers?

I feel stupid, I can't seem to figure out how that site works. How do I actually attempt to solve something? Do I have to log in first?

You do seem to have to log in first, that is a bit confusing.

GoGrinder
There is a cheap app for PC and mobile called GoGrinder. (see also)
From my experience as well as what I heard from others it's a useful piece of software at a very reasonable price.