Matt Sargent
United States Portland Oregon

Is Dominion a solvable game? The answer is clearly no. But what about subsets of Dominion? Don't certain combinations of kingdom cards have a pretty clear best strategy? Let's see what people think about a set of kingdom cards that everyone has played: the recommended "first game" set.
EDIT: by "solvable" I mean what Guy suggests downthread. The set is solvable if the ideal player tends to buy similar cards every game. (chess) The set is not solvable if the strategy employed by the ideal player varies wildly depending on her opponents' actions. (rockpaperscissors)
And yes, your answer may vary depending on how many players you are considering are playing, but just pick the poll option that feels most right to you.

John Anderson
United States Moorhead Minnesota

Can you clarify your definition of solvable in the context of Dominion? Usually the term is reserved for games where luck literally doesn't exist, like chess, go, connect four, etc. In that context, "solving" a game means discovering a method of winning every time. I don't know if that would be possible in any set of Dominion, as there are crazy fringe strategy that could flop 90% of the time, but in that other 10% could dominate your otherwise superior strategy.

Guy Srinivasan
United States Kirkland Washington

Erm... are we assuming the answer is the same for 2, 3, and 4 players? Seems like a terrible assumption in general.
Edit: also in general the best strategy buys different cards depending on how the first few turns play out for each player, and might well depend on seat position... the poll seems to be asking "can the set of winning strategies in the basic set be boiled down to 'no matter what, try to buy this combination of cards' and if so what is the combination?".

Guy Srinivasan
United States Kirkland Washington

puck71 wrote: Can you clarify your definition of solvable in the context of Dominion? Usually the term is reserved for games where luck literally doesn't exist, like chess, go, connect four, etc. In that context, "solving" a game means discovering a method of winning every time. I don't know if that would be possible in any set of Dominion, as there are crazy fringe strategy that could flop 90% of the time, but in that other 10% could dominate your otherwise superior strategy. "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning.
A strategy which is virtually guaranteed to lose 90% of the time is thus nowhere near optimal, even if it "dominates" the other 10%.

John Anderson
United States Moorhead Minnesota

GreedyAlgorithm wrote: "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning. By that definition, doesn't there then have to be a solution? Even if it's nearly impossible to determine, for every set of 10 there must be one strategy that's statistically better than every other.

Guy Srinivasan
United States Kirkland Washington

puck71 wrote: GreedyAlgorithm wrote: "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning. By that definition, doesn't there then have to be a solution? Even if it's nearly impossible to determine, for every set of 10 there must be one strategy that's statistically better than every other. Yes, there does have to be a solution. Which is why the only coherent interpretation of the poll I can come up with is "do all of the solutions share components such that they all look like 'buy this card and 2 of that and all of that' rather than 'in this circumstance, buy this sequence of cards, in that circumstance, buy this completely unrelated sequence of cards'".

Sean McCarthy
United States Seattle Washington

puck71 wrote: GreedyAlgorithm wrote: "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning. By that definition, doesn't there then have to be a solution? Even if it's nearly impossible to determine, for every set of 10 there must be one strategy that's statistically better than every other.
Yes. Though keep in mind that having a solution doesn't necessarily mean it's solvable in a practical sense, which is how I would interpret the question. Chess, for example, theoretically has a solution, but we're not about to find it. My guess is yeah, the first set is solvable, but I don't think it's a given.

Sean McCarthy
United States Seattle Washington

Quote: 3. Assuming there is a solution to the firstgame set, which cards will most likely be bought by someone playing the perfect strategy?
Snarky observation: I think you might end up Remodeling a copper into a Moat, but I don't think you'd buy one, which is what the question asked.

Chris Ferejohn
United States Mountain View California
Pitying fools as hard as I can...

puck71 wrote: GreedyAlgorithm wrote: "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning. By that definition, doesn't there then have to be a solution? Even if it's nearly impossible to determine, for every set of 10 there must be one strategy that's statistically better than every other.
Except that's going to shift based on what other people are doing when attack cards are involved...

Matt Sargent
United States Portland Oregon

I suppose that when I think of an unsolvable game, I think of RockPaperScissors, in which winning depends on the predictability of your opponents, rather than a mechanical solution. I think that letting people use their own definition of solvable while answering the poll could give us information on whether people's definition of solvable coincides, at least if we assume that one we know what solvable means it is easy to determine if Dominion meets those criteria. It's certainly easier on the person making the poll not to have to define solvable.
EDIT: actually I like Guy's definition, so I've added it to the OP.

Erik Henry
United States Houston Texas

Interesting  but maybe not surprising  that so many different cards are getting votes.
To those who answered that they have solved or are close to solving this set, it would be interesting to hear your answers to the third question (if you're willing to share, and maybe after people have had a chance to vote on their own). I'm wondering whether you've each come up with the same answer....

John Anderson
United States Moorhead Minnesota

cferejohn wrote: puck71 wrote: GreedyAlgorithm wrote: "Solving" for games with luck means finding the strategy(ies) (possibly mixed) which yield the highest probability of winning. By that definition, doesn't there then have to be a solution? Even if it's nearly impossible to determine, for every set of 10 there must be one strategy that's statistically better than every other. Except that's going to shift based on what other people are doing when attack cards are involved... There still has to be a single strategy that will be statistically better than all others, including strategies that involve attacking, etc. That doesn't mean it will always win, but it will win a higher percentage of games than any other strategy.

Paul W
United States Eugene Oregon

puck71 wrote: There still has to be a single strategy that will be statistically better than all others, including strategies that involve attacking, etc. That doesn't mean it will always win, but it will win a higher percentage of games than any other strategy.
I think part of the problem is that "strategy" is illdefined here. The OP suggests that chess is solvable because the ideal player would play the same moves every game. That's actually not true. The ideal player would play the exact same set of moves *contingent on the opponent's moves*. There isn't a single move order in chess that you're going to play while completely ignoring the opponent's response: the solution to chess is rather a huge table of conditional moves. So if the definition of solvable is "you always play the same way every game without responding to your opponent's actions", then chess isn't solvable either. I'd submit, however, that that's a pretty poor definition of "solvable".
Similarly, if your question is whether there's a set of actions that will dominant regardless of your opponent's actions, the answer is probably not (though it's plausible in games where the cards allow minimal player interaction). Rather, the dominant strategy will be some table of actions conditioned on both your opponent's actions and your knowledge of the state of your deck.



Eh, every game is solvable. I think solvable in this context should mean "solvable in a reasonable amount of time during a game", which is still vague but a decent general guideline.
If the best strategy was always smithybot every time Smithy was out, I'd call the game solvable. If I had some sort of strategy tier like:
1. Chapel + lab 2. Witch + throne room 3. Workshop + gardens 4. Smithybot 5. Big money
and I could just go down the list to pick the topranked one that was out, with say 20 strategies, then I'd call the game solvable.
If attacks and other kingdom cards that are out create a lot of ifs, but the first three strategies are always dominant (except against each other), then I'd probably call the game solvable... with a but.
Beyond that, I don't know.

Brad Weage
United States Atlanta Georgia

I too would be much more comfortable with the third question if it was worded more like "what kingdom cards are most likely to end up in the winning deck"  as opposed to which get "bought". But that may be just as big a distortion. You not only want to know what the final deck manifest is (including nonkingdoms), but you need a picture of when each type is getting added. It is likely that, based on an overview of good strategies, that "buying a province" is a more consitent part of a win than any one of the ten kingdoms.
I would also agree that the best strategy must shift based on how many players are involved, and shift if attack cards are involved. But I would go further and say, even without attack cards, the best strategy changes depending on what the other players are doing. If you are in a 4player game, and two players are pursuing a specific strategy (and look likely to continue doing so) the lineofattack that may give you the best chance of winning may not be anything like the best general strategy. Even in something as simple as TicTacToe, if you are playing against a bad player, you increase your chance to win if you play "wrong". For Dominion, I don't see that there must be a "single best strategy" that is statistically better than all others. There might be a very complex tree that defines the best move to make at every point, taking into account everything every other player has done, and what cards you have in hand and have already seen/positioned/discarded. But that seems like a rather complex concept to which to apply a "highlevel" term like "strategy" or even "a line of play".
Of course we could define some parameters for our solution. I could decide to ignore the other players entirely. I might select a rule like "can never buy more than 4 of a specific kingdom" and pick a goal criterion based on how many hands I get, how early on, that allow me to spend 8 gold at once. If you narrow it down like that  then the solution for most any set of 10 morebasic kingdom cards (there are a few kingdoms with behaviors that are more difficult to model) is well within the computing power and programming ability of most home computers and many competent home programmers. Each time you perform a virtual shuffle, you just keep track of every possible deck order. This is simplified by the duplicates, though you have to weight each ordering by how often the equivalent ones occur. Each time you get to buy, buy every possible card  creating a new branch for each one. You don't even need to program it to play the hand well  just have it try every possible order for playing the cards.
Given that every time you add a card to your deck, that it is from a set of less than 20 choices  and deciding that you can set a cutoff of some kind for overall number of turns (essentially arbitrarily deciding that a path is too slow to be effective)  this turns out to be solvable in a pretty short time. This basically would tell you how "fast" is each sequence of card additions (possibly subtractions) for a given set of 10 kingdoms. You would probably find many of the best sequences to be quite "playable" in a real game  if they eventually depend on 4 of any specific kingdom then they either depend on buying those early enough that you can get that share of them during actual play, or they are tolerant enough to allow you to buy some of those earlier than projected if others are buying them as well.
This, in a limited sense, is solvable. Does it give you the best strategy? Obviously, not. It wouldn't take into account any path involving more than 4 of a given kingdom. It doesn't take into account the idea that victory cards are limited  and a game can be decided by who acquired that last province. It would give you a reasonable measure of how "efficient' is a specific deck makeup, and by comparing different ways to arrive there, what is the better order to acquire those cards. Although I am convinced that some players might play better with this information (after all, I know people buying duchies and dukes who don't yet know they always want three more duchies than dukes) I do think it might reduce the fun and lead to more boring games.

Randy Miranda
United States Chicago Illinois

okay, enough theoretical crap.
here' a suggested way of playing:
using the recommended first set, with 3/4 i'll open workshop/remodel, then proceed to get all the villages i can, by buying, remodeling, or workshopping. if i have a hand with only coins and remodel, i'll make a moat. after, they're gone, buy smithies on 4 or workshop for smithy. 5, market. 6 or 7, gold. 3, silver. make sure to get cellars on a bad draw or if you have a plus buy (from the markets). make sure to pick up one militia. when you got a decent engine running, cellar all the coins, in order to pull out all your villages, smithies and markets, so you'll draw you're entire deck. when you have a healthy lead, buy remodels, and remodel your gold and provinces into more provinces to end the game.
have fun!

Jonathan Morton
Sweden Vällingby Stockholm

fungamebob wrote: here' a suggested way of playing: ...
Are you suggesting this as a starting point to be refined, or as an optimal strategy?
PS, what's up with bogus play recording?

Dave Goldthorpe
United Kingdom

I don't think there can be a solution as such. I'd suggest that any strategy which takes you down the same lines with a 2525 draw as a 3434 draw is unlikely to work.

Randy Miranda
United States Chicago Illinois

Jonny5 wrote: fungamebob wrote: here' a suggested way of playing: ... Are you suggesting this as a starting point to be refined, or as an optimal strategy? PS, what's up with bogus play recording?
for 3 or 4 players and that opening split, it's a pretty sexy starting point.
as for bogus play recording,
it's an estimate, smart guy. i counted bsw, too. i update it whenever i feel like it, not whenever i play. darf!

Jonathan Morton
Sweden Vällingby Stockholm

Darf indeed!
I don't record my BSW plays on BGG because BSW records them for me on BSW, and I don't see those plays as the same thing as playing a game face to face. But you're right, man darf record his plays however he likes.



noon wrote: I suppose that when I think of an unsolvable game, I think of RockPaperScissors, in which winning depends on the predictability of your opponents, rather than a mechanical solution. I think that letting people use their own definition of solvable while answering the poll could give us information on whether people's definition of solvable coincides, at least if we assume that one we know what solvable means it is easy to determine if Dominion meets those criteria. It's certainly easier on the person making the poll not to have to define solvable. EDIT: actually I like Guy's definition, so I've added it to the OP. I don't think you understand what "strategy" or "solvable" means in this context. I don't want to nitpick on rhetorics but when asking a technical question like this it is vital because otherwise we are just polling people on their defintions of "solvable" or "strategy" instead of the actual question. At any rate neither is very interesting because mathemetics already have clear definitions/answer for these.
And according to Guy's definition of solvable, there would be a solution to Dominion. Note that a solution could be buy these given situation A, buy these given situation B, etc. If you go into Puerto Rico thinking either to employ a shipping strategy if X, or building strategy if Y, that is one strategy. By definition, everyone plays a game with one strategy.

Jeff Chamberlain
United States Tracy California

Only 19 people think the game is solvable, but 21 of them think village is part of the solution?

David desJardins
United States Burlingame California

Games like Dominion generally do not have a solution. E.g., a common scenario (and one that can't be excluded here) is that if two out of three players pursue an attackoriented strategy, then one of those attacking players is likely to win, but if two out of three pursue a nonattacking strategy, then one of those nonattacking players is likely to win. In that case, you can't say that either the attacking or nonattacking strategy is betterit depends on what the other players do. If both other players decide to attack, then your nonattacking strategy will work poorly. But if they both decide not to attack, then your attacking strategy will work poorly.

Matt Hoffman
United States St. Paul Minnesota

DaviddesJ wrote: Games like Dominion generally do not have a solution. E.g., a common scenario (and one that can't be excluded here) is that if two out of three players pursue an attackoriented strategy, then one of those attacking players is likely to win, but if two out of three pursue a nonattacking strategy, then one of those nonattacking players is likely to win. In that case, you can't say that either the attacking or nonattacking strategy is betterit depends on what the other players do. If both other players decide to attack, then your nonattacking strategy will work poorly. But if they both decide not to attack, then your attacking strategy will work poorly.
Ha! Once I saw this thread title, I knew The Dominion Thread Buzzkiller would be on the scene.



DaviddesJ wrote: If both other players decide to attack, then your nonattacking strategy will work poorly. But if they both decide not to attack, then your attacking strategy will work poorly.
Doesn't that really depend on the nature of the attack? If they decide to attack with something like Bureaucrat, you can be at an advantage if you thin out your initial estates and delay your province buys. If they use deckcycling attacks like Thief or Minion, a highvariance "drawing" deck can be a winner. However, if they are ganging up on you with Witch, Sea Hag, Ambassador, etc. you will be in a world of hurt unless you get creative with the defense.


