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Author Topic: Times when the Big Money test is less helpful  (Read 1779 times)

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jotheonah

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Times when the Big Money test is less helpful
« on: December 11, 2011, 08:32:15 pm »
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Today I tried to play Big Money on iso (partly for fun and partly because I wanted the BOM achievement). Anyway, it was 3-player and Tribute was on the board and as a result the player to my right (I think) could pretty much guarantee his Tribute would net him $4 (later on, 2 draw and $2). He won by a lot.

I was thinking about how whenever we talk about simulators to test Combos we use Big Money as a benchmark - Does it beat big money? But if Tribute beats big money it doesn't mean Tribute is good, it just means Tribute is good specifically against Big Money. Other cards might be the same way -Jester? Masquerade?

I was just sort of wondering what y'all simulator buffs thought about that sort of conceptual problem.
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hobo386

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Re: Times when the Big Money test is less helpful
« Reply #1 on: December 11, 2011, 08:45:30 pm »
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Short answer: Yes, you are right.

Long answer: There are very few cards that are only good against big money, except things like Pirate Ship/Thief/Noble Brigand.  And they are all pretty obvious.  The more important thing to look for is cards that aren't particularly great with big money, but are good elsewhere (like chapel).
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DG

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Re: Times when the Big Money test is less helpful
« Reply #2 on: December 11, 2011, 09:18:06 pm »
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It doesn't take much to beat pure money. A single moat with treasure beats pure money. The money benchmark is only mentioned for the benefit of beginners who put together poor action decks that can't beat a strategy that's available for every kingdom.
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Davio

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Re: Times when the Big Money test is less helpful
« Reply #3 on: December 12, 2011, 04:10:39 am »
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Well, this is the problem with simulations in general. Every robot just plays his own strategy without concerning himself with the opponent. In real life, this is of course very foolish.

But expanding the simulations with adaptive AI properties is next to impossible because of the inherent randomness. Chess has no random elements at all. A computer can calculate every move White would like to make and every move Black could make, rate the board position after each move and decide whether the move is good or bad.

If there was an accurate way to rate Dominion decks (see the forums for an attempt), a computer would still have to calculate several hundreds or maybe thousands of playthroughs for every decision. And this number increases really fast. If we start with a $5/$2 start and there are only $2 cards in the kingdom (no Young Witch or Black Market or Hinterlands-pre-shuffle-activation cards), a player can do 16 things with $5: Buy a Duchy/Estate/Curse, Silver/Coppper, any of 10 Kingdom cards or buy nothing. With his $2 he can still do 14 things. So that's 16*14 = 224 possible opening moves. Then there's the shuffling. With anywhere from 10 to 12 cards, there are already hundreds of shuffling probabilities. And for each of those shuffles, a computer would continue branching, buy nothing or something and shuffle again at the end of the deck. Even with pruning (not pursuing unfruitful branches), this takes immense calculation power.

So you have to take any simulation with a grain of salt and they work best (closes to their results) if there is no or little interaction with your opponents.

Also, don't be afraid to move on from the simulation: You could have bought a Tribute yourself and if it gives you at least $2 every time (direct or via drawn cards), it's already better than Silver! Would you have bought a Festival if it was available? Well, not if you wanted the achievement, but you catch my drift.
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DStu

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Re: Times when the Big Money test is less helpful
« Reply #4 on: December 12, 2011, 04:45:04 am »
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If there was an accurate way to rate Dominion decks (see the forums for an attempt), a computer would still have to calculate several hundreds or maybe thousands of playthroughs for every decision. And this number increases really fast. If we start with a $5/$2 start and there are only $2 cards in the kingdom (no Young Witch or Black Market or Hinterlands-pre-shuffle-activation cards), a player can do 16 things with $5: Buy a Duchy/Estate/Curse, Silver/Coppper, any of 10 Kingdom cards or buy nothing. With his $2 he can still do 14 things. So that's 16*14 = 224 possible opening moves. Then there's the shuffling. With anywhere from 10 to 12 cards, there are already hundreds of shuffling probabilities. And for each of those shuffles, a computer would continue branching, buy nothing or something and shuffle again at the end of the deck. Even with pruning (not pursuing unfruitful branches), this takes immense calculation power.

I would not be so pessimistic, or better would think that "rating the deck" would indeed have to deal with all this, and find a way to give some simple numbers to include all these possiblities. It's not so much different from chess. In chess, you also can't compute the game to its end, but have to stop at some point and take a heuristic on "how good" the game state is. And in chess you also have lots of possibilities, a free Queen in the middle of the board can move to 27 positions.
A human player also does not rate the state of Dominion by thinking about all possible outcomes. But you rate your deck and your choices by some heuristics, like "importance" of a card, and "collision probabilites" (for good: Village-Smithy, or bad Smithy-Smithy). And you don't think that you have a 27.4% prob that you will draw 5-4-2 the nex tshuffle, and a 19.0% prob to draw 6-3-3 etc. But you will think about somethink like: "Ok, the next few turns, I should be able to buy a $5 card or a Gold, when I'm lucky it will be two, and 2 or 1 cards for $4--."
I'm not an expert of chess, but in Dominion I think the problem for a good rating is that there are lots of important variants how the deck in the end looks like, and so it's really difficult to rate how good a rate is at the moment. I guess in chess there is no strategy where it is really a good idea to sacrifice the Queen and two Bishops for nothing, but Dominion decks look really different.
There are lots of combos which rely on just two cards, and even don't want something different, like NV/Bridge, HP/Baron, lots of BM-trick but even if you exclude these, engines are build in very different ways, depending on which Village, which draw, even which +buy is on the board, if there are alternative VPs, if there is Workshop/Ironwork/HoP/Quarry/Talisman, which attacks threaten the engine, or want to be mixed into it...?  And all these engines want to be built differently, and it's very difficult to find a single (or two or three) metrics that describe which buy is "good" for these engine in a given situation.

I think the randomness is not a great problem if you would solve that. Draw 100 samples per decision and that's it, to get a bot that plays as fast as a human you could even affort 10.000. That's more than enough to get a good approximation. You maybe will not look as far in the future as you can in chess, but in both cases you can't look until the end of the game, and the important part is to have a good heuristics there to rate the state of the game.
« Last Edit: December 12, 2011, 08:09:38 am by DStu »
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Davio

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Re: Times when the Big Money test is less helpful
« Reply #5 on: December 12, 2011, 05:48:53 am »
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Those heuristics may be the most difficult part indeed.

Still I think it's easier in Chess, because the results become clear somewhat sooner. If a Queen sacrifice isn't paying off until at least 10 moves later, there's a big chance it won't pay off at all.

It would be a big challenge to actually build a competitive AI player. This would be an enormous feat with a preset kingdom, let alone with random cards. The relative value of cards doesn't help for this. A Queens is always a good piece (and valued at about 9, Pawns are 1, Rooks are 5 etc..), but a Bureaucrat is almost always worthless except for those niche kingdoms.
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hobo386

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Re: Times when the Big Money test is less helpful
« Reply #6 on: December 12, 2011, 08:07:44 am »
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but a Bureaucrat is almost always worthless except for those niche kingdoms.

Offtopic, but those are much more common than you'd think, especially considering the resurgence of BM engines and an abundance of alternate victory cards.  Great hall and nobles especially, but also cards like island, harem, and tunnel.  Not to mention that bureaucrat is fairly strong in a gardens war (adds cards, adds money, makes opponent wait an extra turn till reshuffle).
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