Consider a Dominion game where the only cards are Copper, Silver, Gold, Estate, Duchy, Province and Mine, i.e. the only action card is Mine.
Is there an obvious optimal strategy/strategies in this simplified game?
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4I suppose that a question this specific is unlikely to help others in future, as this is not a situation that comes up naturally during a game.– tsuma534Feb 24, 2016 at 6:09
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6How is this primarily opinion-based? It's a specific question about strategy in a specific scenario in a specific game. Good answers would provide a good strategy and explain why it's good (even if it's not provably optimal). tsuma534's right that it's a bit of an artificial situation, but that doesn't make it opinion-based.– CascabelFeb 24, 2016 at 14:51
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3I agree that it's not opinion-based, but I'm not sure what a good answer could look like. It seems like a trivial solution; unless his real question is "how many Mines should you buy"? There's very little room to improve or change up a strategy.– GendoIkariFeb 24, 2016 at 15:38
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2@GendoIkari Yes, how many Mines you should buy (and when) is part of the question. It's asking about the whole strategy, not just what to do with a Mine in your hand.– CascabelFeb 24, 2016 at 16:17
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2@tsuma534 I think the answers do actually look useful to future readers. It's an artificial situation, but it's also a pretty good initial stab at how you should approach Mine even if there are other cards available, and in general, how you should approach terminal action cards.– CascabelFeb 25, 2016 at 12:49
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4 Answers
Using the Dominiate Online Simulator I simulated a few Mine and money strategies in two player games against Big Money. The best strategy I could find was to play Big Money, but buy a Mine in preference to Silver if there is enough money. The simulator upgrades Silvers to Gold rather than Coppers to Silvers if there's a choice (the Dominion Strategy Guide agrees with this decision here).
I tested varying the number of Mines to aim for and simulated 1000 games against Big Money. Here are the results:
1 Mine: 59.1% wins
2 Mines: 56.3% wins
3 Mines: 53.1% wins
4 Mines: 49.7% wins
After the first Mine, additional Mines hinder your deck, as you start to draw two terminal actions in some hands. This is backed up by Matt Sargent's investigation where he tried to find the optimal number of various different single cards in 'Single Action plus Big Money' decks.
If you want to try simulating this yourself, here's the strategy I was using:
{
name: 'One Mine and Money'
author: 'tttppp'
requires: ['Mine']
gainPriority: (state, my) -> [
"Province" if my.getTotalMoney() > 18
"Duchy" if state.gainsToEndGame() <= 4
"Estate" if state.gainsToEndGame() <= 2
"Gold"
"Duchy" if state.gainsToEndGame() <= 6
"Mine" if my.countInDeck("Mine") < 1
"Silver"
]
}
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Did you ever try gaining a single Mine over Gold (when you happen to hit $6 before ever having hit $5)? It looks like it hurts the strategy a bit in my tests, but your script is a little different. Feb 24, 2016 at 19:10
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@GendoIkari I didn't try Mine over Gold, but I did try Mine over the second Duchy entry. This made things slightly worse. I had marginal improvements by changing the first Duchy entry line to "Duchy" if state.gainsToEndGame() <= 5, but I didn't think it was significant enough to justify the deviation from Big Money. I tried varying a few other things too, but everything else made things worse.– tttpppFeb 24, 2016 at 19:24
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1One thing about mines is that when you draw them (if you can play them), they are effectively 1 copper. Yes that make your future draws better, but for that turn they are only a copper, so eventually a silver in place of a mine is better. Feb 24, 2016 at 20:16
The best way to answer this type of question is using simulations. There are 2 Dominion simulators available: here and here.
Using Dominate, I ran some simulations of different options; here's what I found:
Buying 1 Mine is slightly better than buying 2 Mines. Very slightly; wins about 54% of the time.
Buying 1 Mine when you could afford Gold is slightly worse that buying 1 Mine only if you couldn't afford Gold. (Loses 55% of the time.)
Here's the script that I used in the simulator:
# 1 Mine
{
name: 'SingleMine'
author: 'Gendo'
requires: ['Mine']
gainPriority: (state, my) -> [
"Province" if my.countInDeck("Gold") > 0
"Duchy" if state.gainsToEndGame() <= 5
"Estate" if state.gainsToEndGame() <= 2
"Gold"
"Mine" if my.countInDeck("Mine") < 1
"Silver"
]
}
The Big Money part of it probably isn't completely optimized, but it was copied from other Big Money scripts. But I kept everything the same except the Mine gaining.
answered Feb 24, 2016 at 19:08
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4+1 I tried our strategies against each other, and they're so similar that I managed to hit 500 wins apiece from 1000 games!– tttpppFeb 24, 2016 at 19:30
If your only action card is mine, there's not much you can do; just buy your first Mine as soon as possible to upgrade your treasures and maybe get at most a second one later on. But, otherwise, you have no other choice than just buying treasures, Gold or Silver. Still, this is not a situation you would normally encounter.
The ideal state is probably that you draw one mine per turn. Any extras are wasted, and any turns without a mine are less efficient than ones that had one. What that means in terms of when you should buy another one would probably be best solved by a computer simulation where you try it different ways and see what gets you the best final score.
