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?
Board & Card Games Stack Exchange is a question and answer site for people who like playing board games, designing board games or modifying the rules of existing board games. It only takes a minute to sign up.
Sign up to join this communityConsider 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?
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"
]
}
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.
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.