Optimal Dominion strategy with only the Mine action card
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) -&gt; [
        "Province" if my.getTotalMoney() &gt; 18
        "Duchy" if state.gainsToEndGame() &lt;= 4
        "Estate" if state.gainsToEndGame() &lt;= 2
        "Gold"
        "Duchy" if state.gainsToEndGame() &lt;= 6
        "Mine" if my.countInDeck("Mine") &lt; 1
        "Silver"
    ]
}