First Player Advantage

I wrote a program that simulates 100 sets of 10,000 2, 3, and 4 player games of Dominion including only provinces, duchys, estates, gold, silver, copper, and curses.

Each player in these games used identical strategies (buy provinces when you can, only buy duchies if the provinces supply is <= 7, buy estates only if the province supply is <= 2 else buy the greater of gold or silver if you can. Never buy copper or curses)

In a 2 player game Dominion Game, using identical strategies:
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player 1 will win ~49.18% of the games (±1.16% with 99% confidence)
player 2 will win ~40.77% of the games (±0.99% with 99% confidence)
player 1 and 2 will tie ~10.04% of the games (±0.37% with 99% confidence)

In a 3 player game Dominion Game, using identical strategies:
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player 1 will win ~34.77% of the games (±1.27% with 99% confidence)
player 2 will win ~27.77% of the games (±1.17% with 99% confidence)
player 3 will win ~24.41% of the games (±1.14% with 99% confidence)
player 1 and 2 will tie ~3.28% of the games (±0.53% with 99% confidence)
player 1 and 3 will tie ~1.60% of the games (±0.35% with 99% confidence)
player 2 and 3 will tie ~1.92% of the games (±0.41% with 99% confidence)
player 1, 2, and 3 will tie ~1.12% of the games (±0.27% with 99% confidence)

In a 4 player game Dominion Game, using identical strategies:
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player 1 will win ~25.44% of the games (±1.13% with 99% confidence)
player 2 will win ~21.08% of the games (±1.10% with 99% confidence)
player 3 will win ~18.26% of the games (±1.13% with 99% confidence)
player 4 will win ~17.41% of the games (±1.03% with 99% confidence)
player 1 and 2 will tie ~2.83% of the games (±0.47% with 99% confidence)
player 1 and 3 will tie ~1.65% of the games (±0.31% with 99% confidence)
player 2 and 3 will tie ~1.90% of the games (±0.33% with 99% confidence)
player 1 and 4 will tie ~0.90% of the games (±0.26% with 99% confidence)
player 2 and 4 will tie ~0.97% of the games (±0.33% with 99% confidence)
player 3 and 4 will tie ~1.20% of the games (±0.25% with 99% confidence)
player 1, 2 and 3 will tie ~0.47% of the games (±0.19% with 99% confidence)
player 1, 2 and 4 will tie ~0.13% of the games (±0.14% with 99% confidence)
player 1, 3 and 4 will tie ~0.13% of the games (±0.15% with 99% confidence)
player 2, 3 and 4 will tie ~0.23% of the games (±0.16% with 99% confidence)
player 1, 2, 3 and 4 will tie ~0.22% of the games (±0.16% with 99% confidence)


My conclusion:

Unless you are playing multiple games with the winner of the
prior game going last in each successive game, the first player
to play has a distinct advantage.

Now, the fun with numbers part:

In a 2 player game: if ties were removed, and a tied game always went to the player who played last:
player 1 will win ~49.18% of the games (±1.16% with 99% confidence)
player 2 will win ~50.82% of the games (±1.16% with 99% confidence)

In a 3 player game: if ties were removed, and a tied game always went to the player who played last:
player 1 will win ~34.77% of the games (±1.27% with 99% confidence)
player 2 will win ~32.75% of the games (±1.25% with 99% confidence)
player 3 will win ~31.21% of the games (±1.17% with 99% confidence)

In a 4 player game: if ties were removed, and a tied game always went to the player who played last:
player 1 will win ~24.32% of the games (±1.13% with 99% confidence)
player 2 will win ~25.48% of the games (±1.16% with 99% confidence)
player 3 will win ~24.25% of the games (±1.23% with 99% confidence)
player 4 will win ~23.70% of the games (±1.16% with 99% confidence)

Perhaps this would be a good house rule to implement if you tend to play only one game at a time.

My next step: determine the best strategies for the game. (ha ha)