This topic was one that i took to heart and did some minor data analysis of. The thread
http://forum.dominionstrategy.com/index.php?topic=54.msg723#msg723Basic gist of it, since i'm really bad at talking about what data i'm presenting really means, is that the p1 win rate is .53 IF both players have an even number of turns, and .65 if they get the extra turn. .55 games end with an uneven number of turns. Strong attack cards such as Mountebank do not affect those numbers by much at all. I didn't check militia and will probably do that right quick (The thought being that the first 3 turns are more important than the ones thereafter, and that mountebank is usually not bought on turn 1-2, where militia is)
The net of that would be that the 1st player advantage is a real thing, amounting to around a 7% delta in winning percentage. Of course, most people know that already. What is more surprising is that the power cards don't seem to amplify that win percentage.
(Although now that i look at the raw data, it seems that i have a little bit of noise included and will have to revise numbers somewhat)
Militia data:
1p win %: .529
Uneven game %: .502
Uneven game 1p win %: .669
Moral of the story: militia (being a strong attack that can always be opened with) Only slightly amplifies(if at all, .02 is a small number) 1p win percentage in games w/ uneven # of turns.
#games: 98470
#games 2p wins: 46301
#games 1p wins: 52169
#games uneven turns: 49486
#games uneven turns 1p wins: 33139
#games uneven turns 2p wins: 16347
#games even turns: 48984
#games even turns 1p wins: 19030
#games even turns 2p wins: 29954
***this data is from a rather old tarball of rrenaud pointed me to, and doesn't include even cornucopia cards. It's dated Jun 17 11.