Turn advantage is a term describing an advantage for a player based on turn order. If the game ends on the first player's turn, they will have taken one turn extra, conferring an advantage. This effect results in the first player winning roughly 58% of high-level two-player games.
Shortly after the release of the base game, Dominion creator Donald X. stated in 2008 that there is no such thing as first-turn advantage, save for the possibility of the first player getting one more turn than the other(s), and that there were no tiebreakers that would solve any problems:
Getting an extra turn is definitely an advantage. But going first is only an advantage if you get that turn. If you go first but don't get an extra turn, a tiebreaker going to the other guy amounts to just randomly stealing a deserved tie from you. You didn't play worse, you just randomly went first. A tiebreaker there doesn't solve the problem of an advantage due to going first (and does nothing for cases with no tie); it just randomly awards victories in some cases where there was no such advantage. It's the same as flipping a coin.
I know some people will find this hard to see. "But he had the advantage of going first!" Going first is only potentially an advantage. If you don't get the turn, it's not an advantage. At the start of the game, you want to go first, because who knows, you could get that extra turn, but at the end, we know whether you got it or not, and there's no prize for not getting it. Say we're walking to a bar when you spy a lottery ticket on the pavement. Huzzah! We get to the bar and each buy a round of drinks. There's a TV at the bar and they show the winning numbers. Aw, your ticket was a loser. Well, one last round of drinks before we leave. Someone says, you should buy this round, because you had that losing lottery ticket. Does that seem fair? That is not what fairness is.
The existing tiebreaker does not break most ties. It does however break all ties that can be broken fairly, without warping strategy. If you require a tiebreaker at all costs - i.e. even when it's unfair or warps the game - then that's up to you. There's nothing I like there.Where going first is really significant is where it gets you an extra turn that you win the game with. It doesn't matter what tiebreaker rule you have there; it isn't invoked. The rules address this case by having the winner go last next game. My friends and I always play a bunch of times in a row, so that's always seemed fine by us. The bias we've noticed is, the better player wins more often. Despite going last! It's perplexing.