#556965
I think some people are getting a bit hung up on the "perfectly equal decks/player" thing, which is- as has been stated numerous times- a hypothetical that we can't really locate concretely in the real world. This is why I rephrased it as, "How much better does Player 2 need to perform to win?" This way we're not looking at "exactly equal" decks, but instead looking at varying degrees of difference of performance. Of course, "performance" is quite a wobbly term, so maybe this still isn't useful enough.
I think if we wanted to catalog the first player advantage as concretely as possible, my suggestion would be to track the following data:
1. What percent of games does the first player win? (It may seem obvious, but it has some hidden problems too.)
2. Of the games where the second player wins, how did the decks rank overall in the tournament? (Even better data would be, how did the decks rank overall in the tournament if you exclude that game?)
The first question is flawed because, as has been pointed out, when there is a significant enough difference in performance, turn order won't matter as much, so assuming a random match up of deck qualities, only a fraction of the games' outcomes will be decided by first-turn advantage. However, the exact size of that fraction is of interest.
The second question gets at, "How much better does player 2 need to be to win on the second turn?" If we look at overall tournament standings, this gives us a general idea about the relative quality of the decks... but these are obviously impacted by the game in which Player 2 beat Player 1. This is why it would be useful to exclude the game in question.
But, to be honest, how much does this part matter? I mean, do we need to statistically prove that the 1st Player advantage is significant enough to warrant a rules change before local-variant playtesting begins to test solutions? Or would it be best to start testing out proposed solutions and see if they really do make games/tournaments more fair?
(P.S. I saw somewhere the line, "How different is a dice roll from a 1-6 random personnel selection?" The difference is, the player chooses the away team that goes into the attempt, and their opponent chooses to seed a dilemma that has a random selection. There is agency in that situation. There is no agency in a die roll.)