AbigailII:and you are right Abigail ... but luckily we are humans and we play human created games ...and  99 percent of those games are not perfectly balanced ... and you know what ? thanks God ... this is why we also created tournaments and matches and every player has a chance to play as player A ... look at Horde Chess , Maharaja Chess, Reversi, Gomoku, Halma, Checkers, Chess and about any possible game ... first player has an advantage and if not, Lady Luck  shows her teeth (backbgammon and the whole family plus card games) ... do you quit playing ? no, you enjoy them despite all these flaws ...
Cheers,
Andy.