Question: How is Russion Roulette played? Do you do it until either you or your opponent is dead, or do you just spin once and if you don't die you win? If it's the latter, I'd go with that. I'm confident that I probably have a more than even chance at winning with chess, but it's hard to beat 5/6 odds of winning.
Depending on the exact rules, I might also want to pick tic-tac-toe or Connect Four (if I could start), because I'd have to be pretty stupid to lose that. Otherwise I'd probably take chess. I'm nothing special at it, but I used to be better than the rest of my school as a kid.