Simulated odds for the first player surviving a game of russian
roulette, when each round lasts until one player dies and then a new
round begins with same player going first. (Unless, of course, the
first player died, but we are only interested in their survival so it
makes no difference.)
Only the first player spins on each round
2 players (first spins): 50099 wins out of 100000 -> 0.50099
3 players (first spins): 33368 wins out of 100000 -> 0.33368
4 players (first spins): 22332 wins out of 100000 -> 0.22332
5 players (first spins): 14878 wins out of 100000 -> 0.14878
6 players (first spins): 12357 wins out of 100000 -> 0.12357
7 players (first spins): 10183 wins out of 100000 -> 0.10183
8 players (first spins): 8483 wins out of 100000 -> 0.08483
9 players (first spins): 7217 wins out of 100000 -> 0.07217
10 players (first spins): 5981 wins out of 100000 -> 0.05981
Every player spins before firing
2 players (each spins): 45294 wins out of 100000 -> 0.45294
3 players (each spins): 27724 wins out of 100000 -> 0.27724
4 players (each spins): 18781 wins out of 100000 -> 0.18781
5 players (each spins): 13291 wins out of 100000 -> 0.13291
6 players (each spins): 10104 wins out of 100000 -> 0.10104
7 players (each spins): 7713 wins out of 100000 -> 0.07713
8 players (each spins): 6112 wins out of 100000 -> 0.06112
9 players (each spins): 4853 wins out of 100000 -> 0.04853
10 players (each spins): 3848 wins out of 100000 -> 0.03848