In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put them on the table in front of them. Then each player looks at the coins tossed by his left and right neighbours. If the neighbours tossed different faces of the coin (one obverse and one reverse), the player in the middle survives for the next turn. Otherwise, if the neighbours both tossed the same face of the coin (both obverse or both reverse), the game is lost for the player sitting in between them.
After everybody knows who's continuing to the next turn, the losers pick up their coins and leave the table.
The game is won when there is exactly one player left sitting at the table, who will be the winner and grab the lucky $10 bonus.
If all players are eliminated at the same time, the game is a tie and nobody gets the bonus. If there are only two players left, since left and right neighbours will be the same opponent, the players will necessarily eliminate each other at the next turn.
You are offered a chance to play this game and grab the lucky $10 bonus. You can choose to play in a game starting with 10, 11, or 12 players including yourself.
What would you choose and why?
If the lucky $10 bonus sounds boring, replace it with 10 rep points or whatever you find worth playing for.