It really is a crapshoot 3

Well it didn’t look like anybody wanted to join the fun.

The 2-player game introduced in the first post of this series is relatively simple. You and your opponent both know that the coin lands heads up 55 percent of the time. If you both keep calling heads nobody will win. If you know your opponent will call heads you can call tails for the first round and then stop. You will have a 45% chance of winning compared to no chance of winning if you keep calling heads.

The 20-player game described in the second post of this series is much more interesting. If the other 19 players all consistently call heads, calling tails makes a lot of sense. Suppose the stake is $1. You expect to lose 11 games out of 20 so for these you’re going to be $11 down. However, you’ll win back $19 for each game that you win so you can expect to be $160 up over 20 games. However, if that $1 represents everything you’ve got, there is a 55% chance that you’ll get wiped out before you can start winning.

Things get much more complicated if the other players become less conservative and are prepared to bet on the less probable outcome. Knowledge is power in this game. Knowing exactly how biased the coin is and what your opponents are going to do will either lead you to a winning strategy or persuade you that this is a game that cannot be won.

Are you sure that you want to be a tosser?