What color hat am I wearing?
... random thoughts , logic , math
tue 2005-may-10 15:07:22 pdt
The 3-player game
As in the 2-player game, three players sit around a table, and each
can see the other players' hats but not her own. Each player may then
write down a guess, "red" or "blue", but this time they have the
option to instead write "no guess". As before, all players must write
down their guess (or lack thereof) without knowing what the other
players have written. The guesses are then revealed and:
if everyone wrote "no guess", they get nothing;
if at least one person made a guess and was wrong, they get
if at least one person made a guess, and everyone who made a guess
was right, then they all get a million dollars.
As always, they agree on strategy in advance but cannot communicate
once the game begins. This time we will assume each hat color is
selected uniformly at random. One simple strategy would be to decide
that no matter what, player 1 will guess "red" and players 2 and 3
will write "no guess"; this gives a 1/2 chance of winning. Can you do
better than 1/2? Can you guarantee a win?
No, you cannot guarantee a win.
(likelihood of winning with an optimal
strategy, and a hint)
Please do NOT post solutions in the comments below. Thanks.