

The Three Hats Game - joosters
http://www.futilitycloset.com/2015/02/17/the-three-hats-game/

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ainiriand
The optimal strategy to maximize the odds is this: -Spoiler-

There has to be at least one guy that sees 2 hats of the same colour. This guy
has to speak and say that his hat is a different color. This maximizes the
odds of winning over 50%.

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area51
This doesn't make sense to me.

See below chart -- The probability that my hat is M/O is the same (50%)
regardless of what the others are wearing.

Others Me

MM M

MM O

MO M

MO O

OM M

OM O

OO M

OO O

~~~
bazzargh
Yes, and when each player says a colour, they're still only right 50% of the
time. But the strategy means the cases where you'd be wrong are the same cases
that others would also vote incorrectly, but the cases where you're right, the
others pass, so you win.

    
    
        MMM O    O     O     Lose
        MMO Pass Pass  O     Win
        MOM Pass O     Pass  Win
        MOO M    Pass  Pass  Win
        OMM O    Pass  Pass  Win
        OMO Pass M     Pass  Win
        OOM Pass Pass  M     Win
        OOO M    M     M     Lose

~~~
joosters
That's a great way of explaining it, thanks!

I had read the solution but it still didn't make sense in my head how seeing
the colour of unrelated hats could somehow improve the chance of you
predicting your own hat colour. But as you explain, no one individual guess is
better than 50%, it's just that the wrong guesses get lumped together.

