When several players cooperate under uncertainty, the key is not always to talk more, but to agree in advance who should speak and who should remain silent.
Ebert's hats
Riddle statement
Three players randomly and independently receive a red or blue hat. Each can see the other two's hats, but not their own.
Before starting, you can agree on a plan. Then, all at once, each person must do exactly one of these three things: say “red”, say “blue” or be silent.
The group wins if these two conditions are met:
- at least one of the three says a color;
- No one who speaks is wrong about the color of their own hat.
What is the highest probability of success that can be guaranteed?