Hat problem

[Joaz Banbeck]

I just added the above post to the 'best of L19' thread.

[mitsun]

MINE WORKS???

Joaz, sorry to burst your bubble, but your "solution" scores 1/16

[cyclops]

4 bridge players are at a table. The tournament director offers them the following proposition:
.........bullets........more bullets.............

After too many casualties the next tournament director is a nicer guy. He offers the following proposition. If at least one guess is right and no guess is wrong they get €100 otherwise they pay a fine. The tournament director prepares the set of 4 hats that will be distributed randomly over the players. All other rules are the same as before. ( to be sure: no one gets shot What fine makes this a fair proposition? Does it make a difference if dummy is excluded from the experiment and only a set of 3 hats is prepared?

I have no idea of the answer but in the second case I include my trivial observation:

The tournament director of course chooses hats of the same color to defeat the solution of original problem. oops, but then the players anticipate on that