Here is yet another puzzle based on
Suppose that there is a game as follows
* There is a host with 10 stamps, 5 red and 5 blue. There are 4 players- A, B, C, and D.
* In the beginning, the host affixes two stamps to each of the 4 players' head. The choice of stamps for each player is completely random (i.e. the host puts all stamps into an opaque bag and then draws them one by one). The remaining 2 stamps go into the host's pocket. Each player can see the stamps on the remaining 3 players, but can not see his own stamps nor the two in the host's pocket.
* Starting from A to D (and then looping back to A and so on), the host asks if each player definitively knows his color (RR, BB, or RB). If the player does not know, the host goes on to the next player. First player to know his color wins. No guessing is allowed.
Suppose that the host likes you, so he secretly offers you a side bet before the game. You have to pay the host 1
dollar before the game starts, and then you can choose whether to be A, B, C, or D. The payout by position if you win is as follows
A: 3.5 dollars
B: 2.5 dollars
C: 6 dollars
D: 7 dollars
Which position should you choose for the greatest expected winnings?