# Up to how much would one pay to play this game? 30 red and 30 blue marbles

There are 30 red marbles and 30 blue marbles. Your opponent may arrange these marbles in any way he/she chooses into 2 urns. You then pick one of these 2 urns. You get 10 dollars if you draw red and 0 dollars if you draw blue. How much would you be willing to pay to play this game?

• How much you would be willing to bet is far too subjective. You might want to simplify your question to "what is the probability of winning?" – Ataraxia Jul 28 '13 at 0:19
• This a recurring convention in this sort of problem that you would be willing to pay up to the expected value of the game. – MJD Jul 28 '13 at 0:24
• @MJD Didn't know that, thanks for the info. – Ataraxia Jul 28 '13 at 0:26

Assuming your opponent is trying to minimize your expected value, you should be willing to pay about $\$2.54$. Your opponent should place one blue marble in one urn, and the rest of the marbles in the other urn. This leaves you with a$15/59$chance of winning the game, which makes your expected value$\$10\cdot 15/59=150/59$, which is a bit over $\$2.54\$.