Maximize expected utility, not expected money. If utility is linear in money, you should put all money on best option. If utility is logarithm of money, you should distribute proportional to probability. In the show (or its version in Russia, in any case), you can only put money on 3 out of 4 options, which means that you should put money proportional to probabilities of the 3 best options (assuming utility is log-money).
Maximize expected utility, not expected money. If utility is linear in money, you should put all money on best option. If utility is logarithm of money, you should distribute proportional to probability. In the show (or its version in Russia, in any case), you can only put money on 3 out of 4 options, which means that you should put money proportional to probabilities of the 3 best options (assuming utility is log-money).