Amount to bet - Game theory

Suppose there is a hand with a positive expected vaulue of 50%- eg, for every $10 bet, you are expected to come away with $15. This scenario is distributed such that there is a 1/6 chance that you will lose $5 and 5/6 chance that you will win $10. Your hand will always be called, and this situation is constatnly repeated. So the next hand you will be in exactly the same situation (this is a hypothetical game theory question, not neccecarily a straightforward poker question). Assuming you have finite funds ($100 for arguement's sake), how much money does the bayes nash equilibrium state that you should invest in the hand, as a proportion of your funds, considering that if you invest all of it there is a 1/6*1/6 likelihood of total loss and elimination. This would probably be best thought of in the context of a tournament.

[danderso8]

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Suppose there is a hand with a positive expected vaulue of 50%- eg, for every $10 bet, you are expected to come away with $15. This scenario is distributed such that there is a 1/6 chance that you will lose $5 and 5/6 chance that you will win $10.

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First off, your question is poorly formed, cause these two sentences contradict one another.

Second, I don't think we are interested in doing your homework for you.

--dan

I'm sorry, that was a typo. I meant a 2/6 probability of a loss of $5 and 4/6 probability of a gain of $10. Second, this isn't homework. It directly correlates to poker and finance theory.
However, perhaps a better example of this situation would be the following: suppose you have $m and the minimum bet increment is $b, but you can bet up to 100% of your bankroll (m) if you want. If your probability of winning is p and the prize for winning is w (so ev of p(w), which is assumed to be >0, how much is correct, from a game theory standpoint, to bet over an infinite period of time assuming that when you go broke you cannot bet again. This is a math question, not a personal opinion question. Is there an equation for bankroll managment that satisfies this system?