how much to bet - Game Theory question

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.