I have a very simple probabilistic process which I have to deal with in the software project I'm involved in, yet I can't figure how to do it. I can describe the situation as a money game (in reality it is not, but this is the most simple way to go):
At each moment $t$ my program gets a probability value $P_t$ on input. I have to output the stake $X_t$ ($X_t$ can be, say, from 0 to 10) and then with probability $P_t$ I will win (get $XA$, where $A > 1$) and with probability ($1 - P_t$) I will lose (get nothing, lose my stake $X$).
What strategy can be considered reasonable here? Make stake proportional to $P$? What should I read to understand the topic?