How do I calculate gambling edge using average win? If given the cost to play, and the average win.  Can I calculate the edge? (probability of winning)
 A: It should intuitively feel like it's not (theoretically) possible -- the cost to play and the average win are determined by a bookie (or a casino, etc.), whereas the probability of winning is determined by the game itself.  Given two games, one with a probability of winning $p_1$ and the other with a probability of winning $p_2$, the bookie can adjust the returns on bets so as the cost of play and average win remain constant.  For example:


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*Consider a tossing coin game, the player bets $1$ dollar, if the coin is "heads" it will return $2$ dollars and if "tales" then there is no return.  So the expected win is $+1-1=0$.

*Now consider a die rolling game, where the player bets $1$ dollar, if the die rolls 6, then 6 dollars are returned, otherwise there is no return.  Here the expected win is $+5-1-1-1-1-1=0$.
In both cases the cost to play is $1$ dollar and in both cases the expected win is $0$, but the probability of winning is different ($1/2$ vs. $1/6$).
In practice, however, you might be able to infer an approximate probability of winning based on past experiences of the bookie, familiarity with the game being played, etc.
