If given the cost to play, and the average win. Can I calculate the edge? (probability of winning)
How do I calculate gambling edge using average win?
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1I don't think this question is appropriate for this site. – 2010-08-16
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1Indeed it might get better answers at http://stats.stackexchange.com/ – 2010-08-16
1 Answers
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:
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.