Thursday, February 25, 2010

Even-Equivalent Probability of Ruin

Epstein (2009) provides a detailed, mathematical analysis of the risk of ruin within the broader context of the basic theorems of gambling. Without loss of generality, it is worth providing a layman’s interpretation of how the probability of ruin impacts the choices made by the average handicapper.
In the classic treatment of ruin, there is a working assumption of unit bets at even-money in order to make the calculation of the risk of ruin more tractable. To avail ourselves of this analytical solution, we need to transform our real-world bets into their even-money equivalents, see Krigman (1999).

For example, if you are in the fortunate position outlined above with a 42% strike rate at an average price of 2.50 then your advantage is the equivalent of having a win probability of 52.02% at 2.00 with both the same expected value and standard deviation (0.25, 6.169) as the original bet and with a probability of ruin equal to 24.07%. Obviously, it is also possible to estimate stake size given a specific price and preferred risk of ruin.