Evens-Equivalent Trades

Risk of Ruin (RoR) (Epstein 2009) provides an easily understood metric (probability of bankroll depletion before doubling it) with which to compare strategies. By way of illustration, let us assume that both you and your brother are recreational handicappers. You trade baseball, home-underdogs and he trades horse-racing, second-favorites, as follows:

Sport	Bank	Trades	Avg. Odds	Avg. Win Rate	Avg. Stake	Evens Odds	Evens Win Rate	Evens Stake	Expect. Value	Std. Dev.	EV.SD	Edge	Rsk Of Ruin
MLB	5,000	500	2.10	51.00%	250.00	2.00	53.37%	263.05	17.75	262.45	219	7.10%	7.11%
H-R	2,500	1,000	3.50	31.00%	100.00	2.00	52.62%	162.10	8.50	161.87	363	8.50%	16.53%

In the classic treatment of ruin, there is a working assumption of even-money trades to make the calculations tractable. To that end, we must first transform our real-world trades into their even-money equivalents with the same edge and volatility, see Krigman (1999). Despite having a smaller edge and a larger stake, you have a lower probability of depletion than your brother principally because you are risking a lower percentage of your bankroll per trade. Ideally, your RoR should be below 5% and to achieve this you both would have to either increase your bankroll or decrease your stake, as follows. [(MLB: 5%, 218.20 or 5730); (H-R: 5%, 54.97 or 4,546)].



Note that Edge's impact only equates with that of Volatility after 219 trades for you and 363 trades for your brother. And it takes a minimum of 806 trades for you and 1336 trades for your brother before you can be at least 95% confident that the combined effects of positive edge and mixed-bag volatility work in your favor to guarantee positive bankroll growth. In other words, despite having potentially successful trading strategies, you both will be well into your second season of handicapping before you can be sure of beginning to reap the benefits!

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.