Keeping your bankroll safe while growing it as quickly as possible – a common problem for sports bettors. Determining the proper bet size to maximize returns while minimizing the risk of ruin is crucial. There is a relatively simple way to utilize a complex mathematical formula to arrive at those bet sizes.
The Kelly Criterion is a formula that describes a way to maximize the long-term growth of repeated bets that have positive expected value, while limiting risk of ruin.
Risk of Ruin
Risk of ruin is quantifiable, and measures the probability that a bettor with an edge (positive expectation) will go broke by making bets of various sizes with certain odds. Risk of ruin is always a number between 0 and 1, and is often expressed as a percentage. A small risk of ruin is the safe approach. Risk of ruin can be reduced by 1) increasing bankroll, 2) decreasing bet sizes, or 3) improving odds (becoming better at handicapping or shopping for better lines, for example).
Technically, the Kelly Criterion has a zero risk of ruin, since the formula never allows a gambler to risk 100% of their bankroll on any given bet. In the real world, however, there is no way to have the infinitely large bankroll or the infinitely small bets that guarantee a true zero risk. Realistically, a bettor on a bad streak would reach a point where the criterion-suggested bet is below the book’s minimum bet.
The purpose of this article is not to dissect the mathematics behind the Kelly Criterion. Suffice it to say that long-term growth is maximized by finding the fraction of the bankroll that reaches the maximum of the logarithm of the results. Readers interested in the mathematical abstracts of the formula can find plenty of information about J.L. Kelly Jr.’s work.
For most gamblers, understanding a simple method of applying a sound mathematical basis to bet sizing without complicated calculations is in order.
The Kelly Criterion in Practical Usage
The simplest expression of the Kelly formula is:
f= bp -q
where f = the fraction of the bankroll to risk
b = the odds “to 1” offered
p = the probability of a win
q = the probability of a loss
Let’s take a simple example of a football sides bettor with a $10,000 bankroll who picks 53% winners (remember that you must win approximately 52.4% of sides when laying 11-10 just to break even). Here, b = 0.909 (10/11 odds), p = 0.53 and q = 0.47. Putting the numbers into the formula, we get f = ((0.909 * 0.53) – 0.47)/0.909 = 0.012, or 1.2%. This bettor’s ideal bet size is 1.2% of $10,000, or $120. In practical usage, this would mean wagering $110 to win $100.
Let’s take it a step further, and examine a baseball money line bet. If the LA Dodgers are +140, and the bettor is 50% confident that they will win the game, the bettor should risk f = ((1.4 * 0.50) – 0.50)/1.4 = 0.1428 = 14.28% of bankroll, or $1428.
Use of the formula can tell a handicapper when to avoid a bet, too. If the baseball money line bettor in the example above was only 40% confident of a Dodgers win, but was considering the bet anyway because of the odds, a check of the formula reveals f = ((1.4 * 0.40) – 0.60)/1.4 = a negative number, indicating the bet should be avoided.
If Kelly Criterion application reveals a result f that is very close to zero, it suggests that the odds offered are not sufficient to give any significant amount of expected value to the bet, and the bet should probably be avoided.
It should be noted that the Kelly Criterion is volatile. One-third of the time, the system will result in a loss of half the bankroll before it is doubled. Some bettors trade a certain amount of rate of return for less volatility by using a “Half Kelly” system, betting one-half the amount recommended.