Using the Kelly Criterion

The Kelly Criterion is a mathematical guide devised for people who bet with their brains more than their gut. Essentially, this money management principle helps punters spread bets to improve their chances of winning over time.

complex maths

Kelly isn't this hard

It is a (comparatively) basic numbers system that tells you how much of your money to stake to maximize the growth rate of your wealth, while ultimately controlling your exposure to risk.

The Criterion was published in 1956 by John Kelly, a worker at AT&T’s Bell Laboratory, in order to solve a problem unrelated to gambling. Soon the betting industry got wind of it and realised its potential all kinds of risk judgements.

In the context of football betting Kelly’s formula helps mathematical punters calculate how much they should stake on bets from their bankroll, based on their past success rate and the odds of future bets.

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The process can be summed up in three steps:

•    Multiply the odds of the match by the probability of you winning based on how well you’ve done in the past.

•    Minus the probability of losing from the number obtained in the first step.

•    Take the number obtained in the second step and divide by the odds.

It helps if you have already built up a log of previous bets (at least 25) with which you can do the calculations. A good punter’s winning ratio will vary between 50-60 per cent, although 60 per cent is unlikely for almost all but very lucky betters.

Let’s say you have a good track record of 56 per cent wins and that the odds are 0.91. Multiplying the two gives you .509. Your chances of losing are 44 per cent so subtract .440 from .509, leaving .069. Divide this figure by the odds (0.91) and you get .075.

Expressed as a percentage that’s 7.5 per cent, which is how much of your bankroll Kelly followers argue you should stake on your bet. Because your winning average changes every time you win or lose you should recalculate with every new bet and stake the new percentage that you arrive at.

This formula, or variants of it, is used by expert betters, City traders and famous investors including Warren Buffet, but clearly it’s not for everyone. Only serious mathematical betters will get anything out of it.

The Kelly Criterion has a few flaws too.

Firstly, the need to recalculate means you can’t bet on more than one thing at once unless you have two or more bankrolls with two separate histories. Another problem is that betters tend to exaggerate their win ratios, therefore staking too much on each bet.

It insists that you keep reinvesting and forces some punters to stake more money than they would like to risk on any given bet. For this last reason some punters divide the Criterion by two (a Half Kelly) – so 7.5 per cent becomes 3.25 per cent of your bankroll.

Many say betting this way takes the fun out of betting, but it certainly helps you bring about a return on your investment. Your personality and your approach to gaming will likely decide whether you choose to use it or not.

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