Betting Strategy: The Kelly Criterion explained

Betting Strategy / Simon Rowlands / 02 September 2008 / Leave a Comment

The general principles of Kelly make perfect sense, says Simon Rowlands.

The recent discussion about staking plans on betting.betfair generated some light as well as a great deal of heat. I was an interested - and at times bemused - spectator, but my ears (metaphorically) pricked up when one particular word was mentioned: Kelly.

Some explanation is required for anyone who has not come across this name in this context before.

The crux of the issue where staking is concerned is how much of your available money you should risk in given circumstances.

Theories of probability are often illustrated by coin-toss experiments, or similar, in which the "true" odds of an outcome are known. In such circumstances it does not take a genius to say what a team of 100 punters with a bank of £1 each and an agreement to share any returns should do when offered 10/1 against heads on independent but fair coin tosses. They should each stake their whole bank in the knowledge that on average 50 of them will be skint at the end of the experiment but the team will be £500 up and the collective payoffs will more than compensate for individual losses. The chance of none of them getting a return is negligible: roughly 1 with 30 zeroes after it to 1.

But what if you are just one punter, not part of a team, and your £1 is all you have? Putting it all on an evens shot that is being offered at 10/1 makes plenty of sense in one respect, but there is still a 50% chance that you won't have the price of a cup of tea at the end of the day.

It is important, in the real world, not only to seek to capitalise on value when it occurs but to do so in a manner that maximises your chance of being around to benefit from that value. Don't stake the farm every time someone offers you a fraction over the odds, in other words.

This conundrum, in a very different context, was what preoccupied a certain John Kelly at the Bell Laboratories in the 1950s. His complex mathematical paper, published in 1956, dealt with telecommunications but was illustrated by way of examples that had a clear and specific application to betting strategy.

Nick Mordin devoted a chapter to the Kelly Criterion in his book Winning Without Thinking, which also had the original paper in the appendix, and it is well worth a read.

In essence, the amount you stake should be dictated by a combination of the edge you have (10/1 as opposed to evens in the example above) and the likelihood of the event occurring (50% in the example above). Mordin helpfully provided a simplified version of Kelly that mere mortals can understand and apply.

I have read plenty of criticisms of the Kelly Criterion as it is applied to real-life situations. These include the undeniable fact that the assessment of "fair" odds in horseracing is always subjective in truth and that for punters staking considerably more than the £1 in the illustration above there is the very real possibility of affecting the price of the event on which they are betting. As a result, even staunch champions of the theory often admit to betting "half Kellys" or some other fraction thereof.

Fair enough, but it should not for a moment be assumed from this that Kelly is flawed. It is not: it is our own ability to evaluate "fair" odds, and sometimes our ability to capitalise on that, that is flawed in real-life situations. Kelly is indeed the best theoretical way in which to maximise the growth of your betting capital. No-one has seriously managed to disprove that.

I know of a few people - mostly big-staking punters who deal with statistical models in which the effects of subjectivity are minimised - who apply Kelly rigorously to their betting, but I do not and I have a hunch I am in the majority where this is concerned.

Nonetheless, the fact that I should stake more on a 10/1 shot if I think it should be 5/1 rather than if I think it should be 8/1, and that I should stake more on something that has a 50% chance of happening than on something that has a 10% chance of happening, informs my punting in general terms. I favour a sort of Kelly-Lite, as it were.

Even if you don't go the whole hog and adopt Kelly as a new religion I suggest that you, like me, take the general principles on board. It makes perfect sense.