Betting the Kelly Stake

Kelly Staking Calculator

Steadily growing your bank requires more than just knowing a good value bet when you see one, as you also need maximize your winnings as much as possible, without risking too much of your bankroll. If you’re simply a person than like to put down £10, £50, even £100 on a match now and again, you probably don’t need to concern yourself much with this (as long as you can afford to lose what you’re betting).

However, for serious punters, the question of how much to risk on any one bet becomes a heck of a lot more important. You obviously want to win as much as possible, but the bookmakers hate losing even more than you love winning. It’s a known fact that consistent winning is frowned upon, and in fact, to such an extent that most bookmakers will close accounts that win too often or else require them to pay high premiums.

This means that if you already know how to spot a good bet, you can’t be wasting your time making a bunch of minor bets, as you should be focused on maximizing your potential. Luckily many smart statisticians have studied the problem before you and there are a number of methods that can help to calculate exactly what you should stake on a given bet.

Knowing how to calculate your stakes for a given bet based on the odds isn’t necessarily easy, and there are surely many different methods used (although many people still surprisingly rely on a gut feeling instead of simple statistics), but the most reliable means has to be calculating the Kelly stake.

The Kelly Stake Explained

The Kelly stake (or Kelly Bet, Criterion, Formula) is a strategy laid out by J.H. Kelly, Jr. in the 50’s that is designed to help determine the optimal stake for a bet. It is probably one of the most widely used betting strategies, and even stock market experts like Warren Buffett have shown it can work if applied correctly.

Kelly’s original work was purely theoretical statistics, calculated based on repeated events with an exact probability. In order for it to be applied, the bettor must have an advantage, which is why it obviously couldn’t work at the roulette table, as the house always holds the advantage.

Now you might be saying to yourself that bookmakers also hold an advantage, which is slightly true as they always offer inflated odds. However, being a smart punter is still about spotting when those odds differ enough from your estimated probability of that outcome to constitute a real value bet. Of course, this still doesn’t mean you should simply risk all of your bankroll, as there is always a fairly high chance you could lose—and this is where the Kelly stake can help.

Calculating the Kelly Stake

In the simplest of terms, Kelly’s strategy was that to maximize their profits a bettor needs only to calculate their advantage and then bet that percentage of their total bankroll. This would be simple in a situation with fixed, exact odds, but it becomes slightly trickier in sports betting, but nonetheless possible.

To see how it works, let’s say you are considering betting on Chelsea to beat Liverpool in an upcoming match and a bookmaker is offering odds of Chelsea: 11/10; Liverpool: 23/10; Draw: 5/2. Now, to figure out how much you should bet, you need to calculate both the bookmaker’s implied probability (in this case, 47.62%) and your own estimate of Chelsea’s probability to win. If the odds are fractional as these, you’ll also need to convert them to decimal odds (Chelsea: 2.10).

Now, you may think that Chelsea has a much better than 50% chance of winning, but If you’re smart, your estimate and the bookmaker’s implied probability shouldn’t be wildly off, even if you’re sure Chelsea will win. For our purposes, let’s say you decide their probability of winning is 52%.

Knowing these two probabilities and the total amount of your bankroll, the appropriate Kelly stake can then be calculated using this formula:

((Your Estimated Probability x Odds) – 1) / (Odds – 1)

So in our case:                                                   ( (.52 x 2.10) – 1) / (2.10 – 1)

(1.092 – 1) / 1.10

.0092 / 1.10 =

0.08 or 8% Kelly stake

Using the Kelly Stake

Using this example, you should be wagering 8% of your total bankroll for the full Kelly stake. Now this may not sound like much to some of you, but in truth, even betting this much could actually see you lose a significant portion of your bank if you hit a run of successive losses (in fact, even with the Kelly stake, you have just as good of a chance of losing half of your bankroll before you double it). Of course, this also applies much more to those with a larger bankroll, as there is a huge difference between £8, £80 and £800 bets.

The major issue is that many punters tend to overestimate their advantage. We already mentioned how smart punters know that their estimated advantage should always be close to the bookmaker’s, as even a few percentage points can cost you some serious cash.

To help with this problem of overestimation, some punters use half-Kelly or even quarter-Kelly bets, which in our case would be 4% or 2% of the total bankroll. These fractional Kelly stakes won’t grow your bankroll as quickly, but they can also help prevent the huge downswings that sometimes occur, or at least lessen their impact. While you have a 1 in 2 chance of losing half your bankroll before doubling it with the full Kelly stake, these odds decrease all the way to 1 in 9 with half-Kelly stakes, showing just how beneficial it can be.

There is no surefire strategy to make you an instant winner, as it’s really all about judging the value of a bet. Still, the Kelly strategy is surely one of the best ways for a good punter for maximize their earning potential.

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