What is the Kelly Criterion in Poker?

What is the Kelly Criterion in Poker?

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Poker is a game of skill, strategy and smart calculations. It also involves a significant amount of patience, humility and some sound background work. If you are here to improve your strategy and up your overall game, then learning about the Kelly Criterion in poker and its application might just be the right place to start!

What is the Kelly Criterion in poker?

The Kelly Strategy or Kelly Bet is a theory that is largely utilised by experienced gamblers to determine the amount of their existing bankroll that they must place in one bet using mathematical operations.

The main purpose of using the Kelly Criterion in poker is to minimise one's risks of ruin. It is to ensure profitability to the gambler in the long run. It promotes calculated risk-taking behaviour in the gambler and ensures that the entire net worth of the gambler is not severely diminished by one wrong call.

It is usually employed as a method to calculate bets in various sports betting and other forms of gambling, especially in cases there is a finite, win-or-loss result.

To illustrate how to use the Kelly Criterion in poker, consider this:

Consider an even money bet wherein there is a 0.7 probability of winning or a 70% chance of winning. On applying the Kelly Bet, which is multiplying the wager size percentage by two and subtracting the result by one, the present bet will leave the optimal wager size to be 40% of the available funds.

Basic Kelly Criterion formula:

To know how to use the Kelly Criterion in poker, you must know the formula.

The Kelly criterion formula is as follows:

f* = (bp-q)/b

Where, f* is the fraction of the current bankroll to bet

b is the odds received on the bet

p is the probability of winning

q is the probability of losing, which is 1 - p

p is our ITM (In The Money)

In order to calculate the odds received on the bet, one must determine the ROI or return on investment. ROI is calculated as,

ROI = (wins-losses)/ investment

Thus, f* can be equated to ROI * ITM / (ROI + 1 - ITM)

For instance, if the equation will stand at b = q/p, then the gambler has zero edge and it is recommended that the gambler bet nothing.

Application of the Kelly Criterion in poker

Employing the Kelly Criterion in poker might be slightly tricky since there are a huge number of variables which complicate the results. It is therefore used in a much broader sense. The Kelly Criterion can be applied in two main aspects of the game - during the game selection and while picking spots in game.

The crux of a good bankroll management strategy is to stay in action and not go bust for which one has to risk only a small percentage of the bankroll at a given game. With regard to this, using the Kelly criterion in poker may serve as the guiding light during game selection by pointing out that the tournament is just one small percentage of the overall bankroll and must be selected based on the results of application of this theory. This scientific method of bankroll management of the player will help sustain the player for the long run.

For example,

If you're playing an NL100 game with a win rate of 10 bb/100hands (big blinds per 100 hands) and a standard deviation of 100 bb/100 hands, then your win rate in terms of percentages may be regarded as

10 = 100*(2p-1)

On solving for p, we get p=55% and your advantage is 10% which means you need to invest 10% of your bankroll to maximize the growth rate of your bankroll.

Applying this helps the player maximise the bankroll growth rates in a scientific, and by extension a less volatile manner.

The application of the Kelly criterion in poker also gives us a slight advantage by giving us the possibility to force the opponents into risking a high proportion of their resources while not risking much themselves.

However, it is important to note that this is not a foolproof formula for success and is fraught with its own drawbacks. The Kelly Criterion in poker makes some crucial assumptions which may go wrong or might not be applicable in certain scenarios.

For instance, the Criterion assumes that the player will be playing an infinite number of games and hence, offers its results based on this. But this formula becomes redundant or sub optimal in case there are a limited number of rounds in the game.

Another issue is that the formula does not address variance especially considering the fact that it computes only expectations. Also, when there are three or more outcomes in a game, the formula does not work since it ignores the additional variance compared to a game with just two outcomes.

To wrap it up

The Kelly Criterion best embodies the words of this popular expression, ‘expect the best, prepare for the worst, capitalize on what comes’. Applying this successfully to your poker game might just give you that added advantage in a game which is otherwise considered to be game of luck.

To practise using the Kelly criterion in poker, download the GetMega app and play poker today!

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