Kelly Criterion formula

What is the Kelly Criterion formula?

The Kelly criterion formula is a money management system that has an exponential growth curve as it maximises profit. It calculates the ideal position size for the next trade to maximise profits.

The same formula can be used When playing a game of blackjack

Goal of the Kelly Criterion formula

The goal of the Kelly Criterion formula is to calculate the optimal position size for the next trade or bet on known data (percent win, loss percentage, average profit, average loss).

The basic requirement is that the above data results in a positive expected value.

So that means the trading/playing strategy has to be profitable.

If that’s the case, the maximum profit can be achieved with the Kelly formula.

Kelly criterion history

In 1956, John Kelly jr. concerned with the question of how much risk should be taken to obtain the maximum capital growth. The reason for this was sports betting, in which someone knew by an advantage to the positive expected value. Kelly realised that the higher the statistical advantage and the lower the risk, the higher the capital outlay for that.

How does the Kelly formula work?

The formula is:

Percentage of capital =% Win – [% Loss / (avg.Win / avg.Loss)]

% Win = percentage profit

% Loss = loss probability in percent

avg.Win = avg. profit

avg.Loss = avg. loss


So you need this data to use the Kelly formula. In trading or blackjack betting you set up a statistics on a trading strategy and thus receives the data from the past of a strategy. More below.


The following data was obtained, for example, in the DAX strategy:

% Win = percent win: 51.64%

% Loss = loss probability in percent: 48.36%

avg.Win = avg. Profit: 40 points

avg.Loss = avg. Loss: 30 points

Calculation: 51.63% – [48.36% / (40/30)]

Result: 15.37%

If data in the future is exactly the same as past data, we should risk 15.37% of our capital in our next trade or bet.This proportion is extremely high.

The following table gives an overview of what proportion of capital should be risked on the next trade or blackjack bet. If the “0” is highlighted in red, there is a negative expectation value.

Kelly formula calculation table. Calculates the ideal percentage risk exposure for the next trade or bet based on the average CRV ( capital risk value) and the profit probability.



Application of the Kelly formula in trading and online blackjack

More and more traders and gamblers are using the Kelly formula while trading and playing. Some funds also use modified forms of the Kelly formula, as they can offer many benefits. Larry Williams has achieved a performance of about 11,000% in one year with the Kelly Formula.

Nevertheless, this formula is a money management system for advanced traders and players who already had experience with the Kelly formula. Especially beginners are unaware of the disadvantages of the Kelly criterion. In addition, the Kelly formula is a very aggressive system. Therefore should therefore only be used by risk-loving traders and gamblers who like to have a game or two of online blackjack


Too high position size

As indicated in our example, good historical data of a trading strategy often yields a high percentage as a result of the Kelly formula.

It is probably not advisable in trading to risk 30% of its capital at the next trade or bet.

Loss phases are difficult

Let’s say the Kelly formula tells us to risk 15% of our capital on the next trade or bet. We have £100,000  of capital in our account and just follow this one strategy, based on which we took the data from the past to calculate the Kelly criterion.

If we had 5 loss levels in a row right at the beginning, then our £100,000 account would shrink to £44,370. (Simplified example with a flat 15% loss / trade or bet)


On the other hand, of course, it should be said that at the beginning of the game. With 5 consecutive winning points (with a CRV of 1.0) we would have £201.135  in our bank account.

So the next disadvantage of the Kelly formula is already noticeable:

Graph showing Kelly versus Kelly fractional betting


Data from history is no guarantee for the future

Calculating the Kelly formula requires a basic thesis: We know the data from which to calculate the optimal position size for the next trade or bet.

In trading, we can only use the data from the past to hope for similar values ​​in the future. Nevertheless, we will not be able to project the exact dates into the future. It may even be that the data could be completely different and we would thus permanently enter the market with the wrong position size.

Violent fluctuations in the wealth curve

Nowadays, using the Kelly formula, the wealth curve can be viewed in a graph using computer simulations. So or something like that would look like the fortune curve in the optimal Kelly use:

You can see that the wealth curve is very fast and exponentially rising – but the fluctuations are very extreme.

“The probability of losing half of the assets is 50%.

As a trader or gambler you have to know and be prepared for this fact.

Thus, the Kelly formula is not suitable for every trader or gambler.

Nevertheless, there are ways to keep the fluctuations low.


For all these reasons, the direct adoption of the Kelly Criterion formula for traders and gamblers is probably not advisable. However, it does provide us with information about what the perfect position size could be. And whether we have effectively exploited our advantage in the market with our position size.

Use Kelly’s formula as a “map” for position size

The Kelly Criterion formula actually provides the optimal position size for maximising profits.The disadvantages are so great that we should not use the Kelly formula for trading or gambling in this form.

Nevertheless, one can use the Kelly criterion formula as a kind of map for the position size. Because it gives us more information about the position size.

The following image shows an overview of prominent points that are generally important for the position size.




The yield curve decreases to the left and to the right of the optimal Kelly criterion. The optimal point is marked with “1” – ie “1 Kelly”.

It is interesting that in “half Kelly” still generated 3/4 of the income. Which would have come about with optimal Kelly use. And that with significantly lower fluctuations in the asset curve. Therefore, the “half Kelly” is often its application.

Furthermore, it is interesting that with double Kelly the yield is zero. (And with a positive expected value)

With a position size that goes beyond the double Kelly criterion. The return is even negative and you lose money in the long term.

What should never happen is that we set a higher position size than the optimal Kelly bet. The graph refers to this as “insane” because. The yield decreases with increasing distance of the optimal Kelly. Use the fluctuation margin in the asset curve increases with increasing position size. Two facts that we should take note of.


Nevertheless, the Kelly Criterion formula to the left of the optimal Kelly use is described as “aggressive” and should therefore be treated with caution.

As previously mentioned this method is used in trading, online blackjack or any kind of betting or gambling.






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