When math is mathing: Discussing the Kelly bet size criterion

When math is mathing: Discussing the Kelly bet size criterion

article by CryptoJelleNL

Risk management plays a major role in the approach of any successful crypto trader, as risk management is what protects you from ruin when one of your trades inevitably does not play out as expected. When browsing Crypto Twitter or similar sources, there is a lot of discussion on risk management, where the consensus seems to be that risk management should be approached with a fixed risk of 1-2 percent per trade, regardless of the odds or win rate of a trader.

It is clear that the majority of new traders blindly copy this, without giving it much thought. While risking just 1-2 percent per trade is not inherently bad (in fact, I believe it's a rather sensible approach for beginners) – mathematicians have found ways to calculate a more optimal bet size.

In today's article, we discuss one of these methods that is popular among gamblers and traders alike; the Kelly bet size criterion.

What is the Kelly criterion?

The Kelly criterion is a mathematical formula that is used to take optimally sized bets and grow your capital at the maximum rate possible. While the criterion was originally developed in 1956, to study the disturbances in long-distance telephone calls, it did not take long for the gambling community to further develop the formula to apply it to horse racing.

After John L. Kelly published his findings in a paper "A new interpretation of the information rate", his formula rose to fame as a general money and portfolio management system in gambling, trading, and investing.

Calculating the Kelly bet size

Calculating the Kelly bet size requires two basic components; the likelihood of winning a given investment or bet (odds), and the risk/reward ratio. The following two data points are fed into the below formula:

Kelly bet size = Odds - (1 - Odds)Risk/reward ratio

The result of this calculation is referred to as the Kelly percentage – which tells investors and gamblers how much of their portfolio to risk on a given investment or gamble.

How to calculate odds and risk-reward ratio

While gamblers have clear odds to work with (for example, the American roulette wheel has 48 percent odds of hitting Red or Black) – traders work with more dynamic odds – which makes using the Kelly strategy slightly more complicated. Over time, traders have found that their win rate for trades based on the same strategy is a reasonably accurate substitute for using clearly defined odds in the Kelly formula.

To calculate win-rate, divide the total number of your winning trades with a certain strategy, by the total number of trades taken – with that same strategy.

Calculating the risk-reward ratio is done by dividing the potential profit of a trade, by the potential loss. If a trade's potential gain is $2000, and the potential loss is $500 – the risk/reward ratio would be 4, as 2000 divided by 500 equals 4.

With these calculations in mind, the crypto-trading Kelly calculation should look something similar to this:

Kelly bet size = Win Rate- (1 - Win Rate)Risk/reward ratio

Applying the Kelly criterion in trading

After calculating the Kelly bet size, you will know how much to risk on each trade. For example, if the outcome of the formula if 0.04, Kelly theory suggests you should risk 3.5 percent of your portfolio on a trade.

Of course, the Kelly bet size should not just be taken at face value. Even if you have done your due dilligence and believe the Kelly strategy is a good way to level up your trading success – there are times to overrule the Kelly bet size.

For example, in certain cases with high odds, the formula will suggest to risk 20, 30 or even 100 percent of your portfolio on a single trade, even though this is incredibly risky. No matter your appetite for risk, I personally do not believe any trader should risk more than 20 percent of their portfolio on a single bet. In these cases, many traders opt to use half of the recommended bet size – a more risk-averse approach that is known as a fractional Kelly bet.

A negative Kelly bet size suggests that the odds are stacked against you. In these cases, Kelly theory suggests the most profitable course of action is to countertrade the strategy, but I believe a better move would be to not bet at all, and find a more successful strategy.

Example of the Kelly calculation

Imagine trader Dmitry has a strategy with an average win rate of 40 percent and a risk/reward ratio of 2. Feeding the data into the formula generates the following outcome:

Kelly bet size = 40%- (1 - 40%)2= 10%

This tells Dmitry to use 10 percent of his account on each trade – but because he prefers being a little more conservative, he uses the fractional kelly approach – risking 5 percent of his account instead

If a trader has no edge (consider a gamble with 50/50 odds, and a 1:1 pay-off), the outcome of the formula is 0, or a recommendation to not bet at all.

Kelly bet size limitations and drawbacks

Even though the Kelly bet size criterion is a very useful formula and model in trading and investing – it is not without limitations.

The most important caveat in using Kelly is that a formula can only work when it is fed reliable data. It is wise to be conservative in estimating your win rate, as using overinflated expectations will lead to financial ruin.

The Kelly calculation assumes fixed odds – and trading is a very dynamic game. If your win-rate changes over time, you are wise to re-calibrate your calculation and change your bet size accordingly.

The Kelly approach is a very aggressive approach, which results in strong volatility in your portfolio. If your strategy is focussed on long-term growth with minimal risk, the Kelly approach makes little sense. Make sure you've read up on the objectives of Kelly investing before deploying the strategy.


In sum, the Kelly strategy is a mathematical approach to portfolio and money management – which can help generate the maximum returns possible while keeping drawdown limited as much as possible.

The approach is only as reliable as the data it is fed, so it is important to do proper calculations and re-calibrate your system frequently. Manage your risks well, and do not blindly follow the outcome of Kelly calculations!

Good luck!

Author's Disclaimer: This article is based on my limited knowledge and experience. It has been written for informational purposes only. It should not be construed as investment advice in any shape or form.

Editor's note: CryptoJelleNL provides insights into the cryptocurrency industry. He has been actively participating in financial markets for over 5 years, primarily focusing on long-term investments in both the stock market and crypto. While he watches the returns of those investments roll in, he writes articles for multiple platforms. From now on, he will be contributing his insights for WOO as well.

Check out his Twitter: twitter.com/cryptojellenl

The content above is neither a recommendation for investment and trading strategies nor does it constitute an investment offer, solicitation, or recommendation of any product or service. The content is for informational sharing purposes only. Anyone who makes or changes the investment decision based on the content shall undertake the result or loss by himself/herself.

The content of this document has been translated into different languages and shared throughout different platforms. In case of any discrepancy or inconsistency between different posts caused by mistranslations, the English version on our official website shall prevail.

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