The Fractional Kelly Bankroll Management System

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The Fractional Kelly Bankroll Management System

April 04, 2021, by Arnaldo Brito

Fractional Kelly Bankroll Management System

The Kelly Criterion is a strategy for managing money when betting. This model states betting an amount proportional to the winning probabilities and the advantage you may have over the bookies' odds. When applying Kelly's criteria, the consequences for overestimating your advantage are serious. For this reason, many bettors prefer to use a more cautious betting strategy: the fractional Kelly system. Instead of betting the percentage given by the Kelly criterion formula, they use a fraction of it. How does the fractional approach work concerning the full Kelly criterion? Is this the best option? Read on to find out.

The Complete Kelly Criterion Problem

One of the big problems with the Kelly method is that bankroll growth is erratic. Even, sometimes the benefits will be interrupted by significant losses. In other words, the bankroll evolution is highly variable. Applying the full Kelly criterion can cause sudden and steep declines in bankroll when losing a favorite big bet. It can happen, for example, that following the Kelly formula, we bet 30% of our funds on a favorite and lose the bet. This is a loss that most bettors cannot tolerate. You don't want to take the volatility risks that come with full Kelly bets? So, the solution is to bet less than what the full Kelly model tells you. But, how exactly will this influence the expected profitability of this money management strategy? Many sources suggest that by betting half the amount indicated by the Kelly formula, bankroll volatility decreases significantly. At the same time, most of the expected returns are maintained.

How To Use The Fractional Kelly Criterion

Usually, bettors applying the fractional Kelly criterion use half a Kelly, a quarter of a Kelly, or an eighth of a Kelly. If the amount of a bet according to the full Kelly criterion was 8% of the bankroll, the half, a quarter, and an eighth of Kelly bets would be 4%, 2%, and 1%, respectively. Logically, the variability in the funds' evolution is maximum with the full Kelly and minimum with the eighth Kelly. Let's suppose you want to bet on the X team wins at 1.95 odds. But, you've estimated a 60% occurring probability for that event, which is better than the implicit probability (51%) given in the odds. According to the full Kelly Criterion, you should bet almost 18% of your funds. However, if you think this is very risky, you can choose to use, for instance, a quarter of a Kelly. In this case, you would only bet 4.5% of your bankroll. Thus, when we go through positive hitting streaks, the complete Kelly strategy is much better than its fractional counterparts. Also, when things don't go well, the full Kelly will generate much larger losses.

Is The Fractional Kelly Criterion A Better Money Management Method?

Fractional Kelly appears to be a solution to Full Kelly's volatility risks, without losing much of the advantage that the Kelly strategy offers compared to fixed-amount bets. This is a reasonable way to handle the inevitable losing streaks we will face, even with favorable bets. Your account will grow in the long term, albeit more slowly, but at least the risks of falling into the red are reduced.

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