What Is the Kelly Criterion?
'If the odds are clearly in your favor, how much should you bet to be optimal?' The Kelly criterion answers this question with math. But using that answer as-is is dangerous.
What Is the Kelly Criterion?
The Kelly Criterion is a formula, proposed in 1956 by John Kelly of Bell Labs, for finding the betting fraction that maximizes the long-term growth rate of your assets.
For a simple bet it is written as:
f* = (b·p − q) / b
f* is the fraction of your assets to bet, b is the net payoff (payoff odds − 1), p is the probability of winning, and q is the probability of losing (1 − p). The larger the resulting f*, the more favorable the bet and the more you should stake; if it is negative, it means don't bet.
A Look at the Numbers
For example, suppose that if you win you get back as much again as you staked (b=1), and the probability of winning is 60% (p=0.6, q=0.4).
f* = (1×0.6 − 0.4) / 1 = 0.2
In other words, staking 20% of your assets theoretically maximizes the long-term growth rate. Bet more than this and the risk of ruin grows; bet less and growth slows down.
Why Practitioners Use Only Half
The fatal premise of the Kelly criterion is that you 'know the winning probability p exactly.' In reality you cannot know p precisely, and even a slight overestimate leads to an actually excessive bet.
Moreover, full Kelly maximizes the growth rate but has very large drawdowns along the way. That is why many experts use 'fractional Kelly,' staking only 25–50% of the calculated value. In particular, half (1/2) Kelly is known to retain about 75% of the long-term growth rate while greatly reducing volatility.
The Kelly criterion is a concept that came out of gambling theory. It is hard to apply directly to investments like stocks or funds, where win rates and payoffs cannot be pinned down cleanly, so it is safer to understand it at the level of the idea that 'you size positions in proportion to how favorable the odds are.'
Frequently Asked Questions
Q. If I follow the Kelly criterion, will I grow my money the fastest?
The long-term growth rate is maximized only when you know the probability exactly. In reality, probability estimates easily miss, and full Kelly has such large drawdowns along the way that it is hard to actually endure. That is why it is common to use a scaled-down version.
Q. Can I use the Kelly criterion for stock investing?
With stocks, win rates and payoffs are not clear, so it is hard to plug them straight into the formula. It is safer to take only the direction—'the higher the chance of winning and the more favorable the odds, the larger the position'—and to avoid concentrating excessively in a single asset. This is a concept explanation, not investment advice.
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