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Risk & Money Management

What Is the Kelly Criterion, in Plain Words

The Kelly criterion gives the share of a pile to stake on a repeated bet so that the pile grows fastest, and it is the win rate less the lose rate divided by the payoff. This paper shows you that sentence worked on two example bets, a quarter of the pile for a 50-50 bet paying 2 to 1 and nothing for a bet with no edge; the idea as the sweet spot on a racquet; the hill of growth against the share staked, with its top at the fraction and the ground at twice it; the wobble, where a five-point change in the win rate moves the answer by seven and a half; and the report on your platform where the two inputs are read.

Difficulty
Intermediate
Reading time
6 min
Pages
8
Reviewed by
Saman Rahbar

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The sentence, worked on two bets

The Kelly criterion is a sentence: the share of the pile to stake on a repeated bet is the win rate, less the lose rate divided by the payoff, where the payoff is how big a win is against a loss. Take a bet that wins half the time and pays two to one: 0.50 less 0.50 over 2, which is 0.25, a quarter of the pile on each bet. Take one that wins forty times in a hundred and pays one and a half to one: 0.40 less 0.60 over 1.5, which is 0.40, so the fraction is zero — the bet has no edge, and the answer is to stake nothing. The figures are examples. Nothing here was measured on a market.

The sweet spot on a racquet

Picture a racquet with its sweet spot. Hit the ball there and it goes fastest for the swing; hit too low and it goes slowly, too high and it comes off the frame. The Kelly fraction is that spot for a pile of money and a bet that is repeated. Stake less than it and the pile grows more slowly than it could; stake more and the swings get bigger while the growth gets smaller, until at twice the fraction the pile does not grow at all. The spot is a place on the strings, not an instruction to hit there. Kelly says where it is, given the bet, and says nothing about whether to play.

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