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The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market

Read the paperopens doi.org in a new tab

What they found

Thorp, who used Kelly in blackjack and then ran one of the first quant hedge funds, wrote this as a practical guide. He walks through Kelly for simple bets, for blackjack with variable edge, for sports betting with many simultaneous bets, and for continuous investment in securities, including the formula for the optimal fraction when returns are approximately normal (edge divided by variance). He shows the drawdown properties of full Kelly (a full-Kelly bettor has a 50% chance of losing half their capital at some point), and argues for fractional Kelly in practice because true edges are uncertain.

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

The spread of outcomes behind an expectancyA histogram of forty trades: a tall block of small losses on the left, a low spread of larger wins on the right, and a line marking the average outcome.NUMBER OF TRADES051024 LOSSES, AVG −$20016 WINS, AVG +$600EXPECTANCY +$120−$400−$200$0+$200+$400+$600+$800PROFIT OR LOSS PER TRADEexpectancy = (40% × $600) − (60% × $200) = +$120 per trade
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.

What you can use

  • For a strategy with excess return m and variance s-squared, the Kelly fraction is roughly m divided by s-squared; this is the formula that translates Kelly to trading.
  • Full Kelly implies a 1-in-2 chance of halving your account at some point; half Kelly reduces that to about 1-in-8.
  • Overestimating your edge is the normal case, so treating half Kelly as the ceiling is a standard practitioner rule.

Caveats

Book chapter rather than a peer-reviewed study. The continuous-time approximation assumes normal returns, which understates fat-tailed risk. A free PDF circulates on academic archives and the author's site.

Tags: risk, position-sizing, kelly, practitioner

Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.