Gambling terms, explained straight

Odds, Probability & Bankroll

Kelly criterion poker

A formula that calculates the fraction of a bankroll to bet on a single wager, aiming to maximise long-term wealth growth rather than short-term profit.

Core formula
f* = p - q / b, where p is win probability, q is loss probability, and b is the net odds received on the wager15
Example
With even payout and p = 0.6, the optimal wager is 20% of wealth7
Application in poker
Used for bankroll management and bet sizing when the player's advantage can be estimated43

Key points

  • The Kelly criterion chooses the stake that maximises the expected logarithm of wealth, not expected profit42.
  • If the wager exceeds the Kelly amount, volatility increases and long-run growth falls; a smaller wager reduces risk but slows growth46.
  • In poker, the criterion applies to bankroll management and bet sizing when the player has a measurable edge43.

Where this term is used

Odds & probability Kelly criterion The general formula for optimal bet sizing across gambling and investing. Odds & probability Kelly criterion betting Applying the Kelly criterion to sports and other fixed-odds bets. Odds & probability Kelly criterion blackjack How card counters use the Kelly criterion to size bets. Odds & probability Kelly betting A synonym for the Kelly criterion and its practical use. Odds & probability Bankroll management poker Broader strategies for protecting and growing a poker bankroll. Odds & probability Odds of quads in poker The probability of being dealt four of a kind in poker.

Sources

  1. Kelly criterion en.wikipedia.org Defines the Kelly criterion and its formula.
  2. Gambling and information theory en.wikipedia.org Explains the logarithmic wealth maximisation principle.
  3. Card counting en.wikipedia.org Mentions card counting as a context for Kelly in poker.
  4. The Kelly Criterion wizardofodds.com Provides a clear explanation of the Kelly criterion and its application.
  5. Variance and Bankroll Management for Player Props wizardofodds.com Gives the alternative formula and bankroll management context.
  6. ケリー基準 jp.wizardofodds.com Supports the point about overbetting reducing growth.
  7. arXiv:1503.06535v2 [math.OC] 1 Aug 2017 arxiv.org Provides the 20% wealth example with even payout.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.