Odds, Probability & Bankroll
Kelly criterion blackjack
In blackjack, the Kelly criterion is a bet-sizing rule for card counters: wager the fraction of your bankroll that matches your current edge, aiming to maximise long-run logarithmic wealth growth.
- Formula (simple even-money)
- Edge = 2p − 1 (where p is win probability); optimal wager is edge times bankroll.3
- Example
- A 60% win rate at even payout gives a 20% edge, so Kelly says bet 20% of bankroll.4
- When edge ≤ 0
- The rule says to bet nothing – it only applies to positive-expectation situations.2
Key points
- The Kelly fraction changes dynamically as the counter’s estimated edge shifts from hand to hand.1
- It maximises the long-run geometric growth rate of bankroll, not short-term profit per hand.6
- For a bet that pays b-to-1, the formula is f* = p − q/b = (p(1+b)−1)/b.5
Where this term is used
Related terms
Odds & probability
Kelly criterion
The general mathematical bet-sizing formula that applies to any favourable gamble or investment.
Odds & probability
Kelly criterion betting
How the Kelly formula is used to size wagers on sports or other binary-outcome bets.
Odds & probability
Kelly criterion poker
Applying Kelly sizing to poker, where edges vary by opponent and session.
Odds & probability
Kelly betting
The broader practice of proportional staking based on perceived edge.
Odds & probability
Blackjack house edge
The built-in advantage the casino has when a player uses basic strategy.
Odds & probability
Martingale system blackjack
A risky double-after-loss progression that is distinct from proportional Kelly betting.
Sources
- The Kelly Criterion wizardofodds.com Provides the core definition, simple even-money formula, and minimisation of bets to double bankroll.
- Card counting en.wikipedia.org Establishes the connection to card counting and the zero-bet rule for negative edge.
- A Quantum Double-or-Nothing Game: An Application of ... - PMC pmc.ncbi.nlm.nih.gov Supplies the even-money formula 2p−1.
- arXiv:1503.06535v2 [math.OC] 1 Aug 2017 arxiv.org Gives the concrete example of 20% bankroll for a 60% win probability.
- Kelly criterion for variable pay-off arxiv.org Provides the general b-to-1 formula f* = p − q/b.
- Kelly criterion en.wikipedia.org Confirms the goal of maximising long-run geometric growth.
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.