Kelly Criterion โ Smart Financial Analysis
Calculate optimal bet size using the Kelly Criterion. Win probability, odds, bankroll, fractional Kelly. Expected growth, risk of ruin, comparison charts.
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The Kelly Criterion is the mathematically optimal bet sizing formula that maximizes long-term growth rate. The formula is f* = (bp - q) / b, where b = net odds (win amount / loss amount), p = win probability, and q = 1 - p (loss probability). In investing, b represents the reward-to-risk ratio (e.g., 2:1 means you make $2 when right, lose $1 when wrong). Fractional Kelly means betting a fraction (e.g., half or quarter) of the full Kelly recommendation.
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Why: The Kelly Criterion is the mathematically optimal bet sizing formula that maximizes long-term growth rate. Developed by John Kelly at AT&T Bell Labs in 1956, it tells you what f...
How: Enter Win Probability (%), Win Amount (odds), Loss Amount to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
Run the calculator when you are ready.
๐ Example Scenarios โ Click to Load
Results
Risk of Ruin (approx)
Kelly Fraction by Win Probability
Bankroll Growth Simulation (Full Kelly vs Half-Kelly vs Fixed)
Optimal Bet Size Comparison
Risk of Ruin Probability
For educational purposes only โ not financial advice. Consult a qualified advisor before making decisions.
๐ก Money Facts
Kelly Criterion analysis is used by millions of people worldwide to make better financial decisions.
โ Industry Data
Financial literacy can increase household wealth by up to 25% over a lifetime.
โ NBER Research
The average American makes 35,000 financial decisions per yearโmany can be optimized with calculators.
โ Cornell University
Globally, only 33% of adults are financially literate, making tools like this essential.
โ S&P Global
The Kelly Criterion is the mathematically optimal bet sizing formula โ used by Edward Thorp to beat blackjack and later Wall Street. Formula: f* = (bp - q) / b, where b=odds, p=win probability, q=loss probability. Betting more than Kelly guarantees long-term ruin. Betting less is suboptimal but safer. Most professional traders use 'Half-Kelly' (50% of the calculated fraction) to reduce variance by 75% while sacrificing only 25% of growth. Warren Buffett reportedly used Kelly-like principles for concentrated bets.
๐ Kelly Criterion History
John Kelly at AT&T Bell Labs (1956) derived the optimal bet size to maximize long-term growth. Edward Thorp applied it to blackjack and later to investing. The formula maximizes geometric growth rate.
Why fractional Kelly? Full Kelly maximizes growth but has high volatility and risk of ruin. Half or quarter Kelly reduces variance while retaining most of the edge.
๐ How the Kelly Formula Works
Kelly maximizes the expected log of wealth: G = pยทln(1+bf) + qยทln(1-f). Taking the derivative and setting to zero yields f* = (bp - q)/b. The term bp is the expected gain per unit bet when you win; q is the loss probability. When bp > q you have positive edge.
โ ๏ธ Risk of Ruin
Betting more than full Kelly increases the probability of going bankrupt. The risk of ruin rises sharply as you exceed the optimal fraction. Half-Kelly typically cuts risk of ruin by 75% or more compared to full Kelly, which is why professionals prefer it.
โ ๏ธ Kelly in Investing vs Gambling
- Gambling: odds and probabilities are often estimated; use fractional Kelly
- Investing: future returns are uncertain; many use 25โ50% of Kelly
- Never bet more than full Kellyโit increases risk without improving growth
โ๏ธ Kelly vs Fixed Betting
| Aspect | Kelly Criterion | Fixed Betting |
|---|---|---|
| Bet size | Adapts to edge & bankroll | Constant % |
| Growth | Maximizes long-term | Suboptimal |
| Risk | Scales with edge | Over/under-bets |
| Variance | Higher at full Kelly | Depends on fixed % |
๐ฏ Expert Bet Sizing Tips
๐ก Half-Kelly = Sweet Spot
Reduces variance by 75% while sacrificing only 25% of growth. Most pros use half-Kelly or less.
๐ก Overestimate Edge = Ruin
If you overestimate your win probability, full Kelly will bankrupt you. Always use fractional Kelly when uncertain.
๐ก Did You Know?
๐ Official Sources
Fortune's Formula (William Poundstone), Ed Thorp Papers, Journal of Portfolio Management
๐ซ Common Kelly Mistakes
- Using full Kelly when edge is estimated โ always use fractional Kelly (half or quarter)
- Confusing American odds with decimal odds โ for -110 odds, b = 100/110 โ 0.909
- Ignoring correlation โ when bets are correlated, use lower fractions
- Betting more than Kelly when on a losing streak โ Kelly is optimal for the long run, not short-term
โ ๏ธ Disclaimer: This calculator provides estimates for educational purposes. Past performance does not guarantee future results. Not financial or gambling advice. Use fractional Kelly when edge is uncertain.
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