- What: Kelly Criterion is a mathematical formula that calculates the exact fraction of your bankroll to risk on any positive-expected-value bet.
- Why it matters: It maximises long-run wealth growth while preventing the ruin that comes from overbetting — the #1 killer of profitable traders.
- Key formula: f* = (bp − q) / b — where b = payout odds, p = your win probability, q = 1−p.
- Bottom line: Use Half Kelly in practice — it captures ~75% of the growth with far less volatility and ruin risk.
The Kelly Criterion: Background
In 1956, physicist John L. Kelly Jr. published "A New Interpretation of Information Rate" in the Bell System Technical Journal. His formula — later called the Kelly Criterion — proved mathematically that there exists an optimal fraction of wealth to wager on any favourable bet that maximises the long-run geometric growth rate of wealth.
The Kelly formula was rapidly adopted by gamblers, poker professionals, Warren Buffett's mentor Benjamin Graham, and eventually algorithmic traders on Wall Street. Ed Thorp — the mathematician who invented card counting — used Kelly Criterion to build a fortune at the blackjack table and later at his quantitative hedge fund, Princeton-Newport Partners. Today it's the foundation of modern bankroll management in prediction markets, sports betting, and quantitative finance alike.
The intuition is elegant: bet too little and you leave compounding on the table. Bet too much and a losing streak destroys your capital before your edge can assert itself. Kelly finds the exact optimal point between these extremes.
The Kelly Formula
b = net payout odds (decimal odds − 1)
p = probability of winning (your estimate)
q = probability of losing = 1 − p
For prediction markets where YES shares trade at price P (between 0 and 1), the formula simplifies to:
b = net profit per dollar risked if YES wins
f* = p − q × P/(1−P)
If f* > 0 → you have positive edge → buy YES
If f* < 0 → skip the trade (or buy NO if large negative)
A Worked Prediction Market Example
Market: "Will the Fed cut rates in Q3 2026?" — YES trading at 52¢
Your estimate based on macroeconomic research: 65% probability of YES
b = (1 − 0.52) / 0.52 = 0.923 (net odds)
p = 0.65 (your probability estimate)
q = 0.35
f* = (0.923 × 0.65 − 0.35) / 0.923
f* = (0.6 − 0.35) / 0.923
f* = 27.1% of bankroll (Full Kelly)
Half Kelly = 13.6% of bankroll
With a $5,000 prediction market bankroll: Half Kelly → stake $680 on this trade. If YES resolves, you profit $680 × 0.923 = $628. If NO resolves, you lose $680.
The expected value at your estimated probabilities: EV = 0.65 × $628 − 0.35 × $680 = $408 − $238 = +$170 expected profit on this trade.
Kelly Fractions: Full, Half, and Quarter
| Strategy | Fraction Used | Growth Rate | Volatility | Best For |
|---|---|---|---|---|
| Full Kelly | f* × 1.0 | Maximum | Very High | Perfectly calibrated edge estimates |
| Half Kelly | f* × 0.5 | ~75% of max | Moderate | Most experienced traders |
| Quarter Kelly | f* × 0.25 | ~50% of max | Low | Beginners, uncertain edge |
| Overbetting (2× Kelly) | f* × 2.0 | Negative | Ruinous | Never — this destroys accounts |
Research by Edward Thorp shows that half Kelly is the practical optimum for most real-world traders: it accounts for uncertainty in edge estimates and reduces drawdowns by ~50% while sacrificing only ~25% of maximum long-term growth rate. Even professional forecasters with strong track records rarely use full Kelly.
When Kelly Says "Don't Bet"
If f* is zero or negative, the Kelly formula is telling you there is no positive edge in this trade. The market's implied probability already reflects the true odds — or worse, you have a negative edge (the market is smarter than you on this one).
A negative Kelly result is equally as important as a positive one. It's a clear signal to skip the trade entirely — or to reconsider your probability estimate. If you're consistently getting negative Kelly outputs on markets you felt good about, it's a sign to recalibrate your models.
One useful heuristic: if your edge is below 3 percentage points (e.g., you estimate 68% but market says 65%), the Kelly output is so small after transaction costs that it's generally not worth the trade. Focus your capital on high-edge markets where Kelly outputs exceed 5% before discounting to half.
Kelly Criterion for Portfolio Management
The Kelly formula also generalises to multi-asset portfolios, where you allocate capital optimally across multiple simultaneous positions. This is especially relevant for prediction market traders who often hold 5–20 open positions simultaneously.
Key principle: The Kelly fractions across all open positions should sum to no more than 100% of your bankroll. If they exceed 100%, scale all positions proportionally down.
But there's a subtler point about correlation: Kelly was derived assuming independent bets. In prediction markets, many markets share underlying drivers — five political markets may all move together on a single election outcome. Treat correlated clusters as a single Kelly bet, not five separate ones. The total allocation to a correlated cluster should be your Kelly output for that cluster as a whole.
Practical workflow for portfolio Kelly:
- Calculate Kelly fraction for each open position
- Group positions by correlation cluster
- Cap cluster allocation at your single-bet Kelly output
- If total portfolio exceeds 60% of bankroll, scale all down proportionally
- Re-evaluate after every major news event that affects your positions
Common Kelly Criterion Mistakes
Even traders who understand the formula fall into these traps:
- Using full Kelly with uncertain edge: If your probability estimate is off by even 5 percentage points, full Kelly can severely over-bet. Always use half or quarter Kelly unless your calibration is proven over 50+ resolved trades.
- Ignoring Polymarket fees: Polymarket charges 2% of net winnings. Subtract this from your payout (b) before calculating Kelly — it reduces optimal stake meaningfully on small edges.
- Not tracking calibration: Kelly only works if your p estimates are accurate. Track every trade, compute your Brier Score monthly. If it's above 0.20, reduce Kelly fraction until you've identified and corrected the bias.
- Treating every bet as independent: Correlated markets require treating the cluster as one bet. Five election markets don't give you five independent Kelly stakes — they're one concentrated position.
- Kelly on illiquid markets: Thin order books mean you can't fill at the price you see. If your expected fill price is 3–5¢ worse than displayed, recalculate Kelly at that worse price. A favourable edge can vanish entirely with slippage.
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Frequently Asked Questions
What is the Kelly Criterion formula?
f* = (bp − q) / b, where f* is the fraction of bankroll to bet, b is the net odds received on the bet (payout per unit staked), p is the probability of winning, and q is the probability of losing (1 − p). A positive f* means you have an edge; negative means skip the trade.
Is "Kelly Criteria" the same as "Kelly Criterion"?
Yes — "Kelly Criteria" is a widespread misspelling. The correct term is Kelly Criterion (singular), named after John L. Kelly Jr. who published the original 1956 paper at Bell Labs. Both refer to the same mathematical formula for optimal bet sizing.
Why use half Kelly instead of full Kelly?
Full Kelly is theoretically optimal only with perfectly calibrated probabilities. In practice, your probability estimates have estimation error — so full Kelly over-sizes the bet relative to true edge. Half Kelly reduces drawdown by ~50% while sacrificing only ~13% of maximum long-term growth rate, making it the professional standard for prediction market traders.
Can Kelly Criterion be used for crypto trading?
Yes. Any situation with a quantifiable win probability and net odds can use Kelly. In crypto, you might apply Kelly when taking a directional trade with a defined stop-loss (which gives you net odds) and a probability estimate from technical or on-chain analysis. Our Kelly Calculator handles crypto trade inputs directly.
What does a Kelly fraction of 0.15 mean?
A Kelly fraction of 0.15 means the formula recommends staking 15% of your bankroll on this bet. If you're using ½ Kelly (recommended), you'd stake 7.5%. On a $1,000 bankroll, that's $75. This is the amount that mathematically maximises long-term compounding given your stated edge — assuming your probability estimate is accurate.
How do I track whether my Kelly estimates are accurate?
Keep a trading log with every bet: the market, your stated probability p, the market price, and the outcome. After 30+ resolved trades, compute your Brier Score. If your Brier Score is below 0.15, your edge estimates are well-calibrated. Above 0.20 means you're systematically overconfident — reduce to quarter Kelly until calibration improves.