A formula that tells you the optimal percentage of your bankroll to bet, given your estimated edge over the bookmaker. Developed by John Kelly at Bell Labs in 1956, originally for information theory. Found its way into gambling and investing.
Kelly handles stake sizing. You still need Value Betting to identify which bets are worth sizing — without it, Kelly is just a fancy way to lose money faster.
The idea: bet more when your edge is large, less when it’s small. Never bet everything. Never bet nothing.
The Formula
f = (bp − q) / b
Where:
f— fraction of bankroll to betb— decimal odds minus 1, your potential profit per unit riskedp— your estimated probability of winningq— 1 minus p, the probability of losing
Example
You estimate Team A has a 55% chance of winning. The bookmaker offers odds of 2.00.
b = 2.00 − 1 = 1.00
p = 0.55
q = 0.45
f = (1.00 × 0.55 − 0.45) / 1.00 = 0.10 = 10%
Kelly says: bet 10% of your bankroll. With a $1,000 bankroll, that’s $100.
Another Example
Same 55% edge, but odds are 3.00:
b = 2.00
p = 0.55
q = 0.45
f = (2.00 × 0.55 − 0.45) / 2.00 = 0.325 = 32.5%
Higher odds with the same edge → Kelly says bet more. Because each win pays more, the optimal stake increases.
Why Full Kelly Is Dangerous
The formula assumes you know your true probability exactly — an assumption that never holds. A small error in estimation creates a large error in stake size.
If your real edge is 52% but you estimate 55%, Kelly overbets you. If your real edge is 48% and you bet at all, you’re losing money.
Overbetting is worse than underbetting. Losing your entire bankroll means you can’t recover.
Fractional Kelly
Most professionals use half-Kelly or quarter-Kelly:
- Full Kelly — mathematically optimal if your estimates are perfect.
- Half Kelly — 50% of the recommended stake. Cuts variance significantly. Only ~25% less profit than full Kelly over time.
- Quarter Kelly — 25% of the recommended stake. Very conservative, almost no risk of ruin, but slow growth.
Half Kelly is the practical sweet spot for most people. You give up some upside in exchange for not going broke.
When Kelly Works
Kelly is most useful when:
- You have a reliable edge — not just a gut feeling
- You can estimate probabilities accurately — backed by data, not hope
- You’re betting on a large number of events — the math works over many bets, not a few
- Commitment to stick to the formula
If you can’t honestly say all four of these apply, Kelly won’t help you. The edge part is critical — without it, Kelly just tells you not to bet.
Common Mistakes
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Using Kelly without an edge. If your probability estimate is the same as the implied odds, Kelly says bet 0%. Without edge, Kelly is a “don’t bet” signal.
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Estimating too aggressively. Overestimating your probability by even a few percent leads to overbetting.
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Ignoring variance. Kelly maximizes long-term growth rate, but short-term results can be brutal. Half-Kelly reduces this.
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Betting on too few events. Kelly assumes repeated trials. A single bet with Kelly sizing is just a large gamble.
Kelly vs Other Systems
| Approach | What It Does | Edge Required |
|---|---|---|
| Kelly | Optimizes bet size for growth | Yes |
| Flat Betting | Fixed stake per bet | Yes — required for profit |
| Martingale | Doubles after loss | No — guaranteed loss |
Kelly sizes your bets given an edge. Without the edge, it’s just an expensive way to lose money.
See Also
- Value Betting — how to find the edge that Kelly sizes
- Martingale Strategy — what happens without proper sizing
- Betting Strategies — overview of all approaches