Kelly Criterion Explained Visually: How To Stake With Math
Kelly Criterion is the mathematically optimal staking formula for repeat bets with edge. It is also the formula most likely to wipe out beginner bettors because the math punishes overconfidence brutally. Here is what Kelly really does, when to use it, and when to walk away.
What Kelly actually optimises
Kelly Criterion maximises the long-run growth rate of a bankroll. It does not maximise expected value per bet, and it does not minimise variance. It specifically maximises the geometric mean of returns across infinite placements, which is the mathematical right answer for serial repeat bets where you reinvest the bankroll continuously.
Why most bettors should not use full Kelly
Full Kelly is mathematically optimal only when you know the true probabilities with certainty. In real betting you estimate probabilities. A 5% overestimation of your edge produces a 5% over-stake, which compounds badly across losing streaks. Full Kelly is also brutally volatile - a 50% bankroll drawdown is normal even when the methodology is correct.
Half Kelly captures roughly 75 percent of the growth of Full Kelly with substantially lower variance. Quarter Kelly captures 50 percent of the growth with low variance comparable to flat staking. Most professional bettors use Half Kelly or less. Almost no professional uses Full Kelly because the estimation error compounds catastrophically when wrong.
Modified Kelly variants compared
| Variant | Stake Formula | Growth Rate | Recommended For |
|---|---|---|---|
| Full Kelly | Edge ÷ Odds-1 | 100% | Math purists only |
| Half Kelly | (Edge ÷ Odds-1) × 0.5 | ~75% | Experienced bettors |
| Quarter Kelly | (Edge ÷ Odds-1) × 0.25 | ~50% | Most casual bettors |
| Flat Stake | Fixed % regardless | varies | Beginners, simplicity |
When Kelly fails completely
Practical recommendation for most bettors
For 95% of bettors, flat staking at 1.5-2% of bankroll produces better real-world results than Kelly. The reason is psychological: flat staking is easy to maintain through losing streaks, easy to recalculate after wins, and produces predictable variance that does not break discipline. The 25% theoretical growth-rate advantage of Half Kelly does not survive contact with real betting psychology for most people.