The Kelly Criterion is designed to maximize long-term logarithmic bankroll growth when the probability estimate is accurate. The problem is that real betting estimates are rarely perfect. Full Kelly can grow quickly, but it can also create sharp drawdowns when variance or model error appears.
This Kelly Criterion Growth Simulator compares Full Kelly, Half Kelly and Quarter Kelly across repeated bets. It shows how different Kelly fractions affect final bankroll, maximum drawdown and volatility under the same estimated edge.
Important: this is a Monte Carlo simulator, not a guarantee. Every click can produce a different path. Kelly staking only works as intended if your edge estimate is realistic. If you overestimate your win probability, Full Kelly can become dangerous.
Kelly Growth Simulator
Compare Full Kelly, Half Kelly and Quarter Kelly over repeated bets.
| Strategy | Stake Fraction | Avg Final | Median Final | Avg Max Drawdown | Below Start |
|---|
What This Simulator Shows
The calculator answers a different question from the standard Kelly Criterion Calculator. The standard tool tells you the recommended stake for one bet. This simulator shows how those stake fractions can behave over many repeated bets.
| Kelly fraction | Growth profile | Main risk |
|---|---|---|
| Full Kelly | Highest theoretical log-growth if the edge is correct. | Large drawdowns and sensitivity to probability errors. |
| Half Kelly | Lower growth, usually much smoother bankroll path. | Still volatile if the edge is overstated. |
| Quarter Kelly | Conservative growth with lower drawdown pressure. | Slower compounding when the edge is real. |
Why Many Bettors Use Fractional Kelly
Full Kelly assumes that your probability estimate is accurate. That is a strong assumption. In sports betting, model probabilities can be wrong because of bad data, market movement, lineup changes, correlation, vig, or simple overconfidence.
Fractional Kelly reduces the stake size:
- Half Kelly uses 50% of the Full Kelly stake.
- Quarter Kelly uses 25% of the Full Kelly stake.
- Tenth Kelly is sometimes used when the edge estimate is very uncertain.
The trade-off is clear: lower Kelly fractions usually reduce drawdown and volatility, but they also reduce theoretical growth when the edge is real.
How to Use the Simulator
- Enter bankroll: the starting bankroll used for the simulation.
- Enter odds: the average decimal odds for the repeated bet type.
- Enter estimated win probability: your model’s view of the true chance.
- Set number of bets: the length of the simulated sequence.
- Set simulation paths: more paths produce a more stable summary but take slightly longer.
- Compare results: review average final bankroll, median final bankroll, worst drawdown and the chance of ending below the starting bankroll.
Kelly Formula Recap
The standard Kelly formula is:
f* = (bp – q) / b
- f* = Full Kelly fraction of bankroll
- b = decimal odds minus 1
- p = estimated probability of winning
- q = probability of losing, or 1 – p
The simulator applies this fraction repeatedly as bankroll changes. That is why Kelly stake size grows after wins and shrinks after losses.
Example: 55% Win Probability at 2.00 Odds
At decimal odds of 2.00, break-even probability is 50%. If your model estimates a true win probability of 55%, Full Kelly is:
10% of bankroll
On a $1,000 bankroll:
- Full Kelly: $100 initial stake
- Half Kelly: $50 initial stake
- Quarter Kelly: $25 initial stake
Full Kelly grows fastest in theory, but it also puts more bankroll at risk on every bet. A short losing run can create a large drawdown.
Model Error Risk
The most dangerous Kelly mistake is not variance. It is overestimating your edge.
| Estimated edge problem | Effect on Kelly staking |
|---|---|
| Your true probability is lower than estimated. | Kelly stakes are too large. |
| The market moves after your calculation. | The edge may shrink or disappear. |
| You ignore no-vig probability. | You may mistake bookmaker margin for value. |
| You use Full Kelly on a noisy model. | Drawdowns can become severe. |
For margin removal, use the No-Vig Calculator. For one-bet stake sizing, use the Kelly Criterion Calculator.
Frequently Asked Questions
What is a Kelly growth simulator?
A Kelly growth simulator runs repeated betting paths using Kelly-based stake sizes. It helps show how Full Kelly, Half Kelly and Quarter Kelly can differ in growth and drawdown.
Why is Full Kelly risky?
Full Kelly is sensitive to probability-estimation errors and can create large drawdowns. It assumes your edge estimate is accurate, which is often unrealistic in betting markets.
Is Half Kelly better than Full Kelly?
Not always mathematically, but often practically. Half Kelly reduces volatility and model-error risk while still keeping exposure to a positive edge.
Does Kelly guarantee profit?
No. Kelly staking only helps size positive-EV bets. If the edge estimate is wrong or the bet is negative EV, Kelly cannot create profit.
Why do simulation results change every time?
The simulator uses random Monte Carlo paths. Each run is one sample of possible outcomes. Look at the summary statistics rather than one path alone.
Responsible gambling notice: Kelly simulations estimate staking volatility. They do not guarantee profit or protect against bad probability estimates. Use conservative stakes and never risk money you cannot afford to lose.