Kelly Criterion
This page demonstrates the Kelly Criterion interactively. Use the slider to scale the optimal fraction.
Return vs. Volatility
Parameters
- Odds: Winnings multiplier (1.0 = even odds, 2.0 = double your money)
- Edge: Probability of winning
- Sims: Simulated trials for return/volatility analysis
- Paths: Number of independent simulation runs (10-50 range)
Details
Top Chart (Return vs. Volatility):
- X: Kelly multiplier
- Y1: Expected log growth rate (blue curve)
- Y2: Standard deviation of log growth (red curve)
- Y3: Risk-adjusted growth (Green dotted)
- Green shaded refers to optimal risk-adjusted Kelly range
- Yellow shaded refers to growth maximizing range
- Red shaded refers to ruin range
Middle Chart (Monte Carlo Paths):
- Shows 4 Kelly multiplier strategies: 0.25×, 0.5×, 1×, 1.5× Kelly
- Each line shows multiple simulation paths with average highlighted
- Uses 10% of sims for trials to conserve bandwidth
- Click "New Simulation" to generate fresh random paths
Bottom Chart (Ending Value Distribution):
- Histogram showing distribution of final portfolio values
- Overlaid histograms for each Kelly multiplier
- X-axis shows log₁₀ of final portfolio values (linear scale)
- Shows probability density of different outcomes
Recommended bet size should be below 0.8 K. At K greater than 1.5, your chances of ruin gets extremely high.
In fact, you notice that ruin can happen even before K reaches 1.5 when your edge or odds goes high enough.
That is another way of saying Kelly sometimes gets too overconfident in certain games, and recommends you to bet extremely big (more than 60% of your portfolio), which may work out well in few iterations, but one big loss is enough to wipe you off.
Note
When odds get large enough, you notice a K=0.7 would outperformed a K=1 strategy 50% of the time within 100 games, from the probability density chart.
However, if you simply observe the average results from a Monte Carlo simulations, you would have think that K=1 is always the best strategy.
This is one of the problems with going full Kelly -- it tends to bet too much during times when it feels too certain about an outcome.
This is the kind of information what most people ends up missing. What works in theory is not always the most practical strategy in real life.
In practice, going full Kelly and setting a bet size limit of 50% is a good heuristic to follow.
Heatmap
Parameters
- Max odds: Maximum winnings multiplier to display (e.g., 2.0 = double your money)
- P steps: Number of probability intervals (more = smoother heatmap)
- Odds steps: Number of multiplier intervals (more = smootherheatmap)
- K: Kelly multiplier
Axis
- X: Assumed probability of winnings
- Y: Assumed profit from winnings
- Z: Kelly recommended bet size