Interactive Simulation

Kelly Criterion

The mathematically optimal strategy for maximizing long-term wealth while minimizing risk of ruin

Parameters
Win Probability 55%
10%90%
The probability that your investment will be profitable
Win/Loss Ratio 1:1
0.5:13:1
How much you win relative to your bet (1:1 = win equals stake)
Volatility (Std Dev) 20%
5% Calm50% Wild
Return fluctuation — higher volatility = more uncertainty
Optimal Kelly Fraction

Bet This Fraction

10%
Balanced strategy
f* = (0.55 × 1 - 0.45) / 1 × 0.80 = 8%
vol_adj = 1 - (volatility / 100) → Higher volatility reduces Kelly

Medium Volatility

Standard market conditions

Why Kelly Matters

Betting more than Kelly guarantees ruin in the long run. Watch the "Aggressive" strategy crash!

Strategy Comparison
Kelly Optimal
10% per bet
$10,000
Betting: $1,000
+0.00%
Aggressive
40% per bet
$10,000
Betting: $4,000
+0.00%
Conservative
5% per bet
$10,000
Betting: $500
+0.00%
Kelly Optimal
Aggressive (40%)
Conservative (5%)
Simulation Statistics
Total Bets
0
Win Rate
—
Kelly Peak
$10K
Aggressive Bust?
No
How It Works

The Kelly Formula

f* = (bp - q) / b
f* = Fraction to bet
b = Win/loss ratio
p = Win probability
q = Loss probability (1-p)

Volatility Impact

Higher volatility = more uncertainty. Kelly is automatically reduced:

Volatilityvol_adjEffect
5-15%0.95-0.85Full Kelly
16-30%0.84-0.70Reduced
31-50%0.69-0.50Half Kelly

Over-betting Danger

Betting more than Kelly = "Gambler's Ruin"
The 40% strategy will almost certainly bust.

Under-betting Cost

Being too conservative is safe but...
You'll never reach maximum potential.

The Origin Story

John L. Kelly Jr., a physicist at Bell Labs, published the Kelly Criterion in 1956. He was inspired by his colleague Claude Shannon's Information Theory — realizing that the same math used to optimize data transmission over noisy channels could optimize betting over uncertain outcomes. Shannon himself used it to beat Las Vegas and the stock market.