The Mathematics of Ruin: The Kelly Criterion
The Mathematics of Ruin: The Kelly Criterion
The only formula that mathematically guarantees optimal wealth growth. Why betting too big is just as dangerous as betting on a loser.
Executive Summary
- The Problem: You have a winning edge (e.g., a stock with a 60% chance of winning). If you bet 1% of your capital, you grow too slowly. If you bet 100%, one loss wipes you out. What is the optimal number?
- The Formula (f*): Kelly Criterion calculates the exact percentage of your bankroll to bet to maximize Compound Growth (CAGR).
f* = (Odds * Win Probability – Loss Probability) / Odds
It balances the greed for growth with the fear of ruin. - Half-Kelly: In the real world, we don’t know the probabilities perfectly. So, pros use “Half-Kelly” (betting half the optimal amount). This captures 75% of the growth but reduces volatility (risk) by 50%. It is the “sleep well” optimization.
The Variance Drain
If you bet more than the Kelly optimal (“Over-betting”), your long-term return actually decreases due to “Volatility Drag” (mathematical friction), even if you keep winning. Sizing is more important than stock picking. A great pick sized wrong can destroy a portfolio.
Mechanic: The Optimal Bet Size
Maximize G
Geometric Growth
Zero Ruin
Survival Priority
Half-Kelly
Safety Margin
Over-Bet
Wealth Killer
Simulation: Betting on a 60% Win Rate (Coin Flip Bias)
Wealth Outcome after 100 Bets
| Feature | Arithmetic Approach | Kelly Approach (Geometric) |
|---|---|---|
| Goal | Highest Average Return | Highest Compound Growth |
| Risk Handling | Ignore variance | Penalize variance heavily |
| Application | One-off bets | Repeated bets (Investing) |
“To make money, you must have an edge. To keep money, you must not bet too much. The Kelly Criterion tells you exactly how much ‘too much’ is.”
Essential Resources
INTERNAL
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