## The Most Important Formula in Bankroll Management
The Kelly Criterion, developed by J.L. Kelly Jr. in 1956, calculates the mathematically optimal fraction of your bankroll to stake on a bet, given your estimated edge and the odds.
## The Formula
Kelly Fraction (f*) = (bp - q) / b
Where:
- **b** = net decimal odds (decimal odds − 1). At 2.50 odds, b = 1.50.
- **p** = your estimated probability of winning
- **q** = 1 − p (probability of losing)
**Example:**
Odds: 2.50. Your estimated win probability: 45% (implied: 40%).
f* = (1.50 × 0.45 − 0.55) / 1.50
f* = (0.675 − 0.55) / 1.50
f* = 0.125 / 1.50 = **0.0833 = 8.33% of bankroll**
## What Full Kelly Means
At full Kelly, you are mathematically maximising the long-run geometric growth of your bankroll. This is not the same as maximising expected value per bet — it is maximising the rate of bankroll growth over many bets.
## The Kelly Constraint
Kelly only makes sense when you have genuine edge: p > 1/(1+b). If p < this value, Kelly gives a negative fraction — meaning you should not bet at all.
## Why Bettors Rarely Use Full Kelly
Full Kelly is mathematically optimal but psychologically brutal. A run of incorrect probability estimates can generate enormous stakes, and the resulting drawdowns are extreme. Most practitioners use a fraction of Kelly (described in the next lesson).
## The Key Insight
Kelly connects your probability estimates directly to your staking. The better your estimates, the closer you can safely run to full Kelly. Poor probability estimates = dangerous full-Kelly stakes.
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