Kelly Criterion: Position Sizing for Long-Term Growth

The Problem With Fixed Stakes

Many bettors use a flat stake — say 2% of their bankroll on every bet. It's simple, but it ignores a crucial factor: not all edges are equal.

A bet where you have a 5% edge deserves a different stake than a bet where you have a 1% edge. Staking the same on both means leaving money on the table on strong edges and risking too much on weak ones.

This is where the Kelly Criterion comes in.

The Formula

The Kelly formula tells you the optimal fraction of your bankroll to stake on a bet, given your edge:

f = (bp − q) ÷ b

Where:

• f = fraction of bankroll to stake
• b = decimal odds − 1 (the net odds)
• p = your estimated probability of winning
• q = 1 − p (probability of losing)

Example

• Odds: 3.00 (so b = 2)
• Your probability: 40% (p = 0.40, q = 0.60)

f = (2 × 0.40 − 0.60) ÷ 2 = (0.80 − 0.60) ÷ 2 = 0.10

Kelly says stake 10% of your bankroll. This is the mathematically optimal amount to maximize long-term growth.

Why Full Kelly Is Dangerous

Full Kelly maximizes growth — but it also maximizes volatility. Your bankroll will swing wildly, and a small error in your probability estimate can lead to catastrophic losses.

This is why most professionals use fractional Kelly — typically half Kelly or quarter Kelly.

• Half Kelly (staking 5% instead of 10%): sacrifices some growth for dramatically reduced variance.
• Quarter Kelly (2.5%): even safer, ideal when your probability estimates are uncertain.

The Practical Takeaway

The Kelly Criterion teaches three essential lessons:

1. Stake proportional to edge. Bigger edge, bigger stake. Small edge, small stake.
2. Never over-stake. Going beyond Kelly (or beyond what your bankroll can handle) mathematically guarantees ruin over time.
3. Protect against estimation error. Your probability estimates will be wrong sometimes. Fractional Kelly gives you a buffer.

Key Takeaways

• Kelly tells you the optimal stake for long-term growth given your edge.
• Full Kelly is too volatile for real-world use — use fractional Kelly instead.
• Stake proportional to edge, not flat across all bets.
• Protecting your bankroll is always more important than maximizing growth.