Kelly Criterion Staking

The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 to maximize the long-run growth rate of a bankroll. It tells you the optimal fraction of your bankroll to bet given your estimated edge and the odds on offer.

The Kelly Formula

The formula is: f = (bp - q) / b

Where:

• f = fraction of bankroll to bet
• b = decimal odds minus 1 (the net profit per unit wagered)
• p = your estimated probability the bet wins
• q = 1 - p (probability the bet loses)

For a bet at -110 (decimal 1.909) where you estimate a 55% win rate: b = 0.909, p = 0.55, q = 0.45 f = (0.909 x 0.55 - 0.45) / 0.909 = (0.500 - 0.45) / 0.909 = 0.055

Kelly says bet 5.5% of your bankroll.

Why Kelly Works

Kelly maximizes the geometric mean of your wealth over time. Bet more than Kelly and you grow slower over the long run and risk ruin faster. Bet less than Kelly and you grow slower but more safely. Kelly is the point where long-run growth is fastest.

The Problem With Full Kelly

Full Kelly can require very large bets when you believe you have a significant edge. A bettor who estimates 60% on a coin flip would bet 20% of their bankroll on a single toss. Most professional bettors find this volatility psychologically unmanageable, and the downswings can be severe enough to force you to quit a mathematically profitable approach.

Fractional Kelly

Most professionals use half-Kelly or quarter-Kelly. If full Kelly says bet 5%, half-Kelly says bet 2.5%. This dramatically smooths out variance at the cost of slightly slower growth. For most recreational bettors, quarter-Kelly is ideal.

Edge Estimation Is Everything

The Kelly formula is only as good as your probability estimate. If you think you win 55% of the time but your true rate is 51%, Kelly will tell you to bet far more than you should. Overestimating your edge is the most common mistake. Many bettors using Kelly would be better served by flat betting simply because their edge estimates are not reliable enough.

Applying Kelly in Practice

Start by keeping detailed records of your bets and outcomes. After 500 or more bets, calculate your actual win rate by bet type, sport, and market. Use those historical rates as your probability estimate. Apply half-Kelly to those estimates. Review and recalibrate quarterly.

Kelly and Multiple Simultaneous Bets

When you have multiple bets live at the same time, the standard Kelly calculation is no longer strictly optimal. Simultaneous Kelly requires solving a system of equations. In practice, most bettors simply divide their Kelly fraction by the number of simultaneous open bets to approximate safe sizing.