Kelly Criterion

The Kelly Criterion is a staking formula that John L. Kelly Jr. cooked up in 1956 to pin down the mathematically optimal slice of your bankroll to put on a positive-expected-value bet. It threads the needle between two goals that pull in opposite directions: growing your bankroll as fast as possible and never blowing it up. By scaling every wager to your perceived edge and the price on offer, Kelly compounds faster than any rival staking method over the long haul, all while refusing to risk so much on one bet that a single loss wrecks you.

Here is the engine: Kelly % = (bp - q) / b, where b is the decimal odds minus 1, p is your win probability, and q is your loss probability (1 - p). The output is the fraction of your bankroll to stake. In the real world, plenty of bettors run a fractional Kelly, staking a quarter or a half of the full number to tame the volatility that aggressive sizing brings. Full Kelly is optimal on paper, but the swings it produces are stomach-churning for most people.

Example

Say you peg a team at a 60% chance to win and the book hangs +120 (decimal 2.20). Plug it in: b = 1.20, p = 0.60, q = 0.40. Kelly % = (1.20 x 0.60 - 0.40) / 1.20 = (0.72 - 0.40) / 1.20 = 0.267, or 26.7% of your bankroll. On a $1,000 bankroll, full Kelly says stake $267. Most bettors would dial that back to half Kelly ($133.50) or quarter Kelly ($66.75) to smooth the ride and hedge against the chance that 60% read is a touch off.

Key Points

• Maximizes long-term growth: Of every fixed-fraction staking strategy out there, Kelly compounds a bankroll fastest when your probability reads are accurate.
• Sensitive to probability errors: Get your true win probability even a little wrong and Kelly can hand you stakes that are too big, ramping up your drawdown risk.
• Fractional Kelly is standard practice: Seasoned bettors usually run a fraction (25% to 50% is common) of full Kelly to cut volatility and build in a cushion for estimation mistakes.
• Never bets on negative EV: With no edge, the formula spits out zero or a negative figure, confirming you should stake nothing.
• Dynamic sizing: Kelly resizes automatically as your bankroll moves, betting more after wins and less after losses.