What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to stake: f = (bp − q) ÷ b, where b is decimal odds minus 1, p is your estimated win probability, and q = 1−p. It maximises long-term bankroll growth for a given edge.

Why should I use fractional Kelly?

Full Kelly stakes can be very large when edge is high, creating significant drawdown risk. Most professional bettors use half or quarter Kelly to reduce variance. Half Kelly at the same expected edge delivers roughly 75% of full Kelly growth with dramatically less drawdown.

What happens if you bet more than Kelly suggests?

Over-betting beyond Kelly reduces long-term growth and increases ruin probability. Even a small over-bet (e.g. 1.5× Kelly) makes long-term growth negative. Kelly is an upper bound — betting below it is safe; betting above it is strictly worse in the long run.

The Kelly Criterion: The Math Behind Optimal Staking

The Formula

Kelly Criterionf* = (b × p − q) ÷ b
f* = fraction of bankroll to stake
b = decimal odds minus 1 (the net profit per unit)
p = your estimated probability of winning
q = 1 − p (probability of losing)

Worked Example

Available odds: 2.50. Your estimated win probability: 45%.

b = 2.50 − 1 = 1.50
p = 0.45, q = 0.55
f* = (1.50 × 0.45 − 0.55) ÷ 1.50 = (0.675 − 0.55) ÷ 1.50 = 0.125 ÷ 1.50 = 8.33%

Full Kelly says stake 8.33% of your bankroll. On a £1,000 bankroll that's £83.30.

Why Most Professionals Use Fractional Kelly

Full Kelly is theoretically optimal but brutal in practice — your probability estimates are never perfectly accurate, and even small errors can cause dramatically oversized bets. The standard professional approach is half Kelly (50%) or quarter Kelly (25%):

Version	Stake (£1,000 bankroll)	Drawdown risk	Growth rate
Full Kelly (100%)	£83.30	High	Maximum theoretical
Half Kelly (50%)	£41.65	Moderate	~75% of full Kelly
Quarter Kelly (25%)	£20.83	Low	~50% of full Kelly

Kelly's Key Assumptions

Your probability estimate is accurate — if it's wrong, Kelly prescribes the wrong stake
You are reinvesting winnings — Kelly is a growth formula, not a fixed-profit formula
You bet repeatedly on similar situations — it is a long-run optimiser
There are no withdrawal constraints — in practice, professional bettors adjust for bankroll management goals

When Kelly Gives a Negative Number

If f* is negative, the formula is telling you the bet has negative expected value — do not place it. This is Kelly's built-in filter: it automatically rejects -EV bets.

For a comprehensive look at how Kelly fits into an overall staking system, see our bankroll management guide and full Kelly Criterion breakdown.

The Kelly Criterion: Math Behind Staking

The Formula

Worked Example

Why Most Professionals Use Fractional Kelly

Kelly's Key Assumptions

When Kelly Gives a Negative Number