Betting Stake Calculator

Developed by Bell Labs scientist John L. Kelly Jr. in 1956, the Kelly Criterion determines the optimal fraction of a bankroll to wager on a positive-expectation bet (+EV) to maximize the long-term geometric growth rate of capital while mathematically driving the probability of ultimate ruin to zero.

Formula: f* = (b × p - q) / b = (p × (b + 1) - 1) / b; Optimal Stake ($) = Bankroll × f* × Kelly Fraction

• f*: Fraction of current bankroll to wager on the wager
• b: Net decimal odds received on the wager minus 1 (profit per dollar staked, b = Decimal Odds - 1)
• p: Estimated true win probability (between 0.0 and 1.0)
• q: Estimated true loss probability (q = 1 - p)
• Kelly Fraction: Damping factor: Full Kelly (1.0), Half Kelly (0.5), Quarter Kelly (0.25)

• Standard +EV Bet at Even Money (+100 / 2.00): Decimal = 2.00 (b = 1.0); True win prob p = 54% (0.54), q = 0.46; f* = (1.0 × 0.54 - 0.46) / 1.0 = 0.08 (8%) = Full Kelly = $80 on a $1,000 bankroll; Half Kelly = $40 (4%)
• American Odds Favorite (-125 / 1.80 Decimal): Decimal = 1.80 (b = 0.80); True win prob p = 60%, q = 0.40; f* = (0.80 × 0.60 - 0.40) / 0.80 = 0.10 (10%) = Quarter Kelly recommended stake = $25 on $1,000 bankroll (2.5%)

While Full Kelly is mathematically optimal for compound growth, it is notoriously volatile in practice: bankroll drawdowns of 50% or more occur in over a third of simulations due to estimation error in true win probability. Professional sports bettors almost universally employ Half-Kelly (0.5x) or Quarter-Kelly (0.25x), which retains 75% to 85% of the growth rate while slashing bankroll volatility and variance by 50% to 75%.

Sports betting should strictly be treated as discretionary entertainment with capital you can afford to lose. No staking model guarantees profits or eliminates sports variance. If you or someone you know has a gambling problem, help is free and confidential 24/7. Call or text 1-800-GAMBLER (US) or visit Gamblers Anonymous.