Kelly Criterion Calculator — Optimal Bet Sizing Formula

Using the Kelly Criterion calculator takes only seconds. Enter three values: your estimated win probability as a percentage (e.g. 55%), the decimal odds offered by the bookmaker (e.g. 2.10), and your total bankroll in dollars. Click "Calculate Kelly Stake" and the tool instantly shows your recommended stake in dollar terms across three risk levels.

The primary output is the Half Kelly stake — this is what most professional bettors actually use. The Full Kelly is the theoretical maximum, but it produces extreme bankroll volatility in practice. Quarter Kelly is the conservative option suitable for uncertain probability estimates.

If the calculator shows a "No edge" warning, your estimated win probability is below the break-even threshold for those odds. The Kelly formula returns a negative number in this case, which means the mathematically correct bet size is zero — do not place the wager.

The Kelly Criterion formula calculates the fraction of your bankroll to wager:

1. Define inputs:
   • p = win probability (as a decimal, e.g. 0.55)
   • q = loss probability = 1 − p
   • b = net odds = decimal odds − 1 (e.g. 2.10 − 1 = 1.10)
2. Kelly fraction: f* = (b × p − q) / b
3. Stake: Bet = f* × Bankroll
4. Half Kelly: Bet = (f* / 2) × Bankroll (recommended)
5. Quarter Kelly: Bet = (f* / 4) × Bankroll (conservative)

If f* ≤ 0, the formula signals no positive edge exists at those odds and probability — the correct action is to not bet. The formula only recommends action when your estimated edge is real and positive.

The Kelly formula was published by John L. Kelly Jr. at Bell Labs in 1956 as a method for maximizing the long-run growth rate of a portfolio. It achieves the highest geometric growth rate possible given accurate probability estimates, but it also produces the highest variance — which is why most practitioners use fractional Kelly.

Example 1 — Standard Sports Bet

You believe Team A has a 55% chance of winning. The bookmaker offers decimal odds of 2.0 (even money). Your bankroll is $1,000.

• b = 2.0 − 1 = 1.0
• p = 0.55, q = 0.45
• f* = (1.0 × 0.55 − 0.45) / 1.0 = 0.10 (10%)
• Full Kelly stake: 10% × $1,000 = $100
• Half Kelly stake: $50 (recommended)
• Quarter Kelly stake: $25 (conservative)

At 55% win probability with even money odds, your edge is 10% per bet. The Kelly formula recommends committing 10% of your bankroll. Most professional bettors would use the half Kelly of $50 to reduce variance while still capturing most of the long-run growth benefit.

Example 2 — High-Odds Underdog with Strong Edge

You have strong model-based reasons to believe a team has a 60% win probability, but the market only prices them at 2.5 decimal odds (implying 40%). Bankroll: $5,000.

• b = 2.5 − 1 = 1.5
• p = 0.60, q = 0.40
• f* = (1.5 × 0.60 − 0.40) / 1.5 = (0.90 − 0.40) / 1.5 = 0.50 / 1.5 ≈ 0.333 (33.3%)
• Full Kelly stake: 33.3% × $5,000 = $1,667
• Half Kelly stake: $833 (recommended)

A 33% Kelly fraction is large, which reflects the significant edge you have identified. However, a 60% probability estimate carries uncertainty. The half Kelly of $833 captures most of the mathematical edge while dramatically reducing the risk of bankroll ruin if your estimate is slightly off.

Why Half Kelly is the Standard Recommendation

Full Kelly maximizes the geometric growth rate of your bankroll over the long run — but only if your probability estimate is exactly correct. In practice, all estimates contain error. Research shows that if your true edge is even slightly lower than estimated, full Kelly causes severe drawdowns. Half Kelly reduces variance by 75% while sacrificing only 25% of expected growth rate. For most bettors, this tradeoff is clearly worthwhile.