Kelly Criterion Calculator Guide and Examples

The Kelly fraction is the bankroll percentage supported by your estimated win probability and the available payout. Full Kelly targets maximum theoretical long-run growth, but that target depends on an accurate forecast and executable odds.

A Kelly result at or below zero means your forecast does not beat the offered break-even probability. A wider estimated edge increases the suggested fraction, while a smaller payout or greater chance of losing reduces it.

Half Kelly stakes 50% of the formula result, while quarter Kelly stakes 25%. These smaller allocations sacrifice some theoretical growth to limit drawdowns when forecasts are noisy, biased, or correlated.

At even money, a 60% win estimate produces a 20% full-Kelly stake

Decimal odds of 2.00 break even at 50%, so a 60% win estimate creates a ten-point forecast edge and a 20% full-Kelly fraction. The calculation assumes that 60% estimate is well calibrated.

The 60% even-money inputs and result

●
decimal odds 2.00
●
win probability 60%
●
full-Kelly stake 20%

Use decimal odds to find the full-Kelly fraction

The decimal-odds form of the Kelly formula is:

Formula f* = (p * decimal_odds - 1) / (decimal_odds - 1)

With p=0.60, decimal=2.00, f*=0.20:

Substitution confirms the 20% allocation

Insert a 0.60 probability and 2.00 decimal price:

f* = (0.60 × 2.00 - 1) / (2.00 - 1)

f* = (1.20 - 1) / 1.00

f* = 0.20 / 1.00

f* = 0.20 (or 20%)

Result: A 60% win estimate at 2.00 decimal odds produces a full-Kelly allocation of 20% of bankroll.

Verify the 20% stake →

At +150, a 45% win estimate yields an 8.3% full-Kelly stake

The +150 payout converts to 2.50 decimal odds and a 40% break-even rate, so a 45% forecast leaves five points of edge and an 8.3% full-Kelly fraction.

The +150 underdog inputs and result

●
American +150 (decimal 2.50)
●
p=45%
●
full-Kelly 8.3%

Convert +150 before applying the formula

The +150 line becomes 2.50 decimal odds; use that value for f*:

f* = (p × decimal_odds - 1) / (decimal_odds - 1)

Math: (0.45*2.50-1)/(2.50-1)=0.0833 → 8.3%

Substitution confirms the 8.3% allocation

Insert p=0.45 and decimal odds of 2.50:

f* = (0.45 × 2.50 - 1) / (2.50 - 1)

f* = (1.125 - 1) / 1.50

f* = 0.125 / 1.50

f* = 0.0833 (or 8.3%)

Result: A 45% estimate at +150 produces a positive full-Kelly fraction of 8.3%; whether to act still depends on confidence in that estimate.

Verify the 8.3% stake →

A $1,000 bankroll turns a 10% Kelly fraction into a $100 stake

A 55% forecast at even money generates a 10% fraction, equal to $100 at full Kelly or $50 at half Kelly from $1,000. Solve for the percentage before multiplying by bankroll and applying the reduction.

The $1,000 bankroll inputs and dollar stakes

●
decimal 2.00
●
p=55%
●
bankroll $1000
●
full-Kelly 10%

Calculate the percentage before converting it to dollars

First solve the decimal-odds formula for f*:

f* = (p × decimal_odds - 1) / (decimal_odds - 1)

Math: (0.55*2.00-1)/(2.00-1)=0.10 → 10%

Multiplying by bankroll turns 10% into $100

Insert p=0.55 and decimal odds of 2.00:

f* = (0.55 × 2.00 - 1) / (2.00 - 1)

f* = (1.10 - 1) / 1.00

f* = 0.10 / 1.00

f* = 0.10 (or 10%)

Result: A 55% forecast at 2.00 decimal odds supports a full-Kelly stake of 10% of bankroll.

Multiplying by $1,000 gives a $100 full-Kelly stake; dividing that allocation in half gives $50 at half Kelly.

Check the $100 position →

Half Kelly uses 50% of the full-Kelly bankroll recommendation

A 20% full-Kelly result becomes a 10% bankroll allocation at half Kelly. That smaller commitment preserves more capital when the apparent edge is positive but its probability estimate is uncertain.

Half Kelly reduces exposure by 50%

●
even money
●
win probability 60%
●
full-Kelly 20%
●
half-Kelly 10%

The smaller position absorbs forecast error better

A halved stake reduces volatility and overbetting without abandoning positive expected value. Full Kelly maximizes theoretical growth only when probability and payout inputs are accurate, which real forecasts rarely guarantee.

One division converts full Kelly to half Kelly

Divide the calculated full-Kelly fraction once:

full-Kelly = (p × decimal_odds - 1) / (decimal_odds - 1)

half-Kelly = full-Kelly / 2

Sizing rule: Calculate full Kelly from your stated edge, then halve the result before converting the fraction to dollars.

Quarter Kelly limits the stake to 25% of the full-Kelly result

A 20% full-Kelly result becomes a 5% bankroll position at quarter Kelly. The wider discount better suits fragile estimates and exposures correlated with other positions.

Quarter Kelly reduces exposure by 75%

•
even money
•
win probability 60%
•
full-Kelly 20%
•
quarter-Kelly 5%

Use one-fourth of the calculated fraction

Divide full Kelly by four before multiplying by bankroll. The smaller allocation keeps exposure to the estimated edge while sharply limiting variance caused by a bad probability input.

Dividing 20% by four gives 5%

Take the previously calculated 20% full-Kelly fraction and divide it by four:

quarter-Kelly = full-Kelly / 4

quarter-Kelly = 20% / 4

quarter-Kelly = 5%

Result: A 60% forecast at even money becomes a 5% quarter-Kelly stake, favoring capital preservation over maximum theoretical growth.

Fractional Kelly limits losses caused by an overconfident probability

Full Kelly treats the probability input as accurate, so systematic overconfidence can repeatedly produce oversized positions. Choose a fraction when resilience to model error matters more than maximum theoretical growth.