Kelly Betting Calculator

Use this free Kelly betting calculator to find the optimal bet size for a sports bet. Enter your odds, estimated win probability, and bankroll to calculate a Kelly Criterion bet size.

The Kelly Criterion Formula

The Kelly Criterion formula recommends the percentage of your bankroll to wager on a given bet, with the goal of optimizing your bankroll's growth rate.

Here's the standard formula:

f* = (bp - q) / b

Here's what each variable means:

f* = the fraction of your bankroll to wager
b = the net odds you're being paid ("b" to 1 odds, or decimal odds - 1)
p = your estimate of the win probability (0 to 1)
q = your estimate of the probability of a loss (1 - p)

Basically, the Kelly Criterion compares your edge to the payout. If your bet is +EV, it's recommended to bet a certain percentage of your bankroll. If not, you should bet $0.

How the Kelly Criterion works

To use the formula, you need to know your bankroll, the odds you're getting, and an estimate of the win probability of the bet. Once you plug those numbers in, the formula will give you the optimal bet size.

Example

You estimate your bet has a 55% chance to win and the sportsbook has odds of -110 (that's 1.91 in decimal odds and .5238 in implied probability). If your win estimate of 55% win probability is correct, you have an edge. Looking at the formula:

f* = (bp - q) / b

Then plug in the numbers:

f* = (.91 * 0.55 - 0.45) / .91

f* = 5%

The Kelly Criterion would recommend betting about 5.5% of your bankroll. That's a bet of about $55 with a bankroll of $1000.

Why the Kelly Criterion is relevant

A bettor can know how to spot value still under- or over-bet, and over-betting can lead to ruin. The Kelly Criterion partially address that problem by systematically sizing your bets.

Practical note

The Kelly Criterion is only as good as your probability estimate. If you overestimate your edge, the formula will tell you to bet too much. Most bettors use fractional Kelly rather than full Kelly for this reason.

Full Kelly vs Fractional Kelly

Full Kelly and fractional Kelly use the same formula. The difference comes from how much of the recommended stake you actually bet.

Full Kelly means betting 100% of the Kelly recommendation
Half Kelly means betting 50% of the Kelly recommendation
Quarter Kelly means betting 25% of the Kelly recommendation

If full Kelly says to bet 6% of bankroll, then:

Full Kelly = 6%
Half Kelly = 3%
Quarter Kelly = 1.5%

Full Kelly

Full Kelly is the mathematically optimal strategy for maximizing long term bankroll growth if your edge estimates are perfectly accurate, but that's a big "if".

One problem is that full Kelly is too aggressive for sports betting because there's so much variance in sports outcomes, so edge estimates are almost never exact. That makes it extremely easy to overestimate edge.

Fractional Kelly

Fractional Kelly reduces the size of each bet by using only part of the full Kelly recommendation. This lowers volatility, reduces drawdowns, and gives you more room for error. You can overestimate your edge and still not over-bet.

Fractional Kelly will give you slower bankroll growth than full Kelly, but it's the more practical approach.

Which is better, Fractional or Full Kelly?

Here's a good rule of thumb:

Full Kelly: Don't use for sports betting.
Half Kelly: Use if your edge estimate is based on more than just your own model (e.g., market signals in top-down betting).
Quarter Kelly: Use if your edge estimate comes from your own model or handicapping.

Summary

Full Kelly maximizes growth on paper, but only when win probability can be reliably estimated. Fractional Kelly is much safer, especially for things like sports betting, which are highly volatile.