Kelly Criterion Calculator

The formula is f* = (bp − q) / b, where b is net decimal odds. At −110, b = 0.9091. Here is what Kelly actually recommends at three self-assessed win probabilities — note how fast the stake grows with small changes in p:

All exact formula math. The middle row is the realistic ceiling: a bettor who truly wins 55% against the closing line is very good, and Kelly still says to risk only a few percent. The bottom row is the trap — 58% is a claim almost nobody can back up over a large sample, yet it commands a 12% stake that will produce brutal swings if the true rate is lower.

Kelly assumes you know p exactly. You never do. The asymmetry is what hurts: overbetting a too-optimistic estimate costs more than underbetting a too-pessimistic one. Concretely, suppose your true skill is 52% but you size bets as if it were 58%. At −110, a 52% bettor has EV of 0.52 × 0.9091 − 0.48 = −0.007 per unit — you are actually a small loser, and full Kelly for the imagined 58% edge has you losing 0.7 cents on every dollar while staking 11.8% of your bankroll each time. Fractional Kelly is insurance against your own estimates.

Losing streaks are guaranteed, not hypothetical. Even for a genuine 55% bettor, any given run of five bets ends in five straight losses with probability 0.45⁵ = 1.8%. Across a 250-bet season there are 246 overlapping five-bet windows, so the expected number of such streaks is about 4.5 (an expectation, not a probability — windows overlap). Plan stake sizes so that the inevitable streak is an annoyance, not a wipeout.

Two anchors, one from probability and one from the bundled game data:

• Binomial noise. Over 100 bets, a true 55% bettor lands on 55 wins on average with a standard deviation of √(100 × 0.55 × 0.45) ≈ 5.0 wins. Roughly 95% of such seasons fall between 45 and 65 wins, and the chance of finishing with a losing record (49 wins or fewer) is about 13% (normal approximation). A losing quarter tells you almost nothing about your skill.
• Game-level noise. Across 7,276 completed NFL games from 1999–2025, the final margin missed the closing spread by 10.3 points on average, with a standard deviation of 13.2 points. The market's best estimate misses by a touchdown and a field goal on a typical Sunday — your model will too.

Data: nflverse games.csv bundled with this site (7,276 completed games, 1999–2025), computed by the author. Binomial figures are exact formula math.

Kelly's formula assumes one bet at a time, settled before the next. NFL betting is nothing like that — a typical card has several positions riding the same afternoon. Exact math on why that demands smaller stakes:

• Five half-Kelly bets of 2.75% each (the p = 55% row above) put 13.75% of the bankroll in play at once.
• For a genuine 55% bettor, all five losing has probability 0.45⁵ = 1.8% — roughly one Sunday in 54. Over an 18-week season of similar cards, expect it to happen about once every three seasons.
• And that assumes independence. Two favorites in the same weather system, or a teaser sharing a side with a straight bet, lose together more often than the multiplication suggests.

The practical adjustment used by professionals: compute Kelly per bet, then scale the whole card down so total same-day exposure stays inside your single-bet ceiling — or treat the card, not the bet, as the unit you size. Slower, and much harder to ruin. All figures above are exact formula math on stated assumptions.

• Kelly optimizes growth, not comfort. Even correctly-sized Kelly betting produces drawdowns most people find intolerable; that is a feature of the math, not a bug in the calculator.
• The formula assumes independent, sequential bets. A Sunday slate of simultaneous bets on correlated outcomes (same teams, teasers, parlays) needs smaller stakes than Kelly's one-bet answer.
• Dollar figures on this page are illustrative. The percentages are the content; scale them to money you can afford to lose entirely.
• No stake size turns a negative edge positive. Sizing manages variance; it cannot manufacture EV.