Kelly Criterion Calculator

Worked example: sizing a 55% win probability at -110

Suppose you believe a side has a 55% chance to win, and the sportsbook is offering -110 (decimal odds of 1.909). Converting to Kelly's variables: b is the net odds returned on a win, or 0.909 (1.909 minus 1); p is your win probability, 0.55; q is the probability of losing, 0.45.

Kelly's formula is f* = (bp − q) / b. Multiply b by p: 0.909 × 0.55 = 0.500. Subtract q: 0.500 − 0.45 = 0.050. Divide by b: 0.050 / 0.909 = 0.055, or 5.5% of bankroll. On a $1,000 bankroll, full Kelly recommends a $55 stake on this single bet.

Half-Kelly cuts that recommendation to 2.75% of bankroll, or $27.50 on the same $1,000 bankroll; quarter-Kelly trims it further to 1.375%, or roughly $13.75. Each fractional step gives up some theoretical long-run growth in exchange for meaningfully smoother bankroll swings — a trade most bettors accept because a 55% estimate is itself uncertain, and full Kelly sizing is unforgiving of an overstated edge.

Full Kelly vs. fractional Kelly vs. flat staking

Full Kelly maximizes the expected logarithmic growth rate of a bankroll over a long series of bets, but only if every input — the price and, especially, the win probability — is exactly correct. Overstate an edge even slightly and full Kelly systematically oversizes bets, which shows up as sharper drawdowns and a real chance of ruin over a long enough losing streak.

Half- and quarter-Kelly exist because probability estimates are never perfect. Betting a fraction of the full Kelly stake sacrifices some long-run growth in exchange for a smoother bankroll curve and far lower sensitivity to an overconfident probability estimate — a half-Kelly bettor who overstates an edge by a wide margin still ends up in much better shape than a full-Kelly bettor who makes the same mistake.

Flat staking — risking the same fixed unit on every bet regardless of perceived edge — trades away Kelly's theoretical growth advantage entirely in exchange for simplicity and predictable variance. It suits a bettor who isn't confident their probability estimates are well calibrated, since Kelly and its fractional variants only outperform flat staking when the underlying edge estimate is genuinely accurate; a miscalibrated model can make full Kelly sizing actively harmful.

Why Kelly punishes an overstated edge

The 5.5% Kelly stake above assumed the 55% win-probability estimate was correct. Suppose the true win probability is actually only 50%, not 55% — a common-enough sizing error. At -110, breakeven sits at the market's own 52.38% implied probability, so a true 50% win rate means this bet is actually −EV: the bettor loses money on it on average, in the exact scenario where the Kelly formula, fed the wrong 55% input, still says to risk 5.5% of bankroll.

That sensitivity is the core argument for stress-testing a Kelly input before sizing off it, and for scaling down with half- or quarter-Kelly when the probability estimate itself carries real uncertainty. A bettor using flat units in the same spot risks the same fixed amount whether their read was right or wrong; a full-Kelly bettor with an inflated probability estimate compounds that error into every stake size, which is why fractional Kelly is the more common choice outside of a model with a long, verified calibration record.

Kelly reference: stake size at -110 by win probability

Holding the price at -110 and varying only the win-probability estimate shows how directly full Kelly scales with edge: 52% recommends no bet at all, because -110 already needs 52.38% just to break even. 53% recommends 1.3% of bankroll, 54% recommends 3.4%, 55% recommends 5.5%, 56% recommends 7.6%, 58% recommends 11.8%, and 60% recommends 16.0%. At a fixed price, each extra point of win probability above breakeven adds a constant 2.1 points to the recommended stake; the recommendation only starts counting from zero at the breakeven line, which is why the first few points above it produce such an outsized swing in the stake.

The jump from 55% to 60% roughly triples the recommended stake, even though the probability estimate only moved five percentage points — a reminder that Kelly sizing is far more sensitive to a probability estimate near the break-even line than intuition about 'a bit more confident' usually suggests. Small, defensible edges call for correspondingly small stakes; only a large, well-supported edge justifies a double-digit percentage of bankroll on one bet.

Holding the win-probability estimate fixed at 55% and varying only the price tells the complementary story: at -150, full Kelly recommends no bet (breakeven there is 60%); at -130, also no bet (breakeven is 56.52%); at -110, 5.5%; at +100, 10.0%; at +120, 17.5%; and at +150, 25.0%. The same 55% opinion swings from unplayable to a quarter of the bankroll purely because the price on offer changed — which is exactly why shopping for the best available number on a bet you already like is worth as much attention as the probability estimate itself.

Where the Kelly formula comes from

Kelly sizing exists to maximize the geometric growth rate of a bankroll, not the arithmetic average outcome of a single bet — a subtlety that explains why it re-bases every stake off the current bankroll instead of a fixed dollar figure. Starting from a $1,000 bankroll, a win on the $55 stake at -110 pays exactly $50.00 in profit (55 × 100 ÷ 110), growing the bankroll to $1,050; a loss the same day drops it to $945 instead.

The next bet's stake is recalculated as 5.5% of whichever number the bankroll actually is — $57.75 after the win, $51.98 after the loss — never a flat $55 repeated indefinitely. That continuous re-basing on the current bankroll, compounded bet after bet, is what produces Kelly's characteristic geometric growth curve, and it's also why a single catastrophically oversized stake can do outsized damage: a bankroll cut in half needs a 100% gain, not a 50% one, to get back to even.

Kelly across a losing streak

Five consecutive losses at a fixed 5.5% full-Kelly stake — each loss shrinking the base the next stake is drawn from — leave a $1,000 bankroll at roughly $753.63, a 24.6% drawdown, even though no single loss removed more than 5.5% of whatever the bankroll happened to be at the time. That compounding drawdown is the visceral case for half- or quarter-Kelly: the same five-loss streak at half-Kelly (2.75% per bet) leaves the bankroll at roughly $869.86, a much shallower 13.0% drawdown, purely from cutting the stake fraction in half.

The same compounding works in reverse on a winning streak. At -110, a 5.5% Kelly stake happens to grow the bankroll by a clean 5% on every win (0.055 stake fraction × 0.909 net odds ≈ 0.05), so five straight wins take a $1,000 bankroll to roughly $1,276.28 — noticeably more than the $1,250 that five flat $55 wins would produce (each flat win pays the same $50 profit, for $250 total), a roughly $26 gap that comes entirely from each win's profit being calculated on a bankroll that already includes every prior win, and that gap compounds much further over a long enough winning stretch.

A few more stake sizes worth memorizing

A handful of other price-and-probability pairs, for spot-checking this calculator: a 52% win probability at -105 (breakeven 51.22%) recommends 1.6% of bankroll; a 57% win probability at -125 (breakeven 55.56%) recommends 3.25%; a 62% win probability at +105 (breakeven 48.78%) recommends 25.81%; and a 65% win probability at +140 (breakeven 41.67%) recommends a full 40% of bankroll. That last figure is exactly why very large edges deserve extra scrutiny before betting them at full Kelly — a genuine 65%-versus-41.67% mismatch is rare enough that it is worth double-checking the probability estimate rather than trusting the formula's output at face value.