Kelly Criterion

The Kelly Criterion answers one specific question: given a bet where you believe you have an edge, what fraction of your bankroll should you actually risk? It isn’t a way to find winning bets — you still need an independent estimate of the true win probability before Kelly does anything. What it does is turn that probability, combined with the price you’re being offered, into a stake size that maximizes how fast your bankroll compounds over a long series of bets, without betting so big that a bad run wipes you out.

The mechanics: convert the odds to a “net odds” figure, b, which is how much you win per $1 risked. At -110, a $110 bet returns $100 profit, so b = 100/110 = 0.909. At +150, b = 1.5. Let p be your true win probability and q = 1 - p be your loss probability. The Kelly fraction is f* = (bp - q) / b, which can also be written as f* = p - q/b. Plug in your numbers, and the output is the percentage of your bankroll to stake on that single wager.

The formula is sensitive in a way that surprises people the first time they use it. A tiny edge produces a tiny recommended stake — often under 2-3% of bankroll — while a large edge can spit out a number like 20% or more. That’s mathematically correct but practically reckless, because your probability estimate is a guess, not a certainty, and Kelly assumes you know p exactly. Get p wrong by a few points and “full Kelly” can push you into stakes that produce brutal drawdowns even when your long-run edge is real. That’s why almost nobody bets full Kelly in practice — they bet a fraction of it.

Example

Say you handicap an NFL side and land on a number you’re confident is worth 55% to win, but the book has it at -110 on both sides. Your bankroll is $5,000.

First, get b: at -110, b = 100/110 = 0.909.

Then apply f* = p - q/b:

• p = 0.55, q = 0.45
• q/b = 0.45 / 0.909 = 0.495
• f* = 0.55 - 0.495 = 0.055, or 5.5%

Full Kelly says stake 5.5% of $5,000 = $275 on this game.

Now check the math makes sense: at -110, the breakeven win rate is 52.4%. You think this game is a 55% winner, so your edge over the market is 2.6 percentage points. That’s a real but modest edge, and a 5.5% stake reflects that — not a wild swing, not a token bet.

Most disciplined bettors would use half-Kelly here instead, staking 2.75% of bankroll, or about $137.50. Half-Kelly gives up some long-run growth rate in exchange for roughly a 75% cut in variance, which matters enormously when your 55% estimate might really be 53% or 57% depending on how good your model is. If your probability estimate turns out to be even a couple points optimistic, that half-Kelly bet still leaves you solvent enough to keep betting; the full-Kelly bet compounds the error faster.

Key Points

• Your edge is the whole game: Kelly only works if your win-probability estimate is accurate. If you’re just guessing 55% because you like a team, Kelly will confidently size a bet around a number you made up. The formula doesn’t validate your handicapping — it only scales it.
• Use fractional Kelly, not full Kelly: Half-Kelly (or even quarter-Kelly for less-certain edges) sacrifices some theoretical growth rate but dramatically cuts variance and protects against overestimating your edge, which almost everyone does.
• Small edges mean small stakes, and that’s correct: If your model says a bet is only worth 51.5% against a 52.4% breakeven line, Kelly will (correctly) tell you there’s no edge at all — don’t force a bet just because you did the work to evaluate it.
• Recalculate per bet, not once: Your bankroll changes after every result, and so does the correct stake in dollar terms. Kelly is a percentage of current bankroll, so a losing stretch should shrink your stakes and a winning stretch should grow them — flat $100-a-game betting ignores this entirely.
• It’s built for bets you’ll repeat, not one-shot windfalls: Kelly maximizes long-run geometric growth across many wagers with independent edges. A single same-game parlay you’ll never see again isn’t really a Kelly problem — there’s no “long run” for the formula to optimize over.
• Correlated bets break the assumptions: Kelly assumes each stake is evaluated against your whole bankroll independently. If you’re firing five Kelly-sized bets on props from the same game, you don’t actually have five independent edges — you have one big correlated position wearing five different price tags.