The Kelly Criterion: How Much to Bet
Finding a +EV bet is only half the job. The other half is sizing it — bet too big and one cold streak busts you, bet too small and you leave growth on the table. The Kelly criterion solves for the sweet spot.
The problem Kelly solves
Say you've found a genuine 5% edge. How much of your bankroll should ride on it? Bet your whole roll and a single loss wipes you out — even a sure-thing strategy goes to zero if you ever risk everything on a bet that can lose. Bet a single dollar and you'll never grow. Somewhere between "too reckless" and "too timid" is a mathematically optimal stake. That's what the Kelly criterion finds.
Developed by physicist John Kelly at Bell Labs in 1956, it's the bet size that maximizes the long-term growth rate of your bankroll. Bigger edge → bigger bet. Thinner edge → smaller bet. It scales your risk to your advantage, automatically.
The formula
For a single bet, Kelly says wager this fraction of your bankroll:
Work an example. You bet an underdog at +150 (decimal 2.50, so b = 1.5). You believe its true probability is 45% (p = 0.45, q = 0.55):
Full Kelly says bet 8.3% of your roll. On a $2,000 bankroll, that's a $166 bet. Notice the edge here is healthy, so Kelly sizes up. On a razor-thin 1% edge, the same formula would tell you to bet a tiny sliver — which is exactly the point.
Kelly is only as good as your probability estimate. Feed it an inflated edge and it will tell you to bet dangerously large. Garbage probability in, reckless stake out — which is why an accurate, devigged sharp line matters so much.
Why pros bet fractional (half) Kelly
Full Kelly is mathematically optimal only if your probabilities are exactly right. In the real world they never are — you're estimating, and estimates have error. Full Kelly is also savagely volatile: it's normal to see your bankroll cut in half on the way to growth. Most people can't stomach that, and overbetting a slightly-wrong edge can flip you from +EV to going broke.
The fix professionals use is fractional Kelly — betting a fixed fraction of the full Kelly number, most commonly half (or even quarter) Kelly:
| Strategy | Stake on our example | Volatility |
|---|---|---|
| Full Kelly | 8.3% ($166) | Very high |
| Half Kelly | 4.2% ($83) | Far smoother |
| Quarter Kelly | 2.1% ($42) | Conservative |
The trade is remarkable: half Kelly keeps about three-quarters of the growth rate while cutting the volatility roughly in half. For imperfect human edges, that's almost always the better deal — and it builds in a safety margin against overestimating your edge.
Why not just flat-bet?
Flat betting — the same stake every time, say "one unit" — is simple and far better than betting randomly. But it ignores edge size: it risks the same amount on a 1% edge as on a 10% edge. Kelly fixes that by pouring more onto your strongest spots and less onto your weakest, which compounds meaningfully faster over thousands of bets. Flat betting is a fine floor; Kelly is the ceiling.
How it fits the +EV workflow
Stake sizing is the last step of a complete process. To bet a correct Kelly fraction you need a trustworthy probability and a real edge:
- Remove the vig from a sharp line to get a true probability.
- Find a book whose price beats that fair value — a +EV bet.
- Plug the edge into Kelly, then bet a fraction of it.
- Confirm you're beating the closing line over time.
Doing this by hand on every bet is a chore. Iron Marker computes the fractional-Kelly stake for every +EV bet it surfaces, using the same devigged probability it found the edge with — so the right bet size is already on the screen.
Frequently asked questions
What is the Kelly criterion in betting?
The Kelly criterion is a formula that tells you what fraction of your bankroll to wager to maximize long-term growth, given your edge and the odds. Worked example: at +100 (even money) with a true win probability of 52%, Kelly stakes (0.52 × 1 − 0.48) / 1 = 4% of your bankroll. The bigger your edge, the larger the bet; the smaller the edge, the smaller the bet; no edge, no bet. What makes Kelly special is that it balances two competing pressures mathematically — growing the bankroll as fast as possible while making ruin essentially impossible, because stakes shrink automatically whenever the bankroll does.
What is fractional or half Kelly?
Fractional Kelly means betting a fixed fraction of the full Kelly stake — if the formula says 4% of bankroll, half Kelly bets 2% and quarter Kelly bets 1%. Bettors do this because full Kelly is only optimal when your probability estimates are exactly right, and in practice they never are. Overestimating your edge means full Kelly systematically over-bets, which damages long-run growth far more than under-betting does. Fractional Kelly buys a large reduction in volatility at a modest cost in growth — half Kelly keeps roughly three-quarters of full Kelly's growth rate with dramatically smaller swings. That asymmetry is why shading Kelly down is standard professional practice, not a timid deviation from it.
Why not just bet the same amount every time?
Flat betting ignores the size of your edge — it risks the same amount on a razor-thin edge as on a huge one, so your money isn't working hardest where your advantage is largest. It also ignores your bankroll: a flat $100 bet is conservative when you're running well and dangerously large after a drawdown. Kelly sizing fixes both at once — stakes scale up with edge and shrink automatically as the bankroll falls, which is what makes properly sized Kelly bettors nearly impossible to bust. That said, flat betting isn't crazy: it's simple and it protects you from overconfident estimates. A disciplined flat bettor beats an undisciplined Kelly bettor; Kelly is the refinement, not the prerequisite.
What Kelly fraction do most pros use and why?
Half Kelly and quarter Kelly are the standard professional range, and the reasoning is about estimation error, not nerves. Kelly's output is only as good as the win probability you feed it, and every real-world probability is an estimate. If your true edge is smaller than you believe, full Kelly quietly becomes over-betting — and betting beyond the true Kelly stake reduces long-run growth while inflating risk. Shading down makes the strategy robust to being somewhat wrong, which everyone is. Bettors whose probabilities come from a strong reference — like a devigged sharp line — can justify the higher end; bettors relying on their own models or noisy prop markets tend to sit at a quarter or below.
How do I use Kelly when I have several bets open at once?
Strict Kelly theory assumes one bet at a time, settled before the next — real betting isn't like that. The practical approach: compute each bet's Kelly stake from your current bankroll, accept that simultaneous bets push total exposure above what pure theory prescribes, and compensate by running a smaller Kelly fraction overall. Two refinements matter. First, treat correlated bets — same game, same team, the same outcome dressed up in different markets — as one position, because their risk stacks rather than diversifies. Second, cap total open exposure at a fixed share of bankroll and skip the thinnest edges once you reach it. A conservative fraction plus a correlation rule captures most of the theory's benefit without the math degree.
The right stake, already calculated.
Iron Marker finds +EV bets against Pinnacle's sharp line and shows you the fractional-Kelly stake for each one — no spreadsheet required. $39/mo, 7-day free trial.
Start free trialIron Marker is an analytics tool, not a sportsbook, and this guide is educational — not betting or financial advice. The Kelly criterion does not guarantee profit and assumes an accurate edge estimate. Never bet more than you can afford to lose. Must be 21+. Problem gambling? Call 1-800-GAMBLER.