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Why stake size matters
Finding +EV bets is half the job. The other half is betting amounts that let the edge work without a bad run wiping you out. Bet too little and the edge barely moves your bankroll; bet too much and normal variance can cut it in half. A bankroll is money you set aside for betting and can afford to lose. Stakes are sized as a share of it.
The Kelly criterion
Kelly picks the stake that maximises the long-run growth rate of your bankroll, given your edge and the odds:
f* = (b × p − q) ÷ b
b = decimal odds − 1 (net odds), p = fair win probability, q = 1 − p
f* = 0 when the bet is −EV: no bet
Kelly depends on the odds as well as the edge. The same EV at longer odds gets a smaller stake, because the bet loses more often.
Worked examples
Fair 52% at +100: b = 1; f* = (0.52 − 0.48) ÷ 1 = 4.0%; EV +4%
Fair 55% at +100: f* = 10%; EV +10%
Fair 40% at +200: b = 2; f* = (2 × 0.40 − 0.60) ÷ 2 = 10%; EV +20%
The +200 bet has twice the EV of the second one but the same Kelly stake, because it wins only 40% of the time.
The Account page's example uses a +4% EV bet at −105 (decimal 1.95). The fair probability is 1.04 ÷ 1.95 = 53.33%.
Full Kelly = (0.95 × 0.5333 − 0.4667) ÷ 0.95 = 4.21%
Quarter Kelly = 1.05% → $10.53 on a $1,000 bankroll
Full, half and quarter Kelly on one bankroll
A $5,000 bankroll and a bet the market prices at 54% fair, offered at −105 (decimal 1.9524). EV = 0.54 × 1.9524 − 1 = +5.43%.
| Sizing | Share of bankroll | Stake |
|---|---|---|
| Full Kelly | 5.70% | $285.00 (capped to $250.00 at a 5% cap) |
| Half Kelly | 2.85% | $142.50 |
| Quarter Kelly (site default) | 1.425% | $71.25 |
| Flat 1 unit (1%) | 1.00% | $50.00 |
The cap only binds on full Kelly here. Caps exist for the bets where the estimated edge is large, which are exactly the bets where the estimate is most likely to be wrong.
Why an overestimated edge makes full Kelly dangerous
Suppose you think a coin-flip-priced bet at +100 wins 53.5% of the time, but it really wins 51.5%. You've overestimated by two points, an easy mistake with a stale line or a thin market.
Kelly from your estimate: (0.535 − 0.465) ÷ 1 = 7.0%; true Kelly: 3.0%
Expected log growth per bet: g = p × ln(1 + b × f) + q × ln(1 − f), at the TRUE p = 0.515
Betting 7.0% (your full Kelly): g = −3.53 basis points per bet: the bankroll shrinks
Betting 3.5% (your half Kelly): +4.38; betting 1.75% (your quarter Kelly): +3.72
Betting the true Kelly 3.0%: +4.50, the most possible
The bet is genuinely +EV (+3%), and full Kelly on your estimate still loses money over time because it overbets by more than double. Half Kelly on the same wrong estimate keeps 97% of the best possible growth. That asymmetry, overbetting is punished much harder than underbetting, is the real argument for fractional Kelly.
Why bet a fraction
Full Kelly assumes your fair probability is exactly right. It never is. If you overestimate your edge, full Kelly overbets, and overbetting hurts growth far more than underbetting. Full Kelly also swings hard: deep drawdowns are normal along the way. Most professionals bet a fraction, a quarter to a half of Kelly. A half-Kelly bettor keeps most of the growth rate with much smaller swings.
On the site, the Bankroll & staking section of the Account page sets three things that every Kelly figure uses:
- Bankroll: default $1,000.
- Kelly ×: the fraction, default 0.25 (quarter Kelly).
- Cap: the most any single bet can be, default 5% of bankroll.
The +EV finder's Kelly column and the detail drawer's "Why this is +EV" block show the resulting stake in dollars and percent.
Practical rules
- Size off the fair you trust. If a fair is modelled or backed by few books, size down or skip.
- Simultaneous bets. Kelly is for one bet at a time. Many bets on the same slate, or correlated bets on one game, together risk more than any one suggests. A cap helps.
- Re-size as the bankroll changes. Kelly is a share of the current bankroll, not the starting one.
- Flat units are fine. A flat 1% per bet is simpler and close to fractional Kelly for small edges near even money.
Units versus Kelly
Many bettors use flat units: the same 1% of bankroll on every bet. Units are simple, easy to track and hard to get badly wrong. Their weakness is that they treat a 1% edge and a 6% edge the same. Kelly sizes by edge and odds, so strong edges get more and marginal ones get less.
A middle path works well: compute quarter Kelly, then cap it. In the example above, quarter Kelly is 1.43% against a flat 1%, close enough that units lose little on typical near-even-money bets. The difference grows as edges get bigger or smaller: Kelly bets more than a unit on a strong edge and less on a marginal one, while a unit bets the same on both.
Whatever you choose, expect drawdowns. Even a well-sized +EV bettor spends long stretches below a previous high. Write your sizing rule down before a losing run, so you don't change it in the middle of one.
Pitfalls
- Overestimated edges. Stale lines and longshot fairs inflate EV, and Kelly scales your stake with it.
- Limits. The book may not take the stake Kelly suggests.
- Money you need. Never bet money set aside for anything else. If betting stops being fun or affordable, call 1-800-GAMBLER.
In build
This tool is in build on the same tested engine. The app shows what is coming and what already runs.