Selection gets the attention; stake size decides how long you survive. This is the plain-arithmetic version of bankroll management — what a unit is, why flat staking is the sane default, and exactly what the Kelly criterion tells you to bet when you genuinely have an edge.
Two bettors can pick the same games and end up in completely different places, because they staked them differently. Selection decides your edge; staking decides whether you are still solvent long enough to realize it. This is the arithmetic of the second half — how much to put on a bet — starting from the simplest rule and building up to the one that ties stake directly to edge.
The unit
A unit is a fixed fraction of your bankroll, chosen once, that you use to size every bet. If your bankroll is $2,000 and you set a 1% unit, one unit is $20. The point is to keep bets the same size relative to your funds, so a rough patch shrinks your stakes automatically and a good run grows them, without you making an emotional decision each time.
Flat staking, and why it is the default
Flat staking means one unit on every bet, full stop. It sounds unambitious, and that is its strength. It removes the two most common bankroll killers — chasing losses by sizing up and pressing winners past your edge — by taking the sizing decision out of your hands. For a bettor who cannot yet measure their edge precisely, flat staking is not a compromise; it is the correct choice, because every more aggressive method requires an edge estimate you may not have.
The Kelly criterion
Kelly answers a sharper question: if you truly know your edge, what stake maximizes the long-run growth of your bankroll? The formula ties the bet size directly to how much your estimated probability beats the price.
Work an example. You are offered +120 — decimal 2.20, so b = 1.20 — and you estimate the bet is a genuine coin flip, p = 0.50, q = 0.50. The price's own implied probability is 1/2.20 = 45.45%, so a 50% estimate means you think you have an edge.
The structure of the formula carries the lesson. The stake is positive only when b·p exceeds q — that is, only when your estimated probability is higher than the price's implied probability. If you think a +120 shot is exactly a 45.45% chance, Kelly returns zero: fair price, no edge, bet nothing. And if you think it is less likely than that, Kelly goes negative, which simply means the bet is one to lay or leave, not to back.
| You estimate p = 45.45% (= implied) | f* = 0% — no edge, bet nothing |
|---|---|
| You estimate p = 50% | f* = 8.33% of bankroll |
| You estimate p = 55% | f* = 17.5% of bankroll |
| You estimate p = 40% (below implied) | f* negative — do not back it |
Why almost nobody bets full Kelly
Full Kelly maximizes long-run growth on paper, but it is brutally volatile and it assumes your probability estimate is exactly right. In reality your edge is estimated with error, and Kelly is unforgiving of overestimates — betting a too-large edge at full Kelly can shrink a bankroll fast through ordinary variance. The common response is fractional Kelly: bet a half or a quarter of what the formula says. Half-Kelly gives up a little theoretical growth for a large reduction in swings, and it cushions the damage when your edge estimate is too optimistic — which, honestly, it often is.
What this does not promise
- It does not create an edge. Kelly sizes an edge you already have; with no edge, its honest answer is to stake nothing. It cannot turn a losing method into a winning one.
- It is not financial advice. Bankroll sizing is a mathematical framework for managing risk on money you have already decided to wager for entertainment — not investment guidance, and not a recommendation to bet.
- It is not a pick. Every probability in this article is an input you supply; nothing here handicaps a game or tells you what to bet.
Frequently asked
What is a betting unit and how big should it be?
A unit is a fixed fraction of your bankroll used to size every bet — commonly around 1%, so $20 on a $2,000 bankroll. Smaller units survive variance longer; larger ones grow or shrink a bankroll faster. The right fraction depends on your measured edge and your tolerance for swings, not on how good any single bet feels.
What is the Kelly criterion formula?
f* = (b·p − q) / b, where b is the decimal odds minus one (your net profit per unit), p is your estimated win probability, and q is 1 − p. The result f* is the fraction of your bankroll to stake. It is positive only when your estimated probability beats the price's implied probability.
Why do experienced bettors use fractional Kelly?
Full Kelly is highly volatile and assumes your probability estimate is exactly right. Because edges are estimated with error and usually overrated, full Kelly tends to overstake. Betting a half or quarter of the Kelly figure sharply reduces swings and cushions the damage from an over-optimistic edge, at a small cost to theoretical growth.
What does Kelly say to bet if I have no edge?
Nothing. When your estimated probability equals the price's implied probability, the formula returns zero, and when it is below, the result goes negative — meaning the bet is one to leave alone. Kelly only stakes money when you genuinely expect to beat the price.