The Kelly Criterion: What a Staking Formula Says About Bet Size

Ask a room of bettors how much they should stake on a single wager and you will hear rules of thumb: a fixed amount, a small percentage, whatever feels right on the day. The Kelly criterion is an attempt to replace those habits with a formula. It works out what fraction of a bankroll to stake so that the bankroll grows as fast as possible over many bets, given the odds on offer and the true chance of winning. The catch sits in that last phrase, and it is the reason the formula is more useful as a lesson than as a tool.

The formula

For a simple bet that either wins or loses, the Kelly fraction is:

f = (b × p − q) ÷ b

• f is the share of the bankroll to stake.
• b is the net odds: the profit per unit staked if the bet wins. With decimal odds, b is the decimal price minus 1.
• p is the probability that the bet wins.
• q is the probability that it loses, which is 1 minus p.

If the result is zero or negative, the formula says not to bet at all.

A worked example

Take a bet at decimal odds of 2.10, so b is 1.10. The figures below are invented purely to show how the formula responds to different estimates of p.

The break-even point is the probability implied by the price itself, which at 2.10 is roughly 47.6%. Above that, the formula suggests a stake that rises with the size of the edge. Below it, the answer is zero. A small change in the estimate moves the recommended stake a long way.

Why the answer is usually zero

Bookmakers build a margin into their prices, which is why the implied probabilities across all outcomes in a market add up to more than 100%. Our explainer on the vig in sports betting walks through how that margin is built. For a typical bet, the true chance of winning sits below the implied probability of the price, so b × p − q comes out negative and Kelly says to stake nothing.

Casino games make the point even more clearly. Roulette, slots and most table games pay out less than the true odds of winning, so the edge is negative by design. The same applies to number games with fixed payout tables, including the ones covered in our guide to playing Satta King more responsibly. For all of these, the formula never suggests a positive stake. Any play is entertainment with a cost, not a bet that the maths approves.

Where the formula breaks down in practice

Nobody knows p exactly

Kelly assumes you know the true probability. In sport, you only have an estimate, and estimates tend to be optimistic. If p is overstated, the formula recommends stakes that are too large, and staking well above the true Kelly fraction can lower long-run growth even when a real edge exists.

Swings are large even at full Kelly

Staking the full Kelly fraction produces big swings in bankroll size. Long losing runs are normal under the formula, which assumes you will keep betting calmly through them. Real people often do not, and chasing losses after a bad patch is one of the behaviours described in our piece on being on tilt.

Bets are not independent or repeatable

The formula's promise applies over a very long series of independent bets. Several bets on the same day, on related events or within one accumulator break that assumption. So does stopping after a few dozen bets, where luck dominates. The long-run maths behind that is set out in our explainer on gambler's ruin and the law of large numbers.

Fractional Kelly

Because of these problems, people who use the formula often stake only a fraction of what it suggests, such as half or a quarter. This is called fractional Kelly. It gives up some theoretical growth in exchange for smaller swings and more room for error in the estimate of p. It does not change the basic rule: when the edge is zero or negative, a fraction of zero is still zero.

What the Kelly criterion is good for

• It shows plainly that stake size should depend on edge, and that no edge means no bet.
• It makes the price matter: the same opinion of a team can be worth a bet at one price and not at another.
• It warns against large stakes, since even a genuine edge can be wasted by betting too much.
• It explains why fixed budgets make more sense for recreational play than any formula built on guessed probabilities.

For most adults who bet for fun, the practical takeaway is to set a budget before playing, treat it as the cost of the entertainment and keep each stake small relative to it. Betting is for adults only, the rules vary from one place to another, so confirm what is permitted where you live, and the limits and reminders offered by operators are there to be used.