the kelly criterion for bettors: position sizing that survives bad runs

what kelly actually is

The Kelly criterion answers one question: given a bet with a positive edge, what fraction of the bankroll should you stake? It was published by John Kelly in 1956, originally as a problem about transmitting information down a noisy telephone line, and bettors adopted it because it has a property no other staking rule has: over many bets it maximises the growth rate of the bankroll. No other stake size compounds the bankroll faster in expectation. That single property is why it matters, and also why it is dangerous — more on that in a moment.

Two inputs feed the formula, and both have to be real numbers. First, the price, in decimal odds — convert any fractional or American price with the odds converter and value finder and read the implied probability while you are there. Second, your own estimate of the win probability, as a percentage. Where that estimate comes from is a separate skill, covered in the companion article on value betting — find the edge, then size it correctly. Kelly does not tell you whether a bet is value. It tells you how much to stake once you have decided it is. If the price does not beat your probability, Kelly’s answer is exactly zero — no bet.

the formula, with a worked example

The formula is f* = (b p − q) / b. Here b is the decimal odds minus one — the profit per £1 staked — p is your win probability and q is 1 − p, the chance of losing. f* comes out as a fraction of the bankroll, and it is the fraction that maximises long-run growth.

Running example throughout this guide: a £1,000 bankroll, a horse at decimal 3.00 (2/1), which you rate at 40%. Then b = 2, p = 0.40 and q = 0.60, so f* = (0.80 − 0.60) / 2 = 0.10. Full Kelly says stake 10% of the bankroll: £100.

Notice how the stake moves with the numbers. A longer price with the same edge — say decimal 5.00 (4/1) at a 25% estimate — gives b = 4, p = 0.25, q = 0.75, so f* = (1.00 − 0.75) / 4 = 0.0625: 6.25%, £62.50. A thin edge at a short price can come out at 1% or less. The staking calculator does all of this from three inputs — bankroll, decimal odds, win probability — and returns the Kelly fraction plus the cash stakes, so the algebra never has to happen by hand.

full vs fractional kelly: half and quarter

Full Kelly is the theoretical maximum-growth stake, and it is almost never the right stake to actually place. The criterion assumes your probability estimate is exactly right, that the price never moves, and that you re-stake the full new bankroll after every single bet. All three assumptions are false in real betting. The standard fix is fractional Kelly: stake half, or a quarter, of the full Kelly amount. Same formula, same direction, deliberately smaller numbers.

On the running example that means £100 full, £50 half, £25 quarter on the £1,000 bankroll. The staking calculator returns all three at once, side by side, plus a points-staking mode that declares the bankroll as 100 points and gives the cash value of 1, 0.5 and 2 points — the practical way to run a betting log over months.

Why bother halving, if it is not maximum growth? Because the growth curve is flat at the top. In the running example, half Kelly keeps roughly three quarters of full Kelly’s growth rate while staking half as much — and quarter Kelly keeps more than half the growth at a quarter of the stake. You are buying a discount on variance: most of the compounding, a fraction of the swings.

why full kelly is too volatile for realistic edges

Real edges are small and noisy. The market is efficient enough that a genuine 5–10% edge is a good find, and your estimate carries error — you might be sure it is 40% when the truth is 36%. Kelly is exquisitely sensitive to that error, because the error is multiplied into the stake. If you overestimate the probability you overbet, and full Kelly overbets hardest of all. Staking half or a quarter of what the formula says is a cheap insurance policy against your own estimate being wrong, which it will be, regularly.

Full Kelly also assumes bets are independent and sequential, with the bankroll re-sized after each result. Real betting is not like that: several bets a day, often in the same race or the same match, no time for the bankroll to recover between them. The practical consequence of full Kelly staking is enormous variance — routine bankroll swings of 30–50% — and the psychological pressure of those swings is exactly what makes people abandon the plan and start chasing. The plan was never the problem; the stake size was.

drawdown maths: what a losing run does to the bankroll

The uncomfortable part is that even a genuine edge loses, in streaks, and Kelly’s own arithmetic assumes you survive them. The numbers for the running example: staking £100 on a 40% shot means every loss multiplies the bankroll by 0.9. Seven straight losses — 0.9 to the power 7 — leaves 47.8% of the bankroll: a 52% drawdown. Ten straight losses leaves 34.9%: a 65% drawdown. Runs of seven or more losers are not rare at a 40% strike rate; they are a routine part of the distribution, and they arrive exactly when your picks have gone cold.

The same sequence at quarter Kelly: every loss multiplies the bankroll by 0.975, and it takes about 27 straight losses to halve it — 0.975 to the power 27 is roughly 0.50. Twenty-seven straight losers would be a catastrophe for the picking, but the bankroll survives it, and the plan with it. That is the entire point of fractional Kelly: the stake is sized so the bad runs are survivable, because the bad runs are guaranteed to come.

One more piece of arithmetic worth having. The long-run growth rate of a staking plan is g = p ln(1 + bf) + q ln(1 − f), where f is the fraction staked. For the running example at full Kelly, g is about 0.97% per bet; at half Kelly, about 0.73% per bet. Three quarters of the growth, half the stake, half the drawdown. Anyone who has lived through a real losing run knows which one survives contact with reality.

when kelly breaks down

Kelly is a model, and models fail at their assumptions. Two failures matter in practice.

Overestimated edge. If your 40% is really 36%, the true Kelly fraction at 3.00 is (0.72 − 0.64) / 2 = 0.04 — 4%, not 10%. Full Kelly has you staking two and a half times the correct amount, and the overbet adds variance without adding return. Worse, if the true probability is below 33.3% the bet is negative expected value, and Kelly — any fraction of it — drains the bankroll systematically while feeling mathematical. The formula cannot rescue a bad estimate; it only sizes whatever you feed it. This is why the mro.tips approach is to fix the probability first and size second: read the price as a probability, put your own number on the chance, check the edge, and only then ask the staking calculator how much.

Correlated bets. Kelly assumes each bet is an independent trial. Back two selections in the same race and they are not independent — one result settles both. Back a team to win and over 2.5 goals in the same match and a single red card settles both. The two bets share one risk event, so the combined exposure is much larger than the two fractions suggest, and the arithmetic quietly double-counts the bankroll. The dutching calculator shows the book % when you split a stake across selections in one market, and the same caution applies to any two bets that share a result: treat them as one position, and stake for one.

the loop

Kelly is not a way to find winners; it is a way to stay in the game long enough for the edge to show. The loop is unchanged from the rest of the mro.tips method: form the probability, convert the price, check the edge, size by fractional Kelly, repeat. Quarter Kelly on a genuine edge looks boring for months, then quietly compounds. Full Kelly on a guessed edge looks clever for a week, then hands the bankroll back.

And the honest endnote. The bankroll is money you can afford to lose, and if the swings — even quarter-Kelly swings — stop being comfortable, the stake is too big, not the run too long. Bet within your means, and if betting stops being enjoyable, stop. 18+ | BeGambleAware.