The Kelly Criterion Explained Without the Scary Maths
Kelly turns an edge into a stake: your advantage divided by the odds minus one. Built up in plain language, then stress-tested by moving the probability estimate five points the wrong way.
The Kelly criterion answers one question: given how much better than the price you believe a bet is, what share of your bank should go on it. The answer is a single fraction — your edge divided by the odds minus one — and on a ₦50,000 bank a five-point edge at 2.10 comes out at ₦2,270. That is four and a half times a normal ₦500 unit — the first clue as to why almost nobody stakes the full figure. What follows builds the fraction in plain language, then shows what a small error in your own estimate does to it.
In short.
- The stake is edge divided by (odds − 1). A 5% edge at 2.10 is 4.5% of the bank.
- The same 5% edge is worth 10% of the bank at 1.50 and 1.25% at 5.00: the price sizes the stake as much as the edge does.
- Overestimate by five points and the "optimal" stake becomes a losing one — −₦125 per bet instead of +₦114.
- Quarter Kelly keeps 44% of the growth for a quarter of the swings: six straight losses cost 6.6% of the bank, not 24.4%.
- Without a probability of your own, written before you see the price, the formula has nothing to size from.
The question the formula is actually asking
Every staking plan answers "how much". Flat staking says "the same every time"; Kelly says "an amount proportional to how wrong the price is". Its target is the fastest long-run growth of the bank, not the biggest profit on one bet — and the two differ. Staking everything on a 90% shot maximises expected naira and guarantees eventual ruin. Kelly is the largest stake that still leaves the bank growing.
Building the fraction in plain language
Two forces pull on the stake. The first is how much better than the price your estimate is. Rate a side at 50% when the price is 2.10 and every naira staked is expected back as 0.50 × 2.10 = ₦1.05. The extra five kobo is the edge: 5%.
The second force is what a win pays relative to what a loss costs. At 2.10 a winning naira brings back ₦1.10 of profit; at 1.50 it brings back ₦0.50, so the same edge has to be backed with more money to produce the same growth.
Put the two together and the formula appears: fraction = edge ÷ (odds − 1). A 5% edge at 2.10 is 0.05 ÷ 1.10 = 4.5% of the bank, ₦2,273 on ₦50,000. The textbook (bp − q) ÷ b is the same arithmetic with the edge written longhand.
Example. You make a Premier League home side 55% and the app shows 1.90. Edge = 0.55 × 1.90 − 1 = 4.5%; odds − 1 = 0.90; fraction = 0.045 ÷ 0.90 = 5.0%. On a ₦50,000 bank that is ₦2,500 at full Kelly, ₦625 at quarter Kelly.
The same edge, four different stakes
Below, the edge is held at exactly 5% and only the price moves. The probability column is whatever number produces that 5% at that price — the conversion is in turning odds into probability.
| Price | Your probability | Edge | Full Kelly | Stake on ₦50,000 | Quarter Kelly |
|---|---|---|---|---|---|
| 1.50 | 70.0% | 5% | 10.00% | ₦5,000 | ₦1,250 |
| 2.10 | 50.0% | 5% | 4.55% | ₦2,273 | ₦568 |
| 3.00 | 35.0% | 5% | 2.50% | ₦1,250 | ₦313 |
| 5.00 | 21.0% | 5% | 1.25% | ₦625 | ₦156 |
Eight times as much money goes on the 1.50 shot as on the 5.00 one for an identical advantage. That is also what makes the method dangerous: the biggest stakes land on short prices, where an error in your estimate is hardest to notice.
What one wrong probability does to the stake
Keep the 2.10 bet and its 4.55% fraction. You have written 50% in your notes; the price implies 1 ÷ 2.10 = 47.6%, so your claim is that the market is 2.4 points low. The true number is something you never see.
| If the true chance is | Real edge | Expected value per ₦2,273 staked | Over 100 such bets |
|---|---|---|---|
| 55% (you were 5 points too low) | +15.5% | +₦352 | +₦35,200 |
| 50% (you were right) | +5.0% | +₦114 | +₦11,400 |
| 47.6% (the market was right) | 0.0% | ₦0 | ₦0 |
| 45% (you were 5 points too high) | −5.5% | −₦125 | −₦12,500 |
| 43% (7 points too high) | −9.7% | −₦220 | −₦22,000 |
Read the fourth row slowly. Same match, same notes, same formula — yet five points of optimism turn a plan that earns ₦11,400 per hundred bets into one that loses ₦12,500. The errors are not symmetrical either: five points too cautious costs only growth you failed to take, five points too bold changes the sign of the exercise.
Important. Staking roughly twice the Kelly fraction produces, in the standard approximation, no long-run growth at all — the bank swings hard and ends where it started. Since a five-point overestimate can easily double the fraction you calculate, "full Kelly on my own numbers" and "twice Kelly on the true ones" are closer together than they sound.
Full, half and quarter: what each version buys
Fractional Kelly means multiplying the answer by a constant chosen once — a half, a quarter, an eighth. The trade is lopsided in your favour: growth falls slowly, while the swings fall in a straight line.
| Version | Stake on the 2.10 bet | Share of maximum growth | Cost of six straight losses |
|---|---|---|---|
| Full Kelly | ₦2,273 | 100% | −24.4% of the bank |
| Half Kelly | ₦1,136 | 75% | −12.9% |
| Quarter Kelly | ₦568 | 44% | −6.6% |
| Eighth Kelly | ₦284 | 23% | −3.4% |
| Flat ₦500 | ₦500 | not applicable | −6.0% |
The growth column comes from one expression: a fraction c of Kelly retains c × (2 − c) of the maximum growth rate — half gives 75%, a quarter 44%. The last column is compound arithmetic: six losses at 4.55% leave 0.95456 = 75.6% of the bank. Notice where quarter Kelly lands — ₦568, within a hundred naira of the ₦500 unit a flat staking plan would use. The difference is that this number moves with the quality of the bet.
Six bets on a ₦50,000 bank
Quarter Kelly, recalculated on the running balance, stakes rounded to the nearest ₦50. The bank is roughly four months of a ₦12,000 budget.
| # | Price | Your chance | Edge | Quarter Kelly | Stake | Result | Bank after |
|---|---|---|---|---|---|---|---|
| 1 | 2.10 | 50% | 5.0% | 1.14% | ₦550 | Lost | ₦49,450 |
| 2 | 1.65 | 65% | 7.3% | 2.79% | ₦1,400 | Won +₦910 | ₦50,360 |
| 3 | 3.40 | 32% | 8.8% | 0.92% | ₦450 | Lost | ₦49,910 |
| 4 | 1.90 | 55% | 4.5% | 1.25% | ₦600 | Won +₦540 | ₦50,450 |
| 5 | 2.60 | 42% | 9.2% | 1.44% | ₦750 | Lost | ₦49,700 |
| 6 | 1.80 | 60% | 8.0% | 2.50% | ₦1,250 | Won +₦1,000 | ₦50,700 |
Turnover ₦5,000, profit ₦700. Bet 3 shows the mechanism: an 8.8% edge, the biggest so far, attracts the smallest stake of the six, because at 3.40 a loss costs 2.4 times what it would at 1.90 for the same profit.
Run the identical six at other fractions: full Kelly turns over ₦19,750 for ₦2,462, half ₦9,950 for ₦1,290, and a flat ₦500 unit turns over ₦3,000 to finish ₦325 down, because the winners came at short prices. Six bets settle nothing — they only show how far the sizing rule moves the month.
Where Kelly does not belong
When the probability is not yours. The formula magnifies whatever number you feed it. A percentage copied from a tipster, or reverse-engineered from the odds themselves, gives an edge of zero and a stake of zero.
On accumulators and correlated bets. It assumes one independent outcome settling at a time. A four-fold is one ticket with four ways to fail, and two markets on the same match are not two bets — see singles versus accumulators.
When the bank is not the whole bank. Top the account up from your salary whenever it dips and you are not staking 4.5% of anything: the stake keeps growing while the losses stay off the books, the habit priced in the arithmetic of chasing losses.
When the account or your nerve cannot take the stake. A calculated ₦156 may be below the minimum, ₦5,000 above what a restricted account allows. And a 24% drawdown is survivable arithmetically far more often than emotionally: the right fraction is the one you can hold through a bad fortnight.
FAQ
What is a realistic Kelly fraction for an ordinary punter?
A quarter or an eighth of the calculated figure. On the 2.10 example that is ₦568 or ₦284 rather than ₦2,273, and it keeps 44% or 23% of the theoretical growth. Anything above half assumes your probability estimates are accurate to within about two points, which very few records can support.
What happens if I use the bookmaker's implied probability?
The edge computes to zero and the formula returns a stake of zero, which is the correct answer. Kelly only produces a number when your estimate differs from the price. Backing a probability out of the odds and adding a few points "for confidence" is not an estimate — it is the overestimation the table above prices at −₦125 a bet.
Can Kelly be used on GG or over 1.5 markets?
Yes. The formula does not care which market produced the price, only that you have an independent probability for it. The difficulty is that goal markets need a scoring model to produce one, and several selections on the same fixture move together, so they must be sized as a single bet rather than as three.
Should the stake be recalculated after every bet?
Recalculate on the current balance, then round and set a floor. Working from a bank that changes is what makes the plan self-correcting after a losing run. Rounding to the nearest ₦50 costs almost nothing in growth and keeps your slips from advertising that stakes are computed to the naira.
Read next
- Bankroll management — fixing the bank before fixing the fraction.
- The strategy guide — where staking methods sit among the rest.
- Today's predictions — fixtures to price against your own numbers.
This article is for information only and is not an inducement to gamble. Betting involves the risk of losing money — never stake more than you can afford to lose. 18+. If gambling stops being entertainment, read our responsible gambling guide and seek help.
