Guide
The Kelly Criterion, Simply Explained
Quick Summary
- Kelly sizes a bet from your edge and the odds, as a share of your bankroll.
- If you have no edge, Kelly says bet nothing, which covers every casino game.
- Estimates are uncertain, so many people bet half Kelly or less.
- 18+ only
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- Checked 5 Nov 2026
- Know your limit
The Kelly criterion is a formula for deciding how much to stake when you believe a bet has an edge. It came out of 1950s information theory and was later taken up by investors and bettors. Its appeal is that it balances growth against the risk of ruin. Its danger is that it rests on an estimate you might get wrong. This post explains it in plain numbers, works a Taka example and shows why for most people the most useful part of Kelly is when it says zero.
The formula in one line
Kelly says: stake fraction = (b × p − q) ÷ b. Here b is the profit per ৳1 staked (decimal odds minus 1), p is your estimated chance of winning, and q is your chance of losing (1 minus p). The result is the share of your bankroll to stake.
Read it as cause and effect. The top half, b × p − q, is your edge: what you expect to gain per ৳1 on average. If it is zero or negative, the fraction is zero or negative, and Kelly says do not bet. Dividing by b scales the stake down for long odds, because long shots lose more often even when they have an edge.
A worked example in Taka
Suppose, hypothetically, you have a ৳5,000 betting bankroll and you believe a team has a 45% chance of winning. It is priced at 2.50, which implies 40%. So b = 1.5, p = 0.45 and q = 0.55. The edge is 1.5 × 0.45 − 0.55 = 0.125. Divide by 1.5 and the Kelly fraction is about 8.3%, or roughly ৳417 of the ৳5,000.
| Your estimated chance | Price 2.50 implies | Kelly fraction | Stake from ৳5,000 |
|---|---|---|---|
| 40% | 40% | 0% | ৳0 |
| 42% | 40% | 3.3% | ৳167 |
| 45% | 40% | 8.3% | ৳417 |
| 50% | 40% | 16.7% | ৳833 |
Why half Kelly is popular
The table shows how sensitive Kelly is. Moving your estimate from 42% to 50% multiplies the stake by five. If your 50% estimate is really 42%, you are badly overbetting. Overbetting is worse than underbetting: staking twice the Kelly amount produces roughly zero long-run growth with much bigger swings, and beyond that you expect to shrink your bankroll even with a genuine edge.
That is why many people use half Kelly or a quarter. In the 45% example, half Kelly is about ৳208. You give up some growth in exchange for far smaller drawdowns and much more protection against your own overconfidence. Since nobody knows their true edge precisely, a fraction of Kelly is the honest choice.
Why Kelly says zero for casino games
Casino games have a built-in house edge. On a baccarat Banker bet, a roulette spin or a slot, your expected gain per ৳1 is negative. Put any negative edge into the formula and the answer is below zero: Kelly recommends no bet at all. This is not a flaw; it is the formula telling the truth. There is no stake size that turns a negative-edge game into long-run growth.
That does not mean you cannot play casino games for entertainment. It means stake size there should come from your entertainment budget, using a method such as unit betting, not from Kelly. Kelly only has something to say where you genuinely believe you have an edge, mostly in sports betting, and even then the bookmaker's margin means many apparent edges are illusions.
Using Kelly sensibly
If you want to try Kelly on sports bets, keep a record of every estimate and result first. After a hundred or more bets you can check whether your estimates were well calibrated, as our betting ROI post explains. Until then, a flat stake of 1% to 2% of bankroll is a safer default. Never borrow to raise your bankroll, and do not recalculate Kelly upward after a loss to "catch up". The odds guide explains implied probability if you need a refresher.
Three steps
How to apply Kelly in 3 steps
- 1Estimate honestly
Write your chance of winning before looking at the odds, and compare it with the implied chance.
- 2Run the formula
Calculate (b × p − q) ÷ b; if the answer is zero or below, do not bet.
- 3Scale it down
Stake half or a quarter of the Kelly figure, and never more than a small cap such as 5%.