Quick answer: The Kelly criterion is a formula that turns your estimated edge on a bet into a suggested stake as a percentage of your bankroll — but it only works if you truly have a positive edge and a trustworthy estimate of your win probability. Because small errors in that estimate can swing the answer wildly, many people who use it stake only half or a quarter of what the formula says. And if the edge is zero or negative, as it is on every casino game with a house edge, the formula says to stake nothing.
The Formula
For a simple win-or-lose bet, the Kelly fraction is:
f* = (b × p − q) ÷ b
- f* is the fraction of your bankroll to stake.
- b is the net odds: decimal odds minus 1. At decimal odds of 2.10, b = 1.10.
- p is your estimated probability of winning.
- q is the probability of losing, which is 1 − p.
The numerator, b × p − q, is your expected profit per unit staked. If it is positive you have an edge. If it is zero or negative, f* is zero or negative, and the instruction is simple: do not bet.
A Worked Example
Suppose a bet is offered at decimal odds of 2.10 and you believe your true chance of winning is 50%.
- b = 2.10 − 1 = 1.10, p = 0.50, q = 0.50.
- b × p = 1.10 × 0.50 = 0.55.
- 0.55 − 0.50 = 0.05.
- f* = 0.05 ÷ 1.10 = about 0.045, or roughly 4.5% of your bankroll.
On a ₱10,000 bankroll, full Kelly would be about ₱450. Half Kelly is about 2.3%, or roughly ₱230.
What Happens When Your Estimate Is Wrong
The odds of 2.10 imply a break-even win probability of 1 ÷ 2.10, about 47.6%. You only have an edge if your true chance is above that. Here is the same bet with different values of p:
| Your estimate of p | Expected profit per unit staked | Full Kelly | Half Kelly |
|---|---|---|---|
| 0.50 | +0.050 | about 4.5% | about 2.3% |
| 0.49 | +0.029 | about 2.6% | about 1.3% |
| 0.48 | +0.008 | about 0.7% | about 0.4% |
| 0.47 | −0.013 | negative: no bet | no bet |
If your true probability is 0.47 rather than 0.50, then f* = (1.10 × 0.47 − 0.53) ÷ 1.10 = (0.517 − 0.53) ÷ 1.10 = about −1.2%. A negative result means the bet has negative expected value and the correct stake is zero. A three-point error in your estimate turned a 4.5% stake into no bet at all — and if you had staked 4.5% anyway, you would have been consistently overbetting a losing proposition.
Why Fractional Kelly Exists
The formula assumes your probability is exactly right. In real betting it never is; it is an estimate, often an optimistic one. Staking half or a quarter of the Kelly figure is a common safeguard:
- It leaves a margin for error if your edge is smaller than you believed.
- It makes losing streaks shallower. Full Kelly staking is known for large swings in the bankroll even when the edge is real.
- It gives up some theoretical growth in exchange for a more survivable ride. The size of that trade-off depends on your assumptions, so treat any quoted figure with caution.
Betting less than the formula says is not timidity; it is accounting for the uncertainty in your own inputs. Our guide to bankroll management covers simpler flat-staking approaches that need no probability estimate.
Why Kelly Does Not Work on Casino Games
Every standard casino game is priced so that your expected return is below your stake. Take a single-zero roulette even-money bet such as red, which wins 18 times in 37. Here b = 1 and p = 18/37 ≈ 0.4865, so f* = (0.4865 − 0.5135) ÷ 1 = about −2.7%. The formula returns a negative number, which means the correct Kelly stake is zero. The same is true of blackjack, baccarat and slots: there is no stake size at which a negative-edge game becomes profitable. Our explanation of Gambler’s Ruin shows what happens to a bankroll that keeps betting into a house edge.
Where Kelly Might Apply and Where It Does Not
Kelly is a staking tool for situations where a genuine edge may exist, such as a bettor who can price sports markets better than the bookmaker. Even there, remember that bookmakers build a margin into the prices — see understanding the vig — so you need to beat the margin before you have an edge at all. Results also move around a lot; variance can hide a real edge or make a fake one look real for a long time. Most recreational bettors do not have a measurable edge, and for them the practical conclusion is to set a budget for entertainment rather than reach for a formula.
Frequently Asked Questions
Does Kelly guarantee I will not go broke?
No. It is a growth-oriented staking rule that assumes a real edge and an accurate probability. If either assumption is wrong, it can lead to heavy losses. It guarantees nothing.
How do I find my true win probability?
That is the hard part, and the honest answer is that you can only estimate it, using your own research and a track record large enough to be meaningful. Most people overestimate their accuracy.
Is half Kelly always better than full Kelly?
Not “always”, but when your probability is uncertain, which is nearly always, many bettors prefer a fraction because the downside of overestimating is larger than the upside of underestimating.
Can I use Kelly on slots or roulette?
The formula gives a stake of zero for them, because the house edge makes expected value negative. It is not a way to beat these games.
Final Thoughts
The Kelly criterion is a neat piece of maths, but it is only as reliable as the probability you feed into it. If you have no proven edge, it tells you not to bet; if you do have one, staking a fraction of the formula is the more cautious path. Treat any staking system as a way to manage risk, not as a way to create profit.
Betting is for adults aged 21 and over and always carries the risk of losing money, so only stake what you can afford to lose. If gambling has stopped being entertainment, our responsible gambling page lists the support available in the Philippines.