Guide 6 of 8 / 6 min read
The Kelly Criterion Explained (and Why Most People Use Half)
Edge in, stake out
- Win chance
- 52%
- Edge
- 4%
- Half Kelly
- 2%
At a 52% chance and even money (2.00), the edge is 4%. Full Kelly stakes 4% of the bankroll and half Kelly stakes 2%.
The Kelly criterion answers a specific question: given an edge and a price, what fraction of your bankroll should you stake to grow it as fast as possible over the long run without going broke? It was derived by John Kelly in 1956 for a different problem and has been a staple of gambling and investing maths ever since.
Written and reviewed by Alexander Korsager · last reviewed October 1, 2026 · corrections
The short version
The stake follows the edge
The Kelly formula turns a win probability and a price into the fraction of bankroll that grows it fastest over the long run.
Full Kelly is a rough ride
It assumes your probability estimate is exactly right, and even then the drawdowns along the way are deep.
Half keeps most of the growth
Half-Kelly keeps roughly three-quarters of the growth rate while cutting the swings substantially.
It is the theoretically optimal answer to bankroll growth, and also, in its pure form, more aggressive than almost anyone can stomach. Understanding why is the useful part.
01 / 04
The formula
For a bet at decimal odds o that wins with probability p, let b = o - 1 (the profit per unit staked) and q = 1 - p. The Kelly fraction is: f* = (b × p - q) / b.
- Decimal odds
- o =2.00
- o − 1, profit per unit
- b =1
- Chance of winning
- p =0.52
- 1 − p, chance of losing
- q =0.48
f* = (b × p − q) / b
With a 4% edge at even money (o = 2.00, so b = 1) and p = 0.52, f* = (1 × 0.52 - 0.48) / 1 = 0.04, stake 4% of your bankroll. The fraction scales up with your edge and shrinks as the odds get shorter. If the formula returns zero or negative, the bet has no edge at that price and Kelly says stake nothing.
(1 × 0.52 − 0.48) / 10.044%
- Kelly stake
- 4%
- Rest of bankroll
- 96%
If the sum comes out at zero or below, Kelly stakes nothing.
02 / 04
Why full Kelly hurts
Full Kelly maximizes the long-run growth rate, but it assumes your probability estimate is exactly right. It almost never is. If you overestimate your edge even slightly, full Kelly overbets, and the drawdowns become brutal: a full-Kelly bettor faces roughly even odds, not near-certainty, of losing half their bankroll at some point along the way, even with a correctly estimated edge, and spends a lot of time well below their peak.
Share of the best long-run growth rate
- Full Kelly4% stake100%
- 1.5× Kelly6% stake74.9%
- 2× Kelly8% stakeNo growth
Overestimate the edge and the stake you place sits further down this list than you think.
It also has high short-term variance by design. The growth-optimal path is a wild ride, and most people abandon it (and their edge) during a deep drawdown.
- Full Kelly, wider swings
- Half Kelly, narrower swings
One fixed sequence of 180 bets, the one the Kelly Stake tool opens on. An illustration of the swings, not a forecast.
03 / 04
Fractional Kelly
The standard fix is to bet a fixed fraction of the Kelly stake. Half-Kelly keeps roughly three-quarters of the growth rate while cutting the variance and the expected drawdown substantially. Quarter-Kelly is more conservative still, and the step costs more than it sounds: going from half-Kelly to quarter-Kelly gives up about 31 percentage points of growth rate on its own, more than half-Kelly gave up by stepping down from full Kelly in the first place.
What sizing down from full Kelly actually costs
Growth stays close to its best rate for a while as the stake comes down from full Kelly, which is why half-Kelly keeps 75.0% of it. It then falls away faster the further down you go: the next step, from half-Kelly to quarter-Kelly, gives up roughly 31 percentage points of growth rate on its own, more than the first step gave up. That is not a reason to size up toward full Kelly. The flat top of this curve assumes the edge is estimated exactly right, and full Kelly is still the bet most people cannot stomach once a real drawdown hits. Try your own edge and odds in the Kelly Stake tool. Methodology and sourcing below.
Fractional Kelly also gives you a margin of safety against estimation error: if your true edge is smaller than you think, a half-Kelly bet is closer to the correct full-Kelly bet for that smaller edge than a full-Kelly bet would be.
- Estimated edge
- 4%
- True edge
- 2%
Stake, as a share of bankroll
- Full Kelly on the estimate4%
- Half Kelly on the estimate2%
- Full Kelly on the true edge2%
The half-Kelly stake is the one that sits nearer the stake the true edge calls for.
04 / 04
Practical use
Treat Kelly as an upper bound on sensible stake size, not a target. Size to a fraction of it, cap any single bet at a hard percentage of bankroll regardless of what the formula says, and recompute as your edge estimate and bankroll change. Pair it with a risk-of-ruin check so you know the downside you are accepting.
- Quarter Kelly
- 1%
- Half Kelly
- 2%
- Full Kelly (the ceiling)
- 4%
Sensible stakes sit below the full Kelly line, never past it.
Check yourself
Can you size a Kelly stake now?
1 / 3
At even money (2.00) with a 52% chance of winning, what does full Kelly stake?
2 / 3
The formula returns zero or a negative number. What does Kelly say to stake?
3 / 3
How much of full Kelly's growth rate does half-Kelly keep?
Pick an answer to see the working. Nothing is scored or saved.
Try it
Put your own numbers through it
FAQ
- Is the Kelly criterion worth using?
- As a sizing guide, yes, it links stake to edge in a principled way. But almost nobody bets full Kelly. A half or quarter fraction keeps most of the growth with far less risk of a ruinous drawdown.
- What happens if I bet more than full Kelly?
- Your long-run growth rate falls as you overbet. At even-money odds it turns negative once you pass twice the Kelly fraction, even with a real edge; at uneven odds the exact turning point shifts higher, but the same overbetting still eventually turns growth negative. Overbetting is the classic way a winning strategy still goes broke.
- Does Kelly work for a portfolio of simultaneous bets?
- There is a multi-bet version, but correlations between bets matter a lot and the maths gets involved. A common shortcut is to size each bet at fractional Kelly and cap the total fraction of bankroll in play at once.
Where these figures come from
The formula and the worked example in 'The formula' section are this site's own Kelly Stake tool: f* = (b·p − q)/b and the expected log-growth g(f) = p·ln(1 + f·b) + (1 − p)·ln(1 − f) are exactly kellyFraction and growth in src/tools/kelly-stake/math.ts, checked in math.test.ts against the identity that the break-even stake really does give zero growth and that no other fraction beats the best available growth. 'Half-Kelly keeps roughly three-quarters of the growth' was re-evaluated directly from growth() at the guide's own p = 0.52, b = 1 inputs: growth(f/2)/growth(f) = 0.750, matching kelly-stake's own FAQ ('about three-quarters') so the two pages cannot quietly disagree. The 'Fractional Kelly' section's growth-versus-fraction figure and its 31-percentage-point half-to-quarter cost claim are both read from ./figures/kelly-fraction-growth-data.ts, which derives every value from the same kellyFraction, growth, optimalGrowth and shareOfBest functions at these identical inputs, pinned in kelly-fraction-growth-data.test.ts. The even-money 'turns negative once you pass twice the full-Kelly fraction' claim was checked the same way: growth(2f*) evaluates to essentially zero at p = 0.52 (-3×10⁻⁶) and clearly negative at a larger edge, p = 0.6 (-0.00245), consistent with 'once you pass' rather than 'exactly at'. The full-Kelly 'roughly even odds of losing half your bankroll at some point' claim is not something this site's own code computes end to end; it is the standard published result for continuous-time Kelly betting (Kelly, 'A New Interpretation of Information Rate', Bell System Technical Journal, 1956; MacLean, Thorp & Ziemba, The Kelly Capital Growth Investment Criterion, 2010), cited here rather than re-derived.
Verification
Checked against kelly-stake's own math.ts (kellyFraction, growth) and sensitivity-math.ts (optimalGrowth, shareOfBest), both pinned by math.test.ts and kelly-fraction-growth-data.test.ts; MacLean, Thorp & Ziemba's The Kelly Capital Growth Investment Criterion (2010) for the full-Kelly drawdown-probability figure: agrees on the formula itself; half-Kelly's growth share at the guide's own p = 0.52 worked example (0.750); quarter-Kelly's growth share (0.437) and the 31-point half-to-quarter cost; and the even-money double-Kelly growth crossing at or below zero (verified by math.test.ts and kelly-fraction-growth-data.test.ts (kelly-stake), plus a manual re-evaluation of growth() at the guide's own inputs, 2026-10-01).
Know the risk
- Betting the full Kelly fraction the formula returns because the formula is what calculated it. The guide's own point is the opposite: full Kelly assumes the probability estimate is exact, and even then a full-Kelly bettor faces roughly even odds, not near-certainty, of losing half their bankroll at some point along the way.
- Reading a positive number out of the formula as confirmation an edge exists. Kelly's output is a downstream consequence of the p you supplied, and it cannot tell an accurate estimate from an optimistic one; an overestimated edge still produces a stake to bet.
- Assuming betting more than full Kelly just gives up some growth for more upside. At even-money odds, expected growth turns negative once you pass twice the full-Kelly fraction, even with a real edge; at other odds that turning point sits higher, but the mechanism is the same, so overbetting is not a milder version of the same mistake, it can turn a winning strategy into a losing one.
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