Kelly Criterion Calculator
The formula
What the kelly criterion tells you
The plain odds behind kelly criterion: single-event probability, the fair-price payout it implies, and how repetition moves the chance of at least one success.
Calculation: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. Enter your inputs and every substitution is shown below the result.
Reading the result
The fair-payout line is the decision column — any offered price above it carries positive expected value, below it funds the house.
Limitations and best practice
Independence is the assumption; card draws, weather and streaks correlate, which shrinks the repetition column’s real value.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Do odds “even out”?
What changes with repetition?
Source & methodology
Classical probability (Laplace) for equally-likely outcomes.
Kelly Criterion: the number, the method and the caveats
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on a Kelly Criterion page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
In Miscellaneous & Fun the same quantity is often quoted under two or three different conventions. The formula printed above fixes one convention and applies it consistently, which is what makes results from this page comparable with each other.
Fun numbers are still numbers. Kelly Criterion computes p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n honestly, and the 33.33% output is exactly the sort of thing that settles a group chat — with a real formula underneath instead of a joke answer.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to single-trial probability = 33.33% on the default inputs, and the sensitivity section ranks the inputs that move the result — Possible outcomes first, at ≈11.1 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Every input in Kelly Criterion, and what it does to the answer
One formula, published in full: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Favourable outcomes (example value 2) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Possible outcomes (example value 6) is a plain measured quantity — the unit shown in the label is the unit the formula expects. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Repetitions (independent) (example value 3) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
The default Kelly Criterion calculation, written out in full
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Favourable outcomes, Possible outcomes, Repetitions (independent). The endpoint of that chain is 33.33% of single-trial probability, sitting in the “Live odds — worth calculating the payoff” band.
- p = 2 ÷ 6 = 0.3333
- Odds against = (1−p)÷p = 2.00:1
- P(hit within 3 tries) = 1 − 0.6667^3 = 70.4 %
Odds against — 2.00 :1. Compare it against the main result of 33.33% before drawing conclusions.
At least one hit in 3 — 70.4%. Compare it against the main result of 33.33% before drawing conclusions.
Fair payout to break even — 3.00 :1. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Kelly Criterion at ±10 % and ±20 % of the key input
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Kelly Criterion, not an interpolation.
| Possible outcomes setting | Single-trial probability |
|---|---|
| 80 % of the example value | 41.67% |
| 90 % of the example value | 37.04% |
| example inputs | 33.33% |
| 110 % of the example value | 30.30% |
| 120 % of the example value | 27.78% |
The corridor runs from 27.78% to 41.67% across that band — which is the range worth planning inside rather than the single 33.33% point estimate. Reproduce it in the form above by editing Possible outcomes alone; the substitution steps will follow your figures exactly.
What actually moves your Kelly Criterion
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the single-trial probability was recalculated from scratch. For Kelly Criterion the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Possible outcomes +10 % → Kelly Criterion = 30.30% · −10 % → 37.04% (the single-trial probability shifts ≈11.1 %)
- Favourable outcomes +10 % → Kelly Criterion = 36.67% · −10 % → 30.00% (the single-trial probability shifts ≈10.0 %)
Possible outcomes is the dominant lever here: ten percent either way moves the result by about 11.1 %, from 30.30% to 37.04%. Measure that input from a document rather than from memory, and treat Favourable outcomes as the second priority (≈10.0 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
What a Kelly Criterion of 33.33% means in practice
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “Live odds — worth calculating the payoff” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Possible outcomes already spans 30.30% to 37.04%. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
The comparison worth making is not with somebody else’s Kelly Criterion but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
The errors that quietly break a Kelly Criterion figure
Independence is the assumption; card draws, weather and streaks correlate, which shrinks the repetition column’s real value. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing a Kelly Criterion computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
This model has its own particular trap: Possible outcomes carries ≈11.1 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
A final trap is presentation: reporting Kelly Criterion to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Six things to confirm before acting on Kelly Criterion
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Compare the result with one independent method or published benchmark.
- Check Possible outcomes before anything else: it is the measured dominant input, ≈11.1 % of Kelly Criterion per ten percent.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Re-run the calculation with a ±10 % stress on the two most sensitive inputs.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Five steps from raw inputs to a figure you can defend
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — collect, then type. Everything this tool asks for is listed above (favourable outcomes, possible outcomes, repetitions (independent)). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Step 2 — baseline before exploration. Get one defensible Single-trial probability on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. The test of a good estimate is not that it feels right but that it changes what you do.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. Precision is a promise you make about your data; make sure your inputs can keep it.
Step 5 — schedule the next run. In Miscellaneous & Fun the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. If the answer changes your behaviour, it deserves a second run with different assumptions.
The real-world conversations Kelly Criterion settles
Miscellaneous & Fun arguments end at arithmetic or they do not end. Kelly Criterion is the arithmetic: 33.33% on the example inputs, reproducible by anyone who types the same numbers. The point of transparency is that a reader can disagree with a specific line rather than with you.
Used properly this is a five-minute filter that saves weeks. Compute Kelly Criterion, reject what fails, and only then bring in the expensive analysis for the survivors. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Miscellaneous & Fun the expensive mistakes are rarely sudden; they are small changes in Favourable outcomes that nobody recalculated for a year. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Quick answers: what searchers ask about Kelly Criterion
What affects Kelly Criterion the most?
Kelly Criterion is driven above all by Possible outcomes. Perturbing only that field by ten percent either way produced 30.30% against the 33.33% baseline — a ≈11.1 % response, while Favourable outcomes manages ≈10.0 %.
Which matters more: favourable outcomes or possible outcomes?
Possible outcomes, by a factor of about 1.1. Concretely: ten percent on Possible outcomes is worth ≈11.1 % of Kelly Criterion, the same nudge on Favourable outcomes only ≈10.0 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Kelly Criterion?
On the worked example above Kelly Criterion comes out at 33.33%. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Kelly Criterion by hand?
Use the stated model — p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n — and substitute in the order the tool prints (it starts from p = 2 ÷ 6 = 0.3333). On the example inputs the hand route lands on 33.33%, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Kelly Criterion if possible outcomes changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the single-trial probability goes across 30.30% to 37.04%, a swing of roughly 11.1 % around the 33.33% baseline. That ratio is the practical definition of how much this input matters.
Is the Kelly Criterion result of 33.33% good or bad?
The tool answers “what”, not “whether”: 33.33% carries the verdict “Live odds — worth calculating the payoff” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Is Kelly Criterion accurate?
The arithmetic is exact: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 33.33% result as the correct answer to the question you typed — and check the assumptions section before acting on it.
What affects Kelly Criterion the most?
Sensitivity depends on where you start, but the inputs Favourable outcomes and Possible outcomes typically move Kelly Criterion further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Do odds “even out”?
Each trial is memoryless — the law of large numbers guarantees averages over the long haul, not corrections soon.
What changes with repetition?
The at-least-one line compounds (1−(1−p)^n) — 3 % once per try becomes 1−0.97^30 ≈ 60 % across 30 tries.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
Glossary for Kelly Criterion
- Odds against
- 2.00 :1 for the Kelly Criterion worked case; it sits next to the main result because it carries context the headline leaves out.
- At least one hit in 3
- 70.4% for the Kelly Criterion worked case; it sits next to the main result because it carries context the headline leaves out.
- Fair payout to break even
- 3.00 :1 on the example inputs — a companion figure printed beside the headline of Kelly Criterion so that no result is read in isolation.
- Single-trial probability
- The primary output of this tool: 33.33% for the default inputs, computed exactly from p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The plain-language label — here “Live odds — worth calculating the payoff” — mapping the computed figure onto experience-based ranges for Miscellaneous & Fun.
- Sensitivity (±10 %)
- How far the Kelly Criterion moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Kelly Criterion model comes from
Everything above runs on one stated formula, applied without hidden coefficients: p = fav ÷ poss; P(at least one hit in n trials) = 1 − (1−p)^n. Source of record: Classical probability (Laplace) for equally-likely outcomes. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.