Owns
Stake-size math from bankroll, quoted odds, user-estimated probability, and confidence label.
Edge-based stake sizing
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Last updated May 17, 2026
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Formula reviewed May 17, 2026
Kelly Criterion Calculator
This tool estimates Kelly stake size from a quoted price and your own win probability estimate. It is not a no-vig model, not a bankroll-discipline planner, and not a guarantee that a bet is profitable.
This page owns one job: turning bankroll, quoted odds, and your estimated win probability into Kelly stake sizes.
Use it for full, half, and quarter Kelly outputs when you already have a defensible probability estimate. Do not use it as proof that a line is fair, that the bookmaker margin has been removed, or that a wager should be placed at all.
What this Kelly calculator owns
Does not own
True-probability modeling, sportsbook approval, legality, payout limits, tax treatment, or emotional pressure to bet.
Stop using it when
The probability is a hunch, the result creates urgency, you are chasing losses, or the next issue is state, account, support, or bankroll discipline.
Disclosure
If commercial links appear elsewhere on the site, they do not change the formulas, assumptions, labels, or limitations on this page. This calculator is informational and should be paired with careful probability estimation and bankroll discipline.
Privacy note: this calculator runs in your browser. Do not enter account IDs, ticket numbers, login details, addresses, document numbers, card numbers, bank details or private sportsbook data. Copy/share actions include assumptions only.
Responsible-play boundary: if the output creates urgency, chasing, repeated deposits, or pressure to raise stakes, stop. Call or text 1-800-MY-RESET for confidential support. State-specific resources may vary.
Your probability estimate is the real input
Kelly does not discover edge. It only sizes a stake from the probability number you enter. If that probability is guessed, biased, stale, or copied from a market price without removing margin, the output can look precise while being unsafe.
Use this page only after you can explain where your probability estimate came from. Do not use raw quoted odds, a hunch, a pick, or a promo claim as a Kelly input.
Run the calculator
If Kelly is zero or negative, this page shows a no-bet result instead of pretending the model found a positive stake.
Valid input rules
Bankroll
Enter a bankroll above zero. Kelly sizing is meaningless if the bankroll figure is missing or fictional.
Odds
American odds cannot be zero. Decimal odds must be strictly greater than 1.00 because 1.00 makes the Kelly denominator collapse to zero.
Win probability
Enter a percentage such as 55 for 55 percent. The output is only as good as that estimate.
Probability confidence
Use the confidence label to mark whether the input came from a documented model, full-market no-vig comparison, uncertain estimate or guess.
Fair odds mode
Use fair odds or no-vig odds only when you have a full-market source. The tool converts that price into probability; it does not verify the source.
Stake limits and rounding
Rounding, minimum stake and maximum stake fields show practical friction after the Kelly output. They do not prove a sportsbook will accept the wager.
Formula
Edge: (p x decimal odds) - 1
Kelly fraction: edge / (decimal odds - 1)
Full Kelly stake: bankroll x Kelly fraction
Half Kelly stake: full Kelly / 2
Quarter Kelly stake: full Kelly / 4
If the Kelly fraction is zero or negative, the model suggests no bet. A single quoted line does not remove vig or prove that your probability estimate is correct.
Kelly formula registry
| Registry item | Current definition |
|---|---|
| Tool name | Kelly Criterion Calculator |
| Tool type | Educational stake-sizing calculator |
| Formula version | Kelly Stake Sizing Model v2.1, reviewed May 17, 2026 |
| Inputs | Bankroll, odds format, quoted odds, probability input mode, manual probability or fair/no-vig odds, probability confidence, Kelly multiplier, rounding step, minimum stake, maximum stake |
| Outputs | Decimal odds, edge from quoted price, full Kelly percentage, full/half/quarter Kelly stake, selected multiplier stake, rounded/limit-adjusted stake, losing-streak stress, no-bet label, confidence warning |
| Assumptions | The user owns the probability estimate and the bankroll is discretionary. Decimal odds are greater than 1.00. |
| Known exclusions | True-probability modeling, certified no-vig market construction, sportsbook limit approval, risk-of-ruin probability, tax treatment, legal status, payout review and harm-risk assessment |
| Review cadence | Quarterly tools review, plus immediate review after odds, bankroll, RG or source-route changes |
Your probability estimate drives the result
Bad probability estimate = dangerous stake
If your probability estimate is too high, Kelly turns that optimism directly into a larger recommended bet size. That is why a confident-looking output can still be dangerous.
Near breakeven edges are fragile
When the edge is only slightly positive, tiny changes in your estimate can flip the model from bet to no bet or back again.
Probability evidence score
| Input source | Confidence | Recommended action |
|---|---|---|
| Documented tracked model | Higher | Fractional Kelly still preferred; save model notes with the evidence packet. |
| Full-market no-vig comparison | Medium | Use cautiously and verify the full market, not a single line. |
| Small sample estimate | Low | Use tenth/quarter Kelly or skip; do not let the output justify a larger stake. |
| Hunch, pick, promo claim or raw odds | Stop | Do not use Kelly. Build probability evidence first. |
Probability source examples
| Probability source | Example | Use Kelly? |
|---|---|---|
| Full-market no-vig | Two-way market with both sides entered into a no-vig check | Cautious only; still prefer fractional Kelly. |
| Documented model | Tracked and calibrated model with saved assumptions | Fractional Kelly can be considered if bankroll limits still fit. |
| Raw odds | Single quoted line only | No. Raw implied probability includes margin. |
| Newsletter pick | Pick language without a probability method | No. A pick is not probability evidence. |
| Small sample model | Short record, limited sample or untested angle | Use tenth/quarter Kelly or skip. |
Kelly vs bankroll planner decision gate
| User situation | Correct route |
|---|---|
| I only need unit, session or stop-loss limits | Bankroll Planner |
| I have a documented edge estimate | Kelly Criterion Calculator |
| I only have sportsbook odds | Odds Converter or No-Vig Calculator first |
| I am chasing losses or depositing again | Reality Check Tool and support before any calculator |
| I want to recover losses faster | Stop, not Kelly |
Kelly misuse examples
| Misuse | Why dangerous | Correct route |
|---|---|---|
| Using raw implied probability | It includes vig and can make a market look fairer than it is. | No-Vig Calculator |
| Using a hunch | The formula becomes precision theater around an unsupported input. | Build a documented model or skip. |
| Full Kelly on an uncertain estimate | Drawdowns can become severe if the estimate is even slightly wrong. | Half, quarter, tenth Kelly or no bet. |
| Same-game correlated bets | Independence assumptions break when legs move together. | Portfolio Kelly only if correlation is explainable; otherwise skip. |
| Chasing losses | Stake sizing becomes loss recovery pressure, not analysis. | Reality Check Tool and support first. |
No-vig integration before Kelly
Convert market to no-vig probability
Use the No-Vig Calculator when you have the full market. A single quoted line cannot remove vig.
Paste no-vig probability or fair odds here
After the no-vig step, enter the no-vig probability manually or paste fair/no-vig odds into the fair-odds mode. Do not use raw implied probability as Kelly evidence.
How small probability changes affect stake size
| Quoted odds | Your probability | Full Kelly | Interpretation |
|---|---|---|---|
| -110 | 52% | Near zero | This sits close to breakeven. A tiny mistake can erase the edge. |
| -110 | 55% | Meaningful positive stake | Only trust a larger Kelly output if the probability estimate is genuinely credible. |
Losing-streak stress check
This is not a risk-of-ruin model. It simply shows how much of the entered bankroll would be exposed if the selected, rounded stake lost 3, 5, or 10 times in a row.
If this block creates pressure to recover, increase stake, or deposit again, the correct next route is support, not another calculation.
Why fractional Kelly exists
Full Kelly can swing hard
A positive edge estimate can still produce severe drawdowns, especially when the probability estimate is wrong or the market is volatile.
Half, quarter and tenth Kelly reduce exposure
Fractional Kelly is a caution tool, not a guarantee. It lowers stake size when estimate quality, limits, correlation or emotional pressure matter.
Correlation breaks simple math
Multiple bets from the same game, player, market or injury news may move together. If you cannot explain correlation, do not model the set as independent.
Printable Kelly evidence packet
Save assumptions, not private ticket or account data. A useful Kelly record includes quoted odds, probability source, confidence label, bankroll, selected multiplier, stake rounding, stake limits, chosen output and stop rule.
- Odds and odds format used.
- Manual probability or fair/no-vig odds source.
- Probability confidence label.
- Full Kelly and selected fractional Kelly output.
- Rounded stake, min/max stake status and losing-streak stress.
- Bankroll limit, stop-loss rule and support stop-gate.
Worked examples
$1,000 at +150 with 45 percent win probability
Normalized decimal odds 2.50, edge 12.50%, full Kelly 8.33%, full Kelly $83.33, half Kelly $41.67, quarter Kelly $20.83.
$5,000 at -110 with 55 percent win probability
Normalized decimal odds 1.91, edge 5.00%, full Kelly 5.50%, full Kelly $275.00, half Kelly $137.50, quarter Kelly $68.75.
$2,000 at +250 with 35 percent win probability
Normalized decimal odds 3.50, edge 22.50%, full Kelly 9.00%, full Kelly $180.00, half Kelly $90.00, quarter Kelly $45.00.
$5,000 at -150 with 65 percent win probability
Normalized decimal odds 1.67, edge 8.33%, full Kelly 12.50%, full Kelly $625.00, half Kelly $312.50, quarter Kelly $156.25.
Where this calculator can mislead you
Your probability estimate can be wrong
Kelly math is extremely sensitive to the win-probability number you enter. A bad estimate can make the output look precise while pointing you toward the wrong stake.
A single converted line does not remove vig
Quoted odds still include bookmaker margin. Use a full-market no-vig route before comparing your own probability estimate.
No tax or limit modeling here
This root tool does not model state taxes, stake limits, void rules, promo credits, or payout approval. Those are separate questions.
Kelly is not bankroll discipline by itself
If you need session budgeting, stop-loss rules, or unit planning, use the bankroll planner instead of treating Kelly as a full bankroll framework.
Edge evidence checklist before using the Kelly output
- Quoted odds and odds format used in the calculator.
- Your probability estimate and where it came from.
- Whether bookmaker margin, market movement, limits, and rejected-bet risk were considered.
- Whether the bet ticket could be voided, repriced, limited, or settled under special rules.
- Bankroll boundary outside Kelly: session limit, stop-loss, and maximum daily exposure.
- Reason to use half or quarter Kelly instead of full Kelly when estimate quality is uncertain.
How to read full, half, quarter Kelly, and no bet
Full Kelly
This is the mathematically aggressive stake implied by the model. It grows quickly when your probability estimate rises.
Half or quarter Kelly
Fractional Kelly reduces exposure when the edge estimate is noisy or when you want smoother bankroll swings.
No bet
A zero or negative Kelly output means the quoted price does not justify a positive edge-based stake under your inputs.
Do not confuse it with bankroll planning
Kelly answers stake size under an assumed edge. It does not replace stop-loss rules, session budgets, or recordkeeping.
When this tool stops being the right owner
Legal, state, or operator approval question
This tool does not verify legality, state approval, operator status, or license claims.
Use state guidesAccount, payout, or document issue
Move to banking, withdrawal, or scam routes when support, KYC, payment, or account records decide the outcome.
Withdrawal verificationControl, chasing, or harm issue
Use responsible-gambling support before opening another calculator or gambling page.
Responsible gambling basicsNext pages by Kelly problem
Portfolio Kelly Calculator
Use for 2-15 legs with total exposure caps and correlation warnings.
Odds Converter
Use to normalize quoted prices. It does not prove edge.
No-Vig Calculator
Use to normalize a full market before comparing your own probability estimate.
Parlay Calculator
Use for quoted parlay payout math, same-game final-price checks and ticket evidence. It does not prove edge.
Bankroll Planner
Use for session budgets, unit sizing, stop-loss and exposure controls outside Kelly.
Betting Terms
Use when market, settlement, void, push, or cash-out language is unclear.
Sportsbook Limits
Use when stake limits, rejected bets, max payout or bet acceptance can change the practical outcome.
Sportsbook Verification
Use when accepted ticket evidence and account records matter.
Reality Check Tool
Use if Kelly output becomes a reason to chase, increase stakes, or ignore limits.
Kelly QA matrix
| Case | Input | Expected behavior |
|---|---|---|
| Normal positive edge | $1,000, +150, 45% | Full Kelly is positive, half and quarter Kelly display lower exposure. |
| Negative edge | $1,000, -110, 50% | Kelly decision shows no bet instead of a fake positive stake. |
| Invalid bankroll | $0 or negative bankroll | Validation blocks calculation and marks bankroll invalid. |
| Invalid odds | American 0 or decimal 1.00 | Validation explains the odds denominator problem. |
| Probability entered as decimal | 0.5 instead of 50 | Validation copy tells the user to enter a percent. |
| Fair odds mode | Fair decimal odds 2.22 | Tool converts fair odds to probability before Kelly sizing. |
| Custom multiplier | Multiplier 0.10 | Selected stake equals 10% of full Kelly stake before rounding and limits. |
| Stake rounding and max limit | Rounding $5, max stake below selected stake | Adjusted stake is capped and limit status explains the block. |
| Losing-streak stress | Selected adjusted stake | 3, 5 and 10-loss exposure displays as dollars and bankroll percentage, without risk-of-ruin claims. |
| Guess confidence | Confidence set to guess / raw odds | Result warns not to use Kelly until probability evidence exists. |
| High-exposure output | Full Kelly above 25% of bankroll | Result labels the output as high exposure and routes back to bankroll discipline. |
| Share URL | Copy share URL | URL includes assumptions only and canonical remains /tools/kelly/. |
Last local QA pass: May 17, 2026. Scope: odds parsing, fair-odds conversion, edge calculation, multiplier/divisor logic, stake rounding, min/max stake labels, losing-streak stress, negative-edge no-bet label, probability confidence warning, copy/share controls, mobile card tables, schema parity and no-JS formula fallback. Public fixture route: /tools/kelly/test-fixtures.json.
Source register
| Source | Used for | Status |
|---|---|---|
| Internal Kelly Stake Sizing Model v2.1 | Full, half and quarter Kelly outputs, no-bet label, probability-confidence warning | Reviewed May 17, 2026 |
| Internal Odds Conversion Model | American and decimal odds normalization | Cross-linked to Odds Converter |
| NCPG help route | Responsible-gambling stop gate and helpline wording | Checked May 17, 2026 |
| The Playbook USA editorial policy | No profit guarantees, no operator approval, commercial separation | Current internal standard |
Kelly calculator FAQ
Does the Kelly Criterion Calculator prove a bet has value?
No. It sizes a stake only after you supply a probability estimate. If that estimate is weak, the output is weak.
Should I use raw implied probability as the Kelly input?
No. Raw implied probability includes bookmaker margin. Use a full-market no-vig check or your own documented model before entering a probability.
Why does this page show half and quarter Kelly?
Fractional Kelly reduces exposure when the probability estimate is uncertain. It still does not guarantee profit or replace bankroll limits.
What does no bet mean?
A no-bet result means your entered probability does not beat the quoted price under this model.
What if the result makes me want to raise stakes?
Stop using the calculator. Use the Reality Check Tool or call/text 1-800-MY-RESET.
Changelog
May 17, 2026: upgraded to Kelly Stake Sizing Model v2.1; added probability confidence labels, copy/share result controls, formula registry, QA matrix, source register, FAQ schema, stronger privacy and RG boundaries, mobile card tables and no-News navigation.
May 17, 2026 later update: added custom Kelly multiplier/divisor, fair odds and no-vig probability input mode, stake rounding, min/max stake checks, losing-streak stress output, probability evidence score, probability source examples, Kelly misuse examples, root single-bet portfolio preview, Kelly-vs-bankroll decision gate, no-vig integration, fractional-Kelly drawdown explainer, copyable safe explanation, printable evidence packet and public test fixtures.
Apr 24, 2026: earlier Kelly calculator with full, half and quarter Kelly outputs plus probability-risk warnings.
Maintained and reviewed by
Maintained by: the Playbook USA Tools Team.
Written by Michael Johnson, edited by Sarah Roberts, and reviewed for responsible-play boundaries by David Thompson.
Review scope: odds normalization, edge calculation, Kelly fraction outputs, probability-confidence labels, copy/share behavior and route boundaries.
Last updated: May 17, 2026. Formula reviewed: May 17, 2026. Current scope: full, half, and quarter Kelly stake sizing from bankroll, quoted odds, and user-estimated win probability. This page is informational only and is not gambling, legal, tax, or financial advice.
Responsible gambling help
For national help in the U.S., call or text the National Problem Gambling Helpline at 1-800-MY-RESET. Existing access points may remain active, and state-specific resources may vary.
Help routing checked: May 17, 2026. Re-check NCPG phone, text, chat and state-resource wording before each quarterly tools update.
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