{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"kelly-criterion"},"result":{"entity_type":"calculator","id":"kelly-criterion","calculator_id":"kelly-criterion","canonical_url":"https://tttkmbb.com/gaming/kelly-criterion","name":"Kelly Criterion Calculator","title":"Kelly Criterion Calculator – Optimal Stake Fraction, Half Kelly and Expected Growth Rate","category":"gaming","category_name":"Games & Betting Math","tool_name":"calculate_kelly_stake","featured_mcp_tool":false,"description":"Computes the Kelly stake fraction f* = (b·p − q)/b from decimal odds and an estimated win probability, the recommended stake for a bankroll at full or fractional Kelly, and the expected logarithmic growth rate per bet.","use_when":"You know the odds and your estimated win probability and want the bankroll fraction that maximises long-run growth (or a fractional-Kelly stake).","do_not_use_when":"The probability estimate is unreliable (Kelly over-bets badly when p is overstated), the bet has more than two outcomes, or you only need the expected value (use bet-expected-value). Mathematics only; not gambling advice.","inputs":[{"name":"decimal_odds","label":"Decimal odds","type":"number","required":true,"max":1000000,"exclusive_min":1,"description":"Decimal (European) odds including the stake, e.g. 2.20; convert other formats with odds-converter.","example":2},{"name":"win_probability_percent","label":"Estimated win probability","type":"number","unit":"%","required":true,"max":100,"exclusive_min":0,"description":"Your own estimate of the probability that the bet wins, in percent.","example":55},{"name":"bankroll","label":"Bankroll","type":"number","required":false,"default":1000,"max":1000000000000,"exclusive_min":0,"description":"Total funds available for betting (any currency).","example":1000},{"name":"kelly_fraction","label":"Kelly fraction","type":"number","required":false,"default":1,"max":1,"exclusive_min":0,"description":"Multiplier applied to the full Kelly fraction: 1 = full Kelly, 0.5 = half Kelly, 0.25 = quarter Kelly.","example":1}],"outputs":[{"name":"kelly_percent","label":"Full Kelly fraction","type":"number","unit":"%","decimals":2,"description":"f* × 100 = (b·p − q)/b × 100; zero or negative means no edge (no bet)."},{"name":"recommended_stake","label":"Recommended stake","type":"number","decimals":2,"description":"bankroll × f* × kelly_fraction, or 0 when f* ≤ 0."},{"name":"full_kelly_stake","label":"Full Kelly stake","type":"number","decimals":2,"description":"bankroll × f* (0 when f* ≤ 0)."},{"name":"half_kelly_stake","label":"Half Kelly stake","type":"number","decimals":2,"description":"bankroll × f* / 2 (0 when f* ≤ 0)."},{"name":"expected_growth_rate_percent","label":"Expected growth rate per bet","type":"number","unit":"%","decimals":2,"description":"(p·ln(1 + f·b) + q·ln(1 − f)) × 100 at the recommended fraction f = f* × kelly_fraction."},{"name":"edge_percent","label":"Edge (expected return per unit staked)","type":"number","unit":"%","decimals":2,"description":"(b·p − q) × 100 = (p·decimal_odds − 1) × 100; Kelly is edge divided by the net odds b."}],"input_schema":{"type":"object","properties":{"decimal_odds":{"description":"Decimal (European) odds including the stake, e.g. 2.20; convert other formats with odds-converter.","type":"number","maximum":1000000,"exclusiveMinimum":1,"examples":[2]},"win_probability_percent":{"description":"Your own estimate of the probability that the bet wins, in percent. Unit: %.","type":"number","maximum":100,"exclusiveMinimum":0,"examples":[55],"x-unit":"%"},"bankroll":{"description":"Total funds available for betting (any currency).","type":"number","maximum":1000000000000,"exclusiveMinimum":0,"default":1000,"examples":[1000]},"kelly_fraction":{"description":"Multiplier applied to the full Kelly fraction: 1 = full Kelly, 0.5 = half Kelly, 0.25 = quarter Kelly.","type":"number","maximum":1,"exclusiveMinimum":0,"default":1,"examples":[1]}},"additionalProperties":false,"required":["decimal_odds","win_probability_percent"]},"output_schema":{"type":"object","properties":{"kelly_percent":{"description":"f* × 100 = (b·p − q)/b × 100; zero or negative means no edge (no bet). Unit: %.","type":"number","x-unit":"%"},"recommended_stake":{"description":"bankroll × f* × kelly_fraction, or 0 when f* ≤ 0.","type":"number"},"full_kelly_stake":{"description":"bankroll × f* (0 when f* ≤ 0).","type":"number"},"half_kelly_stake":{"description":"bankroll × f* / 2 (0 when f* ≤ 0).","type":"number"},"expected_growth_rate_percent":{"description":"(p·ln(1 + f·b) + q·ln(1 − f)) × 100 at the recommended fraction f = f* × kelly_fraction. Unit: %.","type":"number","x-unit":"%"},"edge_percent":{"description":"(b·p − q) × 100 = (p·decimal_odds − 1) × 100; Kelly is edge divided by the net odds b. Unit: %.","type":"number","x-unit":"%"}}},"formula":"b = decimal_odds − 1; p = win_probability_percent/100; q = 1 − p; f* = (b·p − q)/b; recommended_stake = bankroll × max(f*, 0) × kelly_fraction; growth = p·ln(1 + f·b) + q·ln(1 − f) with f = max(f*, 0) × kelly_fraction","method":"Kelly (1956): betting the fraction f* of the bankroll maximises the expected logarithm of wealth for repeated independent bets with a known edge. Fractional Kelly (0.25–0.5) gives most of the growth with far smaller drawdowns. Probability mathematics only; not gambling advice.","sources":[{"name":"Kelly JL (1956) A New Interpretation of Information Rate, Bell System Technical Journal 35(4):917-926","url":"https://doi.org/10.1002/j.1538-7305.1956.tb03809.x","type":"peer_reviewed","retrieved_at":"2026-09-24"},{"name":"Kelly criterion (Wikipedia)","url":"https://en.wikipedia.org/wiki/Kelly_criterion","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Evens (2.00), 55 % chance, bankroll 1000","inputs":{"decimal_odds":2,"win_probability_percent":55,"bankroll":1000,"kelly_fraction":1},"expected":{"kelly_percent":10,"recommended_stake":100,"half_kelly_stake":50,"expected_growth_rate_percent":0.5,"edge_percent":10},"url":"https://tttkmbb.com/api/v1/calculate/kelly-criterion?decimal_odds=2&win_probability_percent=55&bankroll=1000&kelly_fraction=1"},{"name":"Odds 3.50, 35 % chance, bankroll 5000, half Kelly","inputs":{"decimal_odds":3.5,"win_probability_percent":35,"bankroll":5000,"kelly_fraction":0.5},"expected":{"kelly_percent":9,"recommended_stake":225,"full_kelly_stake":450,"half_kelly_stake":225,"expected_growth_rate_percent":0.74,"edge_percent":22.5},"url":"https://tttkmbb.com/api/v1/calculate/kelly-criterion?decimal_odds=3.5&win_probability_percent=35&bankroll=5000&kelly_fraction=0.5"}],"faq":[{"q":"Why use half Kelly?","a":"Full Kelly assumes the probability is exactly right and tolerates 50 % drawdowns; half Kelly keeps about 75 % of the growth rate with roughly half the volatility and protects against an overstated edge."},{"q":"What does a negative Kelly percentage mean?","a":"The bet has no edge (p·odds < 1): expected value is negative and the recommended stake is 0. A negative f* would only be a bet on the opposite outcome if such a price existed."},{"q":"Is the edge here the same as in bet-expected-value?","a":"No. Here edge is the expected return per unit staked (b·p − q); bet-expected-value reports the edge as the difference in percentage points between your probability and the implied probability."}],"tags":["kelly criterion","kelly stake","optimal bet size","bankroll management","half kelly","growth rate"],"related":[{"calculator_id":"bet-expected-value","reason":"Expected value of the same bet without sizing."},{"calculator_id":"expected-value","reason":"General probability-weighted mean of outcomes."},{"calculator_id":"odds-converter","reason":"Convert American or fractional prices to decimal odds."}],"links":{"html":"https://tttkmbb.com/gaming/kelly-criterion","markdown":"https://tttkmbb.com/gaming/kelly-criterion.md","json":"https://tttkmbb.com/gaming/kelly-criterion.json","api":"https://tttkmbb.com/api/v1/calculate/kelly-criterion","schema":"https://tttkmbb.com/api/v1/calculators/kelly-criterion","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:47:35Z"}