{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"bet-expected-value"},"result":{"entity_type":"calculator","id":"bet-expected-value","calculator_id":"bet-expected-value","canonical_url":"https://tttkmbb.com/gaming/bet-expected-value","name":"Bet Expected Value Calculator","title":"Bet Expected Value Calculator – EV, Edge and Fair Odds from Decimal Odds and Win Probability","category":"gaming","category_name":"Games & Betting Math","tool_name":"calculate_bet_expected_value","featured_mcp_tool":false,"description":"Computes the expected value of a bet from its decimal odds, your estimated win probability and the stake, together with the implied probability, the edge in percentage points and the fair (break-even) decimal odds.","use_when":"You have an estimate of the true win probability and want to know whether a price offers positive expected value, by how much, and what odds would be fair.","do_not_use_when":"You need the stake size that maximises bankroll growth (use kelly-criterion), a general probability-weighted mean of several outcomes (use expected-value), or only a format conversion (use odds-converter). 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":2.2},{"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":50},{"name":"stake","label":"Stake","type":"number","required":false,"default":100,"max":1000000000,"exclusive_min":0,"description":"Amount staked (any currency).","example":100}],"outputs":[{"name":"expected_value","label":"Expected value","type":"number","decimals":2,"description":"Average profit per bet over many repetitions: p·(odds − 1)·stake − (1 − p)·stake."},{"name":"expected_value_per_unit","label":"Expected value per unit staked","type":"number","decimals":4,"description":"expected_value / stake = p·odds − 1."},{"name":"expected_return_percent","label":"Expected return on stake","type":"number","unit":"%","decimals":2,"description":"expected_value_per_unit × 100."},{"name":"implied_probability_percent","label":"Implied probability","type":"number","unit":"%","decimals":2,"description":"100 / decimal_odds: the win probability at which the bet breaks even."},{"name":"edge_percent","label":"Edge","type":"number","unit":"percentage points","decimals":2,"description":"win_probability_percent − implied_probability_percent."},{"name":"fair_decimal_odds","label":"Fair decimal odds","type":"number","decimals":3,"description":"100 / win_probability_percent: the price at which the expected value is zero."},{"name":"is_positive_ev","label":"Positive expected value","type":"boolean","decimals":4,"description":"true when expected_value > 0."}],"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":[2.2]},"win_probability_percent":{"description":"Your own estimate of the probability that the bet wins, in percent. Unit: %.","type":"number","maximum":100,"exclusiveMinimum":0,"examples":[50],"x-unit":"%"},"stake":{"description":"Amount staked (any currency).","type":"number","maximum":1000000000,"exclusiveMinimum":0,"default":100,"examples":[100]}},"additionalProperties":false,"required":["decimal_odds","win_probability_percent"]},"output_schema":{"type":"object","properties":{"expected_value":{"description":"Average profit per bet over many repetitions: p·(odds − 1)·stake − (1 − p)·stake.","type":"number"},"expected_value_per_unit":{"description":"expected_value / stake = p·odds − 1.","type":"number"},"expected_return_percent":{"description":"expected_value_per_unit × 100. Unit: %.","type":"number","x-unit":"%"},"implied_probability_percent":{"description":"100 / decimal_odds: the win probability at which the bet breaks even. Unit: %.","type":"number","x-unit":"%"},"edge_percent":{"description":"win_probability_percent − implied_probability_percent. Unit: percentage points.","type":"number","x-unit":"percentage points"},"fair_decimal_odds":{"description":"100 / win_probability_percent: the price at which the expected value is zero.","type":"number"},"is_positive_ev":{"description":"true when expected_value > 0.","type":"boolean"}}},"formula":"p = win_probability_percent / 100; expected_value = p·(decimal_odds − 1)·stake − (1 − p)·stake; implied_probability_percent = 100 / decimal_odds; edge_percent = win_probability_percent − implied_probability_percent; fair_decimal_odds = 100 / win_probability_percent","method":"The expected value is the probability-weighted average of the profit if the bet wins and the loss of the stake if it loses; it is only as good as the probability estimate you supply. Probability mathematics only; not gambling advice.","sources":[{"name":"Expected value (Wikipedia)","url":"https://en.wikipedia.org/wiki/Expected_value","type":"reference","retrieved_at":"2026-09-24"},{"name":"Odds – moneyline, decimal and fractional odds and implied probability (Wikipedia)","url":"https://en.wikipedia.org/wiki/Odds","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":"Odds 2.20, 50 % chance, stake 100","inputs":{"decimal_odds":2.2,"win_probability_percent":50,"stake":100},"expected":{"expected_value":10,"expected_value_per_unit":0.1,"implied_probability_percent":45.45,"edge_percent":4.55,"fair_decimal_odds":2,"is_positive_ev":true},"url":"https://tttkmbb.com/api/v1/calculate/bet-expected-value?decimal_odds=2.2&win_probability_percent=50&stake=100"},{"name":"Odds 1.80, 50 % chance, stake 50","inputs":{"decimal_odds":1.8,"win_probability_percent":50,"stake":50},"expected":{"expected_value":-5,"expected_return_percent":-10,"implied_probability_percent":55.56,"edge_percent":-5.56,"fair_decimal_odds":2,"is_positive_ev":false},"url":"https://tttkmbb.com/api/v1/calculate/bet-expected-value?decimal_odds=1.8&win_probability_percent=50&stake=50"}],"faq":[{"q":"Is the edge a percentage or percentage points?","a":"Percentage points: a 50 % estimate against a 45.45 % implied probability is an edge of 4.55 points. The expected return on stake (10 % here) is the relative figure."},{"q":"Where does the win probability come from?","a":"It must be your own estimate (model, form analysis, removing the margin from market odds); the calculator cannot know the true probability, and a wrong estimate makes the EV wrong."}],"tags":["expected value bet","ev calculator","betting edge","fair odds","value bet","implied probability"],"related":[{"calculator_id":"expected-value","reason":"Expected value and variance of a general list of outcomes and probabilities."},{"calculator_id":"kelly-criterion","reason":"Optimal stake size for the same odds and probability."},{"calculator_id":"odds-converter","reason":"Convert American or fractional prices to decimal odds."}],"links":{"html":"https://tttkmbb.com/gaming/bet-expected-value","markdown":"https://tttkmbb.com/gaming/bet-expected-value.md","json":"https://tttkmbb.com/gaming/bet-expected-value.json","api":"https://tttkmbb.com/api/v1/calculate/bet-expected-value","schema":"https://tttkmbb.com/api/v1/calculators/bet-expected-value","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:47Z","next_actions":[{"tool":"run_calculator","calculator_id":"bet-expected-value","reason":"Run Bet Expected Value Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/gaming/bet-expected-value.md"}}