{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"lottery-odds"},"result":{"entity_type":"calculator","id":"lottery-odds","calculator_id":"lottery-odds","canonical_url":"https://tttkmbb.com/statistics/lottery-odds","name":"Lottery Odds Calculator","title":"Lottery Odds Calculator – Jackpot Probability and Prize-Tier Odds for Any Pick-k-of-n Game","category":"statistics","category_name":"Statistics & Probability","tool_name":"calculate_lottery_odds","featured_mcp_tool":false,"description":"Computes the number of possible tickets, the jackpot probability and '1 in N' odds for a lottery where k numbers are drawn from a pool of n (optionally with a separate bonus-ball pool), plus a table of the odds of matching each number of main numbers.","use_when":"You want the odds of winning or of matching a given number of balls in a lottery such as 6/49, Powerball (5/69 + 1/26) or EuroMillions (5/50 + 2/12).","do_not_use_when":"Bonus balls are drawn from the same pool as the main numbers (UK Lotto 'bonus ball'), or you need the expected value of a ticket (use expected-value with the prize amounts).","inputs":[{"name":"pool_size","label":"Main pool size (n)","type":"integer","required":true,"min":2,"max":1000,"description":"How many different numbers the main balls are drawn from.","example":69},{"name":"picks","label":"Numbers drawn (k)","type":"integer","required":true,"min":1,"max":20,"description":"How many main numbers are drawn (and chosen on a ticket) without replacement.","example":5},{"name":"bonus_pool_size","label":"Bonus pool size","type":"integer","required":false,"min":1,"max":1000,"description":"Size of a separate pool for bonus balls (e.g. 26 for the Powerball). Omit if there is none.","example":26},{"name":"bonus_picks","label":"Bonus balls drawn","type":"integer","required":false,"default":1,"min":1,"max":5,"description":"How many bonus balls are drawn from the bonus pool (1 for Powerball, 2 for EuroMillions Lucky Stars).","example":1}],"outputs":[{"name":"total_combinations","label":"Possible tickets","type":"number","decimals":0,"description":"C(pool_size, picks) × C(bonus_pool_size, bonus_picks)."},{"name":"jackpot_probability","label":"Jackpot probability","type":"number","decimals":12,"description":"1 / total_combinations for one ticket."},{"name":"jackpot_odds","label":"Jackpot odds","type":"string","decimals":4,"description":"Odds as '1 in N'."},{"name":"matches","label":"Odds by number of main numbers matched","type":"list","decimals":12,"description":"One row per number of main matches (from picks down to 0): matched, ways (count as a string), probability and odds ('1 in N'), plus probability_with_bonus / odds_with_bonus and probability_without_bonus / odds_without_bonus when a bonus pool is given."}],"input_schema":{"type":"object","properties":{"pool_size":{"description":"How many different numbers the main balls are drawn from.","type":"integer","minimum":2,"maximum":1000,"examples":[69]},"picks":{"description":"How many main numbers are drawn (and chosen on a ticket) without replacement.","type":"integer","minimum":1,"maximum":20,"examples":[5]},"bonus_pool_size":{"description":"Size of a separate pool for bonus balls (e.g. 26 for the Powerball). Omit if there is none.","type":"integer","minimum":1,"maximum":1000,"examples":[26]},"bonus_picks":{"description":"How many bonus balls are drawn from the bonus pool (1 for Powerball, 2 for EuroMillions Lucky Stars).","type":"integer","minimum":1,"maximum":5,"default":1,"examples":[1]}},"additionalProperties":false,"required":["pool_size","picks"]},"output_schema":{"type":"object","properties":{"total_combinations":{"description":"C(pool_size, picks) × C(bonus_pool_size, bonus_picks).","type":"number"},"jackpot_probability":{"description":"1 / total_combinations for one ticket.","type":"number"},"jackpot_odds":{"description":"Odds as '1 in N'.","type":"string"},"matches":{"description":"One row per number of main matches (from picks down to 0): matched, ways (count as a string), probability and odds ('1 in N'), plus probability_with_bonus / odds_with_bonus and probability_without_bonus / odds_without_bonus when a bonus pool is given.","type":"array"}}},"formula":"P(match exactly m main numbers) = C(picks, m) × C(pool_size − picks, picks − m) / C(pool_size, picks); P(all bonus balls) = 1 / C(bonus_pool_size, bonus_picks); jackpot = 1 / (C(pool_size, picks) × C(bonus_pool_size, bonus_picks))","method":"Hypergeometric probabilities for the main numbers, multiplied by the independent bonus-pool probability. Odds are for a single ticket per draw and ignore shared jackpots and prize amounts.","sources":[{"name":"Wikipedia – Lottery mathematics","url":"https://en.wikipedia.org/wiki/Lottery_mathematics","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Hypergeometric distribution","url":"https://en.wikipedia.org/wiki/Hypergeometric_distribution","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":"6 of 49","inputs":{"pool_size":49,"picks":6},"expected":{"total_combinations":13983816,"jackpot_probability":7.15e-8,"jackpot_odds":"1 in 13,983,816","matches":[{"matched":6,"ways":"1","odds":"1 in 13,983,816"},{"matched":5,"ways":"258","probability":0.0000184499,"odds":"1 in 54,201"},{"matched":4,"ways":"13,545","probability":0.000968619,"odds":"1 in 1,032"},{"matched":3,"ways":"246,820","probability":0.0176504,"odds":"1 in 56.66"},{"matched":2,"ways":"1,851,150","probability":0.132378},{"matched":1,"ways":"5,775,588","probability":0.413019},{"matched":0,"ways":"6,096,454","probability":0.435965}]},"url":"https://tttkmbb.com/api/v1/calculate/lottery-odds?pool_size=49&picks=6"},{"name":"Powerball: 5 of 69 plus 1 of 26","inputs":{"pool_size":69,"picks":5,"bonus_pool_size":26,"bonus_picks":1},"expected":{"total_combinations":292201338,"jackpot_odds":"1 in 292,201,338","matches":[{"matched":5,"ways":"1","odds":"1 in 11,238,513","odds_with_bonus":"1 in 292,201,338","odds_without_bonus":"1 in 11,688,054"},{"matched":4,"ways":"320","odds_with_bonus":"1 in 913,129","odds_without_bonus":"1 in 36,525"},{},{},{},{}]},"url":"https://tttkmbb.com/api/v1/calculate/lottery-odds?pool_size=69&picks=5&bonus_pool_size=26&bonus_picks=1"}],"faq":[{"q":"Does buying two tickets double my chances?","a":"Yes, two different tickets give 2 / total_combinations, still about 1 in 7 million for a 6/49 game."},{"q":"Why is 'match 5 without bonus' more likely than 'match 5 with bonus' by a factor of 25 in Powerball?","a":"The bonus ball is an independent 1-in-26 draw: of every 26 tickets matching all five main numbers, on average one also matches the Powerball and 25 do not."}],"tags":["lottery odds","lottery probability","6/49 odds","powerball odds","chance of winning the lottery"],"related":[{"calculator_id":"hypergeometric-distribution","reason":"General sampling-without-replacement probabilities."},{"calculator_id":"combinations-permutations","reason":"Count the possible tickets."},{"calculator_id":"expected-value","reason":"Expected value of a ticket from prize amounts and probabilities."}],"links":{"html":"https://tttkmbb.com/statistics/lottery-odds","markdown":"https://tttkmbb.com/statistics/lottery-odds.md","json":"https://tttkmbb.com/statistics/lottery-odds.json","api":"https://tttkmbb.com/api/v1/calculate/lottery-odds","schema":"https://tttkmbb.com/api/v1/calculators/lottery-odds","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:46:03Z"}