{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"poker-outs"},"result":{"entity_type":"calculator","id":"poker-outs","calculator_id":"poker-outs","canonical_url":"https://tttkmbb.com/gaming/poker-outs","name":"Poker Outs Calculator","title":"Poker Outs Calculator – Exact Drawing Odds in Texas Hold'em versus the Rule of 2 and 4","category":"gaming","category_name":"Games & Betting Math","tool_name":"calculate_poker_outs","featured_mcp_tool":false,"description":"Computes the exact probability of hitting one of your outs by the next card or by the river in Texas hold'em from the number of outs and unseen cards, expressed as a percentage and as odds against, and compares it with the rule of 2 and 4 estimate.","use_when":"You know how many cards complete your hand and want the exact probability of hitting by the turn or the river, or the odds against to compare with pot odds.","do_not_use_when":"You need the probability of specific starting hands or made hands (use combinations-permutations or hypergeometric-distribution), or games with a different deck. Mathematics only; not gambling advice.","inputs":[{"name":"outs","label":"Outs","type":"integer","required":true,"min":1,"max":20,"description":"Number of unseen cards that complete your hand (flush draw 9, open-ended straight draw 8, gutshot 4).","example":9},{"name":"street","label":"Cards to come","type":"enum","required":false,"default":"flop_to_river","values":[{"value":"flop_to_river","label":"Flop to river (two cards to come, 47 unseen)","aliases":["flop","two_cards","turn_and_river"]},{"value":"turn_to_river","label":"Turn to river (one card to come, 46 unseen)","aliases":["turn","river","one_card"]},{"value":"flop_to_turn","label":"Flop to turn (one card to come, 47 unseen)","aliases":["next_card"]}],"description":"Which cards are still to be dealt; sets the number of cards to come and the default count of unseen cards (52 minus your 2 hole cards and the board).","example":"flop_to_river"},{"name":"unseen_cards","label":"Unseen cards (override)","type":"integer","required":false,"min":2,"max":50,"description":"Optional: cards not visible to you, if it differs from the default (e.g. 45 with one known folded card). Must be larger than outs.","example":47}],"outputs":[{"name":"probability_percent","label":"Probability of hitting","type":"number","unit":"%","decimals":2,"description":"One card: outs/unseen; two cards: 1 − C(unseen − outs, 2)/C(unseen, 2)."},{"name":"odds_against","label":"Odds against","type":"string","decimals":4,"description":"(1 − p)/p expressed as \"x : 1\", for comparison with pot odds."},{"name":"odds_against_ratio","label":"Odds against (ratio)","type":"number","decimals":2,"description":"(1 − p)/p as a number."},{"name":"rule_of_2_and_4_percent","label":"Rule of 2 and 4 estimate","type":"number","unit":"%","decimals":2,"description":"outs × 2 with one card to come, outs × 4 with two cards to come."},{"name":"exact_vs_rule_difference","label":"Rule minus exact","type":"number","unit":"percentage points","decimals":2,"description":"rule_of_2_and_4_percent − probability_percent; positive means the rule overestimates."},{"name":"cards_to_come","label":"Cards to come","type":"integer","decimals":0,"description":"1 or 2 according to the street."},{"name":"unseen_cards_used","label":"Unseen cards used","type":"integer","decimals":0,"description":"Number of unseen cards the probability was computed with."}],"input_schema":{"type":"object","properties":{"outs":{"description":"Number of unseen cards that complete your hand (flush draw 9, open-ended straight draw 8, gutshot 4).","type":"integer","minimum":1,"maximum":20,"examples":[9]},"street":{"description":"Which cards are still to be dealt; sets the number of cards to come and the default count of unseen cards (52 minus your 2 hole cards and the board).","type":"string","enum":["flop_to_river","turn_to_river","flop_to_turn"],"default":"flop_to_river","examples":["flop_to_river"]},"unseen_cards":{"description":"Optional: cards not visible to you, if it differs from the default (e.g. 45 with one known folded card). Must be larger than outs.","type":"integer","minimum":2,"maximum":50,"examples":[47]}},"additionalProperties":false,"required":["outs"]},"output_schema":{"type":"object","properties":{"probability_percent":{"description":"One card: outs/unseen; two cards: 1 − C(unseen − outs, 2)/C(unseen, 2). Unit: %.","type":"number","x-unit":"%"},"odds_against":{"description":"(1 − p)/p expressed as \"x : 1\", for comparison with pot odds.","type":"string"},"odds_against_ratio":{"description":"(1 − p)/p as a number.","type":"number"},"rule_of_2_and_4_percent":{"description":"outs × 2 with one card to come, outs × 4 with two cards to come. Unit: %.","type":"number","x-unit":"%"},"exact_vs_rule_difference":{"description":"rule_of_2_and_4_percent − probability_percent; positive means the rule overestimates. Unit: percentage points.","type":"number","x-unit":"percentage points"},"cards_to_come":{"description":"1 or 2 according to the street.","type":"integer"},"unseen_cards_used":{"description":"Number of unseen cards the probability was computed with.","type":"integer"}}},"formula":"one card: p = outs / unseen; two cards: p = 1 − C(unseen − outs, 2) / C(unseen, 2); odds_against = (1 − p) / p; rule_of_2_and_4 = outs × 2 (one card) or outs × 4 (two cards)","method":"Hypergeometric drawing probabilities that treat every card you cannot see (including other players' folded cards) as equally likely to be next. Probability mathematics only; not gambling advice.","sources":[{"name":"Poker probability – Texas hold 'em outs and drawing odds (Wikipedia)","url":"https://en.wikipedia.org/wiki/Poker_probability","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":"Flush draw (9 outs) on the flop, two cards to come","inputs":{"outs":9,"street":"flop_to_river"},"expected":{"probability_percent":34.97,"odds_against":"1.86 : 1","odds_against_ratio":1.86,"rule_of_2_and_4_percent":36,"exact_vs_rule_difference":1.03,"cards_to_come":2,"unseen_cards_used":47},"url":"https://tttkmbb.com/api/v1/calculate/poker-outs?outs=9&street=flop_to_river"},{"name":"Flush draw (9 outs) on the turn, one card to come","inputs":{"outs":9,"street":"turn_to_river"},"expected":{"probability_percent":19.57,"odds_against":"4.11 : 1","rule_of_2_and_4_percent":18,"exact_vs_rule_difference":-1.57,"cards_to_come":1,"unseen_cards_used":46},"url":"https://tttkmbb.com/api/v1/calculate/poker-outs?outs=9&street=turn_to_river"}],"faq":[{"q":"Why 47 unseen cards on the flop and 46 on the turn?","a":"52 cards minus your 2 hole cards and the 3 flop cards leaves 47; after the turn card 46. Cards in other players' hands or the muck are unseen and therefore still counted."},{"q":"How do I compare the result with pot odds?","a":"Odds against of 1.86 : 1 means you need the pot to offer at least 1.86 units for every unit you call to break even on this street alone (ignoring implied odds)."},{"q":"Should I count outs that give an opponent a better hand?","a":"No; discount tainted outs (e.g. a flush card that also pairs the board for a possible full house) before entering the number."}],"tags":["poker outs","poker odds","flush draw odds","rule of 2 and 4","texas holdem probability","pot odds"],"related":[{"calculator_id":"hypergeometric-distribution","reason":"Probability of k successes when drawing without replacement, the general form of this calculation."},{"calculator_id":"combinations-permutations","reason":"The C(n, 2) counts used for two cards to come."},{"calculator_id":"probability-of-events","reason":"Combine the drawing probability with other events."}],"links":{"html":"https://tttkmbb.com/gaming/poker-outs","markdown":"https://tttkmbb.com/gaming/poker-outs.md","json":"https://tttkmbb.com/gaming/poker-outs.json","api":"https://tttkmbb.com/api/v1/calculate/poker-outs","schema":"https://tttkmbb.com/api/v1/calculators/poker-outs","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:48Z"}