{"uid":"cap_qW98LBG6HDVIqf9pc3JB_","slug":"dice-pool-probability-calculator-724736e6","name":"Dice Pool Probability Calculator","description":"Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.","url":"https://probability-calc.x402tookit.com/dice-odds?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["dice","faces"],"properties":{"dice":{"type":"integer","description":"Number of dice, 1 to 60 (1 to 8 with dropLowest)"},"faces":{"type":"integer","description":"Faces per die, 2 to 100 (2 to 20 with dropLowest)"},"target":{"type":"integer","description":"Target sum: returns the chance of exactly, at least and at most this sum"},"faceValue":{"type":"integer","description":"Also give the chance that at least one die shows this face (default: no)"},"dropLowest":{"type":"integer","description":"Drop this many lowest dice before summing (4d6 drop lowest = dice 4, dropLowest 1)"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"asOf":{"type":["null","string"]},"mean":{"type":["null","number"]},"pool":{"type":["null","string"]},"maxSum":{"type":["null","number"]},"minSum":{"type":["null","number"]},"source":{"type":["null","string"]},"target":{"type":["null","object"],"properties":{"sum":{"type":["null","number"]},"atMost":{"type":["null","number"]},"atLeast":{"type":["null","number"]},"exactly":{"type":["null","number"]},"oneInNExactly":{"type":["null","number"]}}},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"variance":{"type":["null","number"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"distribution":{"type":["array","null"],"items":{"type":"object","properties":{"sum":{"type":["null","number"]},"ways":{"type":["null","number"]},"probability":{"type":["null","number"]},"cumulativeAtMost":{"type":["null","number"]}}}},"mostLikelySum":{"type":["null","number"]},"totalOutcomes":{"type":["null","number"]},"standardDeviation":{"type":["null","number"]},"mostLikelyProbability":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_CdVhpIkcOCTrlt2iMGOZm","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes exact probability distributions, target sum chances, mean, and variance for dice pools including drop-lowest mechanics like 4d6dl1.","exampleAgentPrompt":"What are the exact odds for rolling at least 15 on 4 dice with 6 faces each, dropping the lowest die — give me the full distribution, mean, and variance?","exampleUseCases":[{"title":"D&D ability score generation odds","prompt":"I'm rolling 4d6 and dropping the lowest die for D&D character stats — what's the exact probability of getting at least an 18, and what's the full distribution with mean and variance?"},{"title":"Tabletop game balance analysis","prompt":"For a game mechanic using 3 dice with 8 faces each, what's the chance of rolling exactly 12, and can I get the full sum distribution so I can balance the encounter difficulty?"},{"title":"Single die face occurrence chance","prompt":"If I roll 5 six-sided dice, what's the probability that at least one of them shows a 6? Also give me the mean and variance for the total sum."}],"resultDescription":"Returns the full probability distribution array (each possible sum with its probability, cumulative probability, and number of ways to achieve it), the mean and variance of the pool, minimum and maximum possible sums, and if a target sum was specified, the probability of rolling exactly that sum, at least that sum, and at most that sum along with 1-in-N odds. Optionally includes the probability that at least one die shows a specific face value.","failureModes":["Invalid dice count (outside 1-60, or 1-8 with dropLowest) returns an error","Invalid face count (outside 2-100, or 2-20 with dropLowest) returns an error","Missing required 'dice' or 'faces' query parameters returns a validation error","dropLowest value equal to or exceeding dice count is likely invalid","Target sum outside possible min/max range may return zero probabilities","Payment of $0.02 USDC required; missing or invalid x402 payment returns 402 error"],"whenToPreferThis":"Choose this endpoint when you need exact, mathematically precise dice pool probabilities rather than simulations or approximations. It is ideal for tabletop RPG mechanics, game design balance analysis, or any scenario involving standard polyhedral dice pools with optional drop-lowest rules. Prefer it over generic statistics APIs because it natively handles the drop-lowest mechanic (e.g., 4d6dl1) and returns a complete discrete probability distribution, not just summary statistics.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-29T13:14:27.283Z","isFirstParty":false,"canonicalSlug":"dice-pool-probability-calculator-724736e6"}