# Probability Calculators

Dice, card and lottery odds, multinomials, expected value, exact distribution tables, gambler's ruin, Bayes and streaks.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://probability-calc.x402tookit.com/openapi.json
- x402 manifest: https://probability-calc.x402tookit.com/.well-known/x402
- Catalog (free): https://probability-calc.x402tookit.com/catalog
- Health (free): https://probability-calc.x402tookit.com/health
- Uptime (free): https://probability-calc.x402tookit.com/uptime

## Endpoints (10)

### GET /bayes — $0.02
Bayes' theorem: posterior probability from a prior, sensitivity and false-positive rate, with natural frequencies and odds form.
Params: prior: number, sensitivity: number, falsePositiveRate?: number, specificity?: number, population?: integer
Example: https://probability-calc.x402tookit.com/bayes?prior=0.01&sensitivity=0.8&falsePositiveRate=0.096

### GET /birthday-problem — $0.02
Birthday problem: chance two people in a group share a birthday, chance someone shares yours, group size for 50 or 99 percent.
Params: people: integer, days?: integer
Example: https://probability-calc.x402tookit.com/birthday-problem?people=23

### GET /card-odds — $0.02
Card odds: 5-card and 7-card poker hand probabilities, chance of hitting your outs by the river, blackjack natural odds.
Params: mode: string, outs?: integer, stage?: string, decks?: integer
Example: https://probability-calc.x402tookit.com/card-odds?mode=outs&outs=9&stage=flop

### GET /dice-odds — $0.02
Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.
Params: dice: integer, faces: integer, target?: integer, dropLowest?: integer, faceValue?: integer
Example: https://probability-calc.x402tookit.com/dice-odds?dice=3&faces=6&target=10

### GET /distribution-table — $0.02
Exact pmf, cumulative and tail tables for geometric, negative binomial, hypergeometric, binomial and Poisson.
Params: dist: string, p?: number, r?: integer, n?: integer, N?: integer, K?: integer, lambda?: number, k?: integer
Example: https://probability-calc.x402tookit.com/distribution-table?dist=hypergeometric&N=52&K=13&n=5

### GET /expected-value — $0.02
Expected value, variance, standard deviation and chance of profit for a list of payoffs with probabilities or weights.
Params: outcomes: string, cost?: number, normalize?: string
Example: https://probability-calc.x402tookit.com/expected-value?outcomes=35%3A1%2C-1%3A37&normalize=true

### GET /gamblers-ruin — $0.02
Gambler's ruin: probability of going broke before hitting a target, and expected number of bets, for repeated unit bets.
Params: p: number, bankroll: integer, target?: integer
Example: https://probability-calc.x402tookit.com/gamblers-ruin?p=0.473684&bankroll=100&target=200

### GET /lottery-odds — $0.02
Lottery odds: jackpot odds and every match tier for pick-k-of-N games with an optional bonus pool (Powerball, EuroMillions).
Params: pick: integer, poolSize: integer, bonusPick?: integer, bonusPool?: integer, jackpot?: number, ticketPrice?: number
Example: https://probability-calc.x402tookit.com/lottery-odds?pick=5&poolSize=69&bonusPool=26

### GET /multinomial — $0.02
Multinomial coefficient (arrangements of repeated items like MISSISSIPPI) and multinomial probability for given odds.
Params: counts?: string, word?: string, probs?: string
Example: https://probability-calc.x402tookit.com/multinomial?word=MISSISSIPPI

### GET /streak-odds — $0.02
Chance of a run: r successes in a row (or r identical outcomes) somewhere in n independent trials, like coin flips.
Params: n: integer, r: integer, p?: number, kind?: string
Example: https://probability-calc.x402tookit.com/streak-odds?n=100&r=5

## Terms

Exact or closed-form probability maths computed locally, provided as is. Gambling, lottery and card odds describe fair, independent, uniformly random draws and ignore house rules, rake, taxes and prize sharing. Not gambling, investment or medical advice, and no system beats a negative-expectation game. Combinatorics basics (nCr, nPr, derangements) and the binomial, Poisson and normal distribution values live in the math-stats shelf and are not repeated here.