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API · /probability-api

Probability API

healthy 4,509 Subscribers

Probability distributions and combinatorics as an API. The binomial endpoint gives the probability of exactly k successes in n trials (PMF), the cumulative probability up to k (CDF), and the mean, variance and standard deviation. The poisson endpoint does the same for the Poisson distribution from a rate λ. The normal endpoint computes the z-score, probability density, cumulative probability (CDF) and percentile for a value under a normal distribution with any mean and standard deviation — and runs in reverse, turning a probability into the value (the quantile / inverse CDF) and its z-score. The combinatorics endpoint computes combinations (nCr), permutations (nPr) and factorials with exact big-integer arithmetic. Everything is computed locally and deterministically, so it is instant and private. Ideal for data science and statistics, quality control and A/B-test planning, gaming and gambling odds, risk modelling, and statistics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 5 endpoints. This is probability theory; for descriptive statistics on a dataset use a statistics API and for general expression evaluation use a math API.

#probability #distribution #normal #binomial #statistics #developer-tools
api.oanor.com/probability-api
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Machine-readable spec so AI agents can integrate this API.

/api/probability-api/openapi.json
/api/probability-api/llms.txt

Discovery: GET /api/index.json lists every API.

Probability API — live data on the oanor API marketplace

API health

healthy
Uptime
100.00%
Server probes · 24h
Avg latency
74 ms
Server probes · 24h
Subscribers
4,509
active
Total calls
95
last 7 days
status Full status page → · 15 probes/24h

Pricing

Pick a tier — billed monthly, cancel anytime.

Free

Free

  • 8,035 calls / month
  • 2 requests / second
  • Hard cap (429 above quota, no overage)
  • 8,035 calls/month
  • 2 req/sec
  • Binomial / Poisson / normal / combinatorics
  • No credit card
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Starter

€9.55 /month

  • 17,550 calls / month
  • 8 requests / second
  • Hard cap (429 above quota, no overage)
  • 17.55k calls/month
  • 8 req/sec
  • PMF / CDF / quantile
  • Email support
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Pro

€29.45 /month

  • 226,500 calls / month
  • 20 requests / second
  • Hard cap (429 above quota, no overage)
  • 226.5k calls/month
  • 20 req/sec
  • Data-science pipelines
  • Priority support
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Mega

€67.45 /month

  • 1,175,000 calls / month
  • 50 requests / second
  • Hard cap (429 above quota, no overage)
  • 1.175M calls/month
  • 50 req/sec
  • Platform scale
  • Dedicated SLA
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Related APIs

Other APIs with overlapping tags.

Lottery Odds API — oanor API marketplace

Lottery Odds API

Lottery combinatorics as an API, computed locally and deterministically and exactly — the real odds behind a ticket, the maths the jackpot poster never shows. The odds endpoint gives the jackpot odds of a pick-N game as the number of possible tickets, C(pool, picks), times the bonus-ball pool if there is one: a 6/49 game is 1 in 13,983,816, a 5/69-plus-1/26 Powerball-style game is 1 in 292,201,338, and every single line is equally unlikely. The match-odds endpoint gives the chance of matching exactly k of the main numbers — a prize tier — from the hypergeometric formula C(picks, k)·C(pool−picks, picks−k) ÷ C(pool, picks), so matching 3 of 6 in a 6/49 game is about 1 in 57. The expected-value endpoint turns a jackpot and ticket price into the expected value and the break-even jackpot (price × the odds), the threshold a jackpot must clear before a ticket is even theoretically worth it — before a shared jackpot, lump-sum and tax pull it back under. Everything is computed locally and deterministically, so it is instant and exact. Ideal for lottery and odds apps, gambling-education and responsible-play tools, probability teaching, and game back-ends. Pure local computation — no key, no third-party service, instant. Exact combinatorics. Live, nothing stored. 3 compute endpoints. Educational — not gambling advice; the odds are always against you.

api.oanor.com/lottery-api

 Roulette Odds API — oanor API marketplace

Roulette Odds API

Roulette odds maths as an API, computed locally and deterministically and exactly — the payout, the true probability and the house edge behind every bet, the numbers a fair game tells you and a casino would rather you ignore. The payout endpoint gives a bet's payout, winning numbers, win probability and house edge for a European (single-zero) or American (double-zero) wheel: a straight-up number pays 35 to 1 but wins only 1 in 37, an edge of 2.70 % European or 5.26 % American, the same on almost every bet because the payout simply ignores the zeros. The expected-value endpoint turns a stake into its expected value — stake × (win probability × (payout + 1) − 1), always negative and equal to minus the stake times the house edge — so €10 on a single number on a European wheel is worth −€0.27 every spin. The martingale endpoint exposes the doubling system: total risked = base × (2^steps − 1), the bet that explodes after a losing streak, and the bust probability — proof on the maths that no progression beats the zero. Everything is computed locally and deterministically, so it is instant and exact. Ideal for casino-game and odds apps, gambling-education and responsible-play tools, game-design back-ends, and probability teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 compute endpoints. Educational — not betting advice; the house always wins long-run.

api.oanor.com/roulette-api

 Dice Probability API — oanor API marketplace

Dice Probability API

Tabletop dice-probability maths as an API, computed locally and deterministically and exactly — the odds behind the rolls, not the rolls themselves. The advantage endpoint gives the D&D-style chances of beating a target on a d20 (or any die) rolling normally, with advantage (roll twice, keep the higher) or with disadvantage (keep the lower): needing an 11+ is 50 % normally, 75 % with advantage and 25 % with disadvantage, and it reports the average roll — advantage lifts a d20 from 10.5 to about 13.8. The pool endpoint handles success-counting systems (World of Darkness, Shadowrun): for a pool of dice that succeed on a face at or above a threshold it gives the chance per die, the expected number of successes and the exact binomial probability of getting exactly, or at least, a target number — six d10s succeeding on 7+ average 2.4 successes with a 45.6 % chance of three or more. The exploding endpoint gives the mean of an exploding ("acing", open-ended) die that re-rolls and adds on its maximum face — a d6 averages 4.2 instead of 3.5. Everything is computed locally and deterministically, so it is instant and private. Ideal for tabletop, virtual-tabletop, game-design and TTRPG app developers, odds-and-probability helpers, and game-master tools. Pure local computation — no key, no third-party service, instant. Exact maths, no simulation. Live, nothing stored. 3 compute endpoints. For random rolls use a dice-roller API.

api.oanor.com/dicepool-api

 Birthday Paradox API — oanor API marketplace

Birthday Paradox API

Birthday-paradox and collision-probability maths as an API, computed locally and deterministically. The probability endpoint computes the chance that at least two of n people share a birthday among d equally likely days, P = 1 − Π(1 − i/d), evaluated in log space for accuracy — the famous result that just 23 people give about a 50.7 % chance, 50 people about 97 % and 70 people about 99.9 %. The people-needed endpoint inverts it: the smallest group size to reach a target probability (23 for 50 %, 57 for 99 %), with the √(2·d·ln(1/(1−p))) approximation. The collision endpoint generalises the birthday bound to any space — pass a number of buckets or a hash size in bits — and returns the collision probability P ≈ 1 − e^(−n²/2d), the rule behind hash collisions and UUID-uniqueness estimates, where a 50 % chance needs roughly 1.177·√d items. Days and buckets default to 365. Everything is computed locally and deterministically, so it is instant and private. Ideal for probability-education, security, cryptography, hashing, data-engineering and statistics app developers, collision-risk and birthday-problem tools, and teaching material. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the birthday/collision probability; for full distributions use a probability API.

api.oanor.com/birthdayparadox-api

Frequently asked questions

Quick answers about pricing, quotas, and integration.

How do I get an API key for Probability API?
Sign up for free at oanor.com, generate an API key from the developer dashboard, and call Probability API with the x-oanor-key header. No credit card needed for the free tier.
What's the rate limit for Probability API?
Free tier allows 1 request per second. Paid plans scale up to 50 requests per second on the Mega tier. Hard limits return HTTP 429 above the quota — no surprise overage charges.
How much does Probability API cost?
Probability API has a free tier with 100 calls / month. Paid plans start at €9.55 / month with higher quotas and faster rate limits.
Can I cancel my subscription anytime?
Yes. Plans are billed monthly and you can cancel anytime from your billing dashboard. No long-term contracts and no cancellation fee.
Is Probability API GDPR-compliant?
All requests to Probability API go through our EU-based gateway. Your upstream API key never leaves our server and no personal data is shared with the upstream provider beyond the request you send.

Pick an endpoint from the list on the left to see its details and try it.

Code snippets

Sign up to get an API key, then call any path under your slug.

curl https://api.oanor.com/probability-api/SOME_PATH \
  -H "x-oanor-key: oanor_test_..."
const res = await fetch("https://api.oanor.com/probability-api/SOME_PATH", {
  headers: { "x-oanor-key": "oanor_test_..." }
});
const data = await res.json();
$ch = curl_init("https://api.oanor.com/probability-api/SOME_PATH");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-oanor-key: oanor_test_..."]);
$response = curl_exec($ch);
import requests
r = requests.get(
    "https://api.oanor.com/probability-api/SOME_PATH",
    headers={"x-oanor-key": "oanor_test_..."},
)
print(r.json())

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