Probability Calculators
Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.
SearchLiveeip155:8453Exactvia cdp
DiceOddsDistributionRpg
Calls · 30d
1
This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far.
$24.31
Verified settled volume
1,175 settlements proven x402 by their on-chain EIP-3009 marker.
$0.020
Listed price
As published in the catalog. Always read the live 402 before paying.
1
Calls · 30d
Upstream's own call count for this endpoint, not ours.
1
Unique payers · 30d
Last called 2026-10-20 20:47Z
—
Upstream on-chain volume
Reported by the source catalog.
Paid to
0xb531320805C5BED1D46AEaDcF4F008FDF172DBDaThe wallet the 402 directs payment to. Its whole payment record — every payer, every chain — is on the merchant page.
Asset 0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913
Provider
The payTo wallet does not resolve to a registered ERC-8004 agent. That is not a verdict on the service — most of the catalog is unregistered.
Live 402 challenge
Captured by the enrichment pass, not read just now. Prices can change — always read the 402 the endpoint answers with.
{
"error": "Payment required",
"accepts": [
{
"asset": "0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913",
"extra": {
"name": "USD Coin",
"version": "2"
},
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact",
"network": "base",
"mimeType": "application/json",
"resource": "https://probability-calc.x402tookit.com/dice-odds",
"description": "Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.",
"outputSchema": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
"dice": 3,
"faces": 6,
"target": 10
}
},
"output": {
"asOf": "2026-10-11T14:44:17.363Z",
"mean": 10.5,
"pool": "3d6",
"maxSum": 18,
"minSum": 3,
"source": "computed locally (exact enumeration and convolution)",
"target": {
"sum": 10,
"atMost": 0.5,
"atLeast": 0.625,
"exactly": 0.125,
"oneInNExactly": 8
},
"reasons": [
"Exact: every outcome of fair, independent dice is counted (convolution, or full enumeration when dropping dice)."
],
"summary": "3d6: mean 10.5, sd 2.95804, range 3-18, most likely 10 (12.50%). Sum 10: exactly 12.50%, at least 62.50%, at most 50.00%.",
"verdict": "COMPUTED",
"degraded": false,
"variance": 8.75,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"loaded or unfair dice",
"exploding dice, rerolls and other house rules",
"…1 more"
],
"distribution": [
{
"sum": 3,
"ways": 1,
"probability": 0.00463,
"cumulativeAtMost": 0.00463
},
{
"sum": 4,
"ways": 3,
"probability": 0.013889,
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}
],
"mostLikelySum": 10,
"totalOutcomes": 216,
"standardDeviation": 2.95804,
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}
},
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{
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"scheme": "exact",
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"description": "Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.",
"outputSchema": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
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}
},
"output": {
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"mean": 10.5,
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"source": "computed locally (exact enumeration and convolution)",
"target": {
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"exactly": 0.125,
"oneInNExactly": 8
},
"reasons": [
"Exact: every outcome of fair, independent dice is counted (convolution, or full enumeration when dropping dice)."
],
"summary": "3d6: mean 10.5, sd 2.95804, range 3-18, most likely 10 (12.50%). Sum 10: exactly 12.50%, at least 62.50%, at most 50.00%.",
"verdict": "COMPUTED",
"degraded": false,
"variance": 8.75,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"loaded or unfair dice",
"exploding dice, rerolls and other house rules",
"…1 more"
],
"distribution": [
{
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"ways": 1,
"probability": 0.00463,
"cumulativeAtMost": 0.00463
},
{
"sum": 4,
"ways": 3,
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}
],
"mostLikelySum": 10,
"totalOutcomes": 216,
"standardDeviation": 2.95804,
"mostLikelyProbability": 0.125
}
},
"maxAmountRequired": "20000",
"maxTimeoutSeconds": 300
},
{
"asset": "0x3c499c542cEF5E3811e1192ce70d8cC03d5c3359",
"extra": {
"name": "USD Coin",
"version": "2"
},
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"scheme": "exact",
"network": "polygon",
"mimeType": "application/json",
"resource": "https://probability-calc.x402tookit.com/dice-odds",
"description": "Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.",
"outputSchema": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
"dice": 3,
"faces": 6,
"target": 10
}
},
"output": {
"asOf": "2026-10-11T14:44:17.363Z",
"mean": 10.5,
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"maxSum": 18,
"minSum": 3,
"source": "computed locally (exact enumeration and convolution)",
"target": {
"sum": 10,
"atMost": 0.5,
"atLeast": 0.625,
"exactly": 0.125,
"oneInNExactly": 8
},
"reasons": [
"Exact: every outcome of fair, independent dice is counted (convolution, or full enumeration when dropping dice)."
],
"summary": "3d6: mean 10.5, sd 2.95804, range 3-18, most likely 10 (12.50%). Sum 10: exactly 12.50%, at least 62.50%, at most 50.00%.",
"verdict": "COMPUTED",
"degraded": false,
"variance": 8.75,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"loaded or unfair dice",
"exploding dice, rerolls and other house rules",
"…1 more"
],
"distribution": [
{
"sum": 3,
"ways": 1,
"probability": 0.00463,
"cumulativeAtMost": 0.00463
},
{
"sum": 4,
"ways": 3,
"probability": 0.013889,
"cumulativeAtMost": 0.018519
}
],
"mostLikelySum": 10,
"totalOutcomes": 216,
"standardDeviation": 2.95804,
"mostLikelyProbability": 0.125
}
},
"maxAmountRequired": "20000",
"maxTimeoutSeconds": 300
}
],
"x402Version": 1,
"alsoAvailable": {
"llms": "https://probability-calc.x402tookit.com/llms.txt",
"catalog": "https://probability-calc.x402tookit.com/catalog",
"message": "Probability Calculators has 10 pay-per-call endpoints (Dice, card and lottery odds, multinomials, expected value, exact distribution tables, gambler's ruin, Bayes and streaks.), from $0.02 a call. See the full menu and send your agents our way.",
"openapi": "https://probability-calc.x402tookit.com/openapi.json",
"related": [
{
"url": "https://probability-calc.x402tookit.com/distribution-table",
"path": "/distribution-table",
"what": "Exact pmf, cumulative and tail tables for geometric, negative binomial, hypergeometric, b…",
"price": "$0.02"
},
{
"url": "https://probability-calc.x402tookit.com/lottery-odds",
"path": "/lottery-odds",
"what": "Lottery odds: jackpot odds and every match tier for pick-k-of-N games with an optional bo…",
"price": "$0.02"
},
{
"url": "https://probability-calc.x402tookit.com/card-odds",
"path": "/card-odds",
"what": "Card odds: 5-card and 7-card poker hand probabilities, chance of hitting your outs by the…",
"price": "$0.02"
}
]
}
}Accepts
The payment requirements as published to the catalog. Read the live 402 before paying — a price here is a claim, not a quote.
0.02USDC≈ $0.02 USD
on Base · exact scheme
Pay 0.02 USDC on Base to 0xb531…2DBDa. The signed payment is good for 5 minutes.
- Paid to
- 0xb531…2DBDa
- USD Coin contract
- 0x8335…02913
- Payment window
- 5 minutes
- As published
- 20000 smallest units
20000units
on solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- DUPiup…eEm8s
- Token contract
- EPjFWd…TDt1v
- Payment window
- 5 minutes
20000units
on Polygon · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- 0xb531…2DBDa
- Token contract
- 0x3c49…c3359
- Payment window
- 5 minutes
20000units
on Arbitrum · exact scheme
That figure is in the token’s smallest units. Roundhouse does not hold this contract’s decimals, so it is shown as published rather than converted.
- Paid to
- 0xb531…2DBDa
- Token contract
- 0xaf88…e5831
- Payment window
- 5 minutes
The catalog’s raw entry
[
{
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"extra": {
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"version": "2"
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"amount": "20000",
"scheme": "exact",
"network": "eip155:8453",
"maxTimeoutSeconds": 300
},
{
"asset": "EPjFWdd5AufqSSqeM2qN1xzybapC8G4wEGGkZwyTDt1v",
"extra": {
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},
"payTo": "DUPiupXtuox38dcGoXUKer5mAydCzmaHjrbQ66qeEm8s",
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"scheme": "exact",
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{
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"extra": {
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"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"amount": "20000",
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"network": "eip155:137",
"maxTimeoutSeconds": 300
},
{
"asset": "0xaf88d065e77c8cC2239327C5EDb3A432268e5831",
"extra": {
"name": "USD Coin",
"version": "2"
},
"payTo": "0xb531320805C5BED1D46AEaDcF4F008FDF172DBDa",
"amount": "20000",
"scheme": "exact",
"network": "eip155:42161",
"maxTimeoutSeconds": 300
}
]Extensions
{
"bazaar": {
"info": {
"input": {
"type": "http",
"method": "GET",
"queryParams": {
"dice": 3,
"faces": 6,
"target": 10
}
},
"output": {
"type": "json",
"example": {
"asOf": "2026-10-11T14:44:17.363Z",
"mean": 10.5,
"pool": "3d6",
"maxSum": 18,
"minSum": 3,
"source": "computed locally (exact enumeration and convolution)",
"target": {
"sum": 10,
"atMost": 0.5,
"atLeast": 0.625,
"exactly": 0.125,
"oneInNExactly": 8
},
"reasons": [
"Exact: every outcome of fair, independent dice is counted (convolution, or full enumeration when dropping dice)."
],
"summary": "3d6: mean 10.5, sd 2.95804, range 3-18, most likely 10 (12.50%). Sum 10: exactly 12.50%, at least 62.50%, at most 50.00%.",
"verdict": "COMPUTED",
"degraded": false,
"variance": 8.75,
"disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
"notChecked": [
"loaded or unfair dice",
"exploding dice, rerolls and other house rules",
"…1 more"
],
"distribution": [
{
"sum": 3,
"ways": 1,
"probability": 0.00463,
"cumulativeAtMost": 0.00463
},
{
"sum": 4,
"ways": 3,
"probability": 0.013889,
"cumulativeAtMost": 0.018519
}
],
"mostLikelySum": 10,
"totalOutcomes": 216,
"standardDeviation": 2.95804,
"mostLikelyProbability": 0.125
}
}
},
"schema": {
"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": {
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"null",
"number"
]
},
"exactly": {
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"null",
"number"
]
},
"oneInNExactly": {
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"number"
]
}
}
},
"reasons": {
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"array",
"null"
],
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}
},
"summary": {
"type": [
"null",
"string"
]
},
"verdict": {
"type": [
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"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": {
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"null",
"number"
]
},
"probability": {
"type": [
"null",
"number"
]
},
"cumulativeAtMost": {
"type": [
"null",
"number"
]
}
}
}
},
"mostLikelySum": {
"type": [
"null",
"number"
]
},
"totalOutcomes": {
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"number"
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},
"standardDeviation": {
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}
}
}Provenance
- Seen in the source catalog
- 2026-10-20 20:47Z
- Last indexed by Roundhouse
- 2026-10-22 06:50Z
- Last enriched (probe, favicon, geo)
- 2026-10-20 23:45Z
- x402 version
- 2
- Max timeout
- 300s
- Liveness probe
- HTTP 402
Hand this page to an agent
Copy the prompt and paste it into Claude, an MCP client or your own agent — it will vet this service and call it over the free read API. No key, no account.
GET api.roundhouseai.io/v0/endpoints
This endpoint's own trailing-30-day call count, as published by the upstream catalog and snapshotted daily. 4 snapshots so far. Verified volume counts only settlements with an on-chain EIP-3009 marker.
Show the promptHide the prompt
Using Roundhouse, look up the x402 service Probability Calculators and tell me whether it is worth paying: what a call costs, whether the endpoint answered when last probed, and what its payment record actually shows. curl -s 'https://api.roundhouseai.io/v0/endpoints?q=Probability%20Calculators' curl -s 'https://api.roundhouseai.io/v0/merchants/<the payTo wallet returned above>' Then call it: read the price from the live 402 at https://probability-calc.x402tookit.com/dice-odds, never from a cached figure, and pay with an x402 client. The /v0 API needs an API key (`authorization: Bearer rh_live_…`) on everything except /v0/unified* and /v0/endpoints. Either pay over x402 (mint a personal key for $0.01 at GET https://api.roundhouseai.io/v0/test/x402), or ask me for an organization key, which I create at https://roundhouseai.io/dashboard/connections. If you have neither, ask before going further. If you do not have Roundhouse tools or skills installed, read https://roundhouseai.io/skill.md first — it is the whole procedure.