# Dice Pool Probability Calculator

> Dice Pool Probability Calculator is a paid API for AI agents from probability-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Computes exact probability distributions, target sum chances, mean, and variance for dice pools including drop-lowest mechanics like 4d6dl1.

## Facts

- Endpoint: GET https://probability-calc.x402tookit.com/dice-odds?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/dice-pool-probability-calculator-724736e6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_qW98LBG6HDVIqf9pc3JB_

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability dice-pool-probability-calculator-724736e6
```

Example prompt: 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?

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Exact odds for dice pools: sum distribution, chance of reaching a target, mean and variance; supports drop-lowest like 4d6.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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": {
         "typ
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/dice-pool-probability-calculator-724736e6/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from probability-calc.x402tookit.com](https://www.zero.xyz/host/probability-calc.x402tookit.com/llms.txt)