{
  "format": "delx/discovery-pack/v1",
  "id": "prediction-market-math",
  "title": "Prediction market math for agents",
  "description": "Odds ↔ probability, de-vig, binary EV/edge, Kelly, Brier, and multi-outcome normalize for prediction-market agents—$0.001 local math, no exchange websocket.",
  "audience": "Prediction-market, forecasting, and research agents",
  "query": "odds implied probability kelly binary EV parlay prediction market API for agents",
  "keywords": [
    "odds to probability API",
    "prediction market Kelly",
    "binary market EV",
    "de-vig two way",
    "Brier score API",
    "parlay probability",
    "x402 prediction markets",
    "implied probability API"
  ],
  "updated_at": "2026-08-23",
  "canonical_url": "https://commerce.delx.ai/packs/prediction-market-math",
  "machine_url": "https://commerce.delx.ai/packs/prediction-market-math.json",
  "entrypoints": {
    "human": "https://commerce.delx.ai/?q=odds%20implied%20probability%20kelly%20binary%20EV%20parlay%20prediction%20market%20API%20for%20agents",
    "intent_search": "https://api.delx.ai/api/v1/x402/start?q=odds%20implied%20probability%20kelly%20binary%20EV%20parlay%20prediction%20market%20API%20for%20agents",
    "graph": "https://commerce.delx.ai/discovery.json"
  },
  "attribution": {
    "header": "x-delx-source",
    "value": "discovery-pack-prediction-market-math"
  },
  "products": [
    {
      "tool_name": "util_odds_decimal_to_prob",
      "service_name": "Decimal Odds → Probability",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/odds-decimal-to-prob",
      "product_url": "https://commerce.delx.ai/products/util-odds-decimal-to-prob",
      "intent_url": "https://commerce.delx.ai/intents/odds-decimal-to-prob-api",
      "machine_url": "https://commerce.delx.ai/intents/odds-decimal-to-prob-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "odds": {
            "description": "Input field: odds.",
            "type": "number"
          }
        },
        "required": [
          "odds"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "odds": 2.5
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/odds-decimal-to-prob -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"odds\":2.5}'"
    },
    {
      "tool_name": "util_prob_to_odds_decimal",
      "service_name": "Probability → Decimal Odds",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/prob-to-odds-decimal",
      "product_url": "https://commerce.delx.ai/products/util-prob-to-odds-decimal",
      "intent_url": "https://commerce.delx.ai/intents/prob-to-odds-decimal-api",
      "machine_url": "https://commerce.delx.ai/intents/prob-to-odds-decimal-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "prob": {
            "description": "Input field: prob.",
            "type": "number"
          }
        },
        "required": [
          "prob"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "prob": 0.4
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/prob-to-odds-decimal -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"prob\":0.4}'"
    },
    {
      "tool_name": "util_odds_american_to_prob",
      "service_name": "American Odds → Probability",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/odds-american-to-prob",
      "product_url": "https://commerce.delx.ai/products/util-odds-american-to-prob",
      "intent_url": "https://commerce.delx.ai/intents/odds-american-to-prob-api",
      "machine_url": "https://commerce.delx.ai/intents/odds-american-to-prob-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "odds": {
            "description": "Input field: odds.",
            "type": "integer"
          }
        },
        "required": [
          "odds"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "odds": -150
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/odds-american-to-prob -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"odds\":-150}'"
    },
    {
      "tool_name": "util_binary_ev",
      "service_name": "Binary EV (Buy Yes)",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/binary-ev",
      "product_url": "https://commerce.delx.ai/products/util-binary-ev",
      "intent_url": "https://commerce.delx.ai/intents/binary-ev-api",
      "machine_url": "https://commerce.delx.ai/intents/binary-ev-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "true_prob": {
            "description": "Input field: true prob.",
            "type": "number"
          },
          "market_price": {
            "description": "Input field: market price.",
            "type": "number"
          },
          "stake": {
            "description": "Input field: stake.",
            "type": "integer"
          }
        },
        "required": [
          "true_prob",
          "market_price",
          "stake"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "true_prob": 0.55,
        "market_price": 0.48,
        "stake": 100
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/binary-ev -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"true_prob\":0.55,\"market_price\":0.48,\"stake\":100}'"
    },
    {
      "tool_name": "util_binary_edge",
      "service_name": "Binary Edge",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/binary-edge",
      "product_url": "https://commerce.delx.ai/products/util-binary-edge",
      "intent_url": "https://commerce.delx.ai/intents/binary-edge-api",
      "machine_url": "https://commerce.delx.ai/intents/binary-edge-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "true_prob": {
            "description": "Input field: true prob.",
            "type": "number"
          },
          "market_price": {
            "description": "Input field: market price.",
            "type": "number"
          }
        },
        "required": [
          "true_prob",
          "market_price"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "true_prob": 0.55,
        "market_price": 0.48
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/binary-edge -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"true_prob\":0.55,\"market_price\":0.48}'"
    },
    {
      "tool_name": "util_devig_two_way",
      "service_name": "Two-Way De-vig",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/devig-two-way",
      "product_url": "https://commerce.delx.ai/products/util-devig-two-way",
      "intent_url": "https://commerce.delx.ai/intents/devig-two-way-api",
      "machine_url": "https://commerce.delx.ai/intents/devig-two-way-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "p_yes": {
            "description": "Input field: p yes.",
            "type": "number"
          },
          "p_no": {
            "description": "Input field: p no.",
            "type": "number"
          }
        },
        "required": [
          "p_yes",
          "p_no"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "p_yes": 0.55,
        "p_no": 0.55
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/devig-two-way -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"p_yes\":0.55,\"p_no\":0.55}'"
    },
    {
      "tool_name": "util_kelly_binary",
      "service_name": "Kelly for Binary Market",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/kelly-binary",
      "product_url": "https://commerce.delx.ai/products/util-kelly-binary",
      "intent_url": "https://commerce.delx.ai/intents/kelly-binary-api",
      "machine_url": "https://commerce.delx.ai/intents/kelly-binary-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "true_prob": {
            "description": "Input field: true prob.",
            "type": "number"
          },
          "market_price": {
            "description": "Input field: market price.",
            "type": "number"
          }
        },
        "required": [
          "true_prob",
          "market_price"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "true_prob": 0.6,
        "market_price": 0.45
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/kelly-binary -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"true_prob\":0.6,\"market_price\":0.45}'"
    },
    {
      "tool_name": "util_brier_score",
      "service_name": "Brier Score",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/brier-score",
      "product_url": "https://commerce.delx.ai/products/util-brier-score",
      "intent_url": "https://commerce.delx.ai/intents/brier-score-api",
      "machine_url": "https://commerce.delx.ai/intents/brier-score-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "prob": {
            "description": "Input field: prob.",
            "type": "number"
          },
          "outcome": {
            "description": "Input field: outcome.",
            "type": "integer"
          }
        },
        "required": [
          "prob",
          "outcome"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "prob": 0.7,
        "outcome": 1
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/brier-score -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"prob\":0.7,\"outcome\":1}'"
    },
    {
      "tool_name": "util_parlay_prob_indep",
      "service_name": "Parlay Prob (Indep.)",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/parlay-prob-indep",
      "product_url": "https://commerce.delx.ai/products/util-parlay-prob-indep",
      "intent_url": "https://commerce.delx.ai/intents/parlay-prob-indep-api",
      "machine_url": "https://commerce.delx.ai/intents/parlay-prob-indep-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "probs": {
            "description": "Input field: probs.",
            "type": "array"
          }
        },
        "required": [
          "probs"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "probs": [
          0.5,
          0.4,
          0.6
        ]
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/parlay-prob-indep -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"probs\":[0.5,0.4,0.6]}'"
    },
    {
      "tool_name": "util_shares_from_budget",
      "service_name": "Shares from Budget",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/shares-from-budget",
      "product_url": "https://commerce.delx.ai/products/util-shares-from-budget",
      "intent_url": "https://commerce.delx.ai/intents/shares-from-budget-api",
      "machine_url": "https://commerce.delx.ai/intents/shares-from-budget-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "budget": {
            "description": "Input field: budget.",
            "type": "integer"
          },
          "price": {
            "description": "Input field: price.",
            "type": "number"
          }
        },
        "required": [
          "budget",
          "price"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "budget": 50,
        "price": 0.25
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/shares-from-budget -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"budget\":50,\"price\":0.25}'"
    },
    {
      "tool_name": "util_multi_outcome_normalize",
      "service_name": "Multi-Outcome Normalize",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/multi-outcome-normalize",
      "product_url": "https://commerce.delx.ai/products/util-multi-outcome-normalize",
      "intent_url": "https://commerce.delx.ai/intents/multi-outcome-normalize-api",
      "machine_url": "https://commerce.delx.ai/intents/multi-outcome-normalize-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "prices": {
            "description": "Input field: prices.",
            "type": "array"
          }
        },
        "required": [
          "prices"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "prices": [
          0.2,
          0.3,
          0.6
        ]
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/multi-outcome-normalize -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"prices\":[0.2,0.3,0.6]}'"
    },
    {
      "tool_name": "util_implied_from_yes_no",
      "service_name": "Implied from Yes/No Prices",
      "category": "signal-normalize",
      "price_usdc": "0.001",
      "method": "POST",
      "route": "/api/v1/x402/implied-from-yes-no",
      "product_url": "https://commerce.delx.ai/products/util-implied-from-yes-no",
      "intent_url": "https://commerce.delx.ai/intents/implied-from-yes-no-api",
      "machine_url": "https://commerce.delx.ai/intents/implied-from-yes-no-api.json",
      "input_schema": {
        "type": "object",
        "properties": {
          "yes": {
            "description": "Input field: yes.",
            "type": "number"
          },
          "no": {
            "description": "Input field: no.",
            "type": "number"
          }
        },
        "required": [
          "yes",
          "no"
        ],
        "additionalProperties": true
      },
      "example_input": {
        "yes": 0.42,
        "no": 0.62
      },
      "agentcash_buy": "npx agentcash@latest fetch https://api.delx.ai/api/v1/x402/implied-from-yes-no -m POST -H 'x-delx-source: discovery-pack-prediction-market-math' --max-amount 0.001 -b '{\"yes\":0.42,\"no\":0.62}'"
    }
  ]
}