{
  "id": "vorici",
  "version": "babb46051a67",
  "status": "published",
  "name": "Vorici Calculator",
  "question": "How many orbs for a Vorici craft?",
  "summary": "Estimates the chance per chromatic orb of rolling the socket colours you want in Path of Exile, from the item’s attribute requirements, and compares the average cost with Vorici’s bench recipes.",
  "category": "game",
  "url": "https://www.acalculator.org/game/vorici-calculator",
  "markdown": "https://www.acalculator.org/game/vorici-calculator.md",
  "kind": "function",
  "method": "socket colour chances from the requirements (Siveran’s model); chance per orb = sum of the multinomial chances with at least the wanted colours; average orbs = 1 ÷ chance",
  "assumptions": [
    "Each socket’s colour is rolled on its own, with the colour chances from Siveran’s model (X = 5, C = 5, on-colour ceiling 90%), which he fitted to player data. Grinding Gear Games does not publish the formula.",
    "Averages treat every chromatic orb as independent. In the game a chromatic orb cannot give the same colours twice in a row, which makes hard outcomes slightly cheaper than shown.",
    "Vorici’s bench recipes and their costs are those from before patch 3.29, which also added white sockets; this calculator does not model white sockets."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "strength": {
        "title": "Strength",
        "description": "The item’s strength requirement, which makes red sockets more likely.",
        "type": "integer",
        "minimum": 0,
        "maximum": 1000
      },
      "dexterity": {
        "title": "Dexterity",
        "description": "The item’s dexterity requirement, which makes green sockets more likely.",
        "type": "integer",
        "minimum": 0,
        "maximum": 1000
      },
      "intelligence": {
        "title": "Intelligence",
        "description": "The item’s intelligence requirement, which makes blue sockets more likely.",
        "type": "integer",
        "minimum": 0,
        "maximum": 1000
      },
      "totalSockets": {
        "title": "Sockets on the item",
        "description": "How many sockets the item has.",
        "type": "integer",
        "minimum": 1,
        "maximum": 6
      },
      "redSockets": {
        "title": "Red sockets",
        "description": "How many red sockets you want.",
        "type": "integer",
        "minimum": 0,
        "maximum": 6
      },
      "greenSockets": {
        "title": "Green sockets",
        "description": "How many green sockets you want.",
        "type": "integer",
        "minimum": 0,
        "maximum": 6
      },
      "blueSockets": {
        "title": "Blue sockets",
        "description": "How many blue sockets you want.",
        "type": "integer",
        "minimum": 0,
        "maximum": 6
      },
      "chromaticPrice": {
        "title": "Chromatic orb price",
        "description": "What one chromatic orb costs, in chaos orbs, to show costs in chaos.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "chance": {
      "label": "Chance per chromatic orb",
      "description": "The chance that one chromatic orb rolls at least the socket colours you want.",
      "format": "percent"
    },
    "chromatics": {
      "label": "Average chromatic orbs",
      "description": "The average number of chromatic orbs to get the colours: 1 ÷ chance per orb.",
      "format": "number"
    },
    "chromaticCost": {
      "label": "Average cost with chromatic orbs",
      "description": "Average chromatic orbs × chromatic orb price, in chaos orbs.",
      "format": "number"
    },
    "best": {
      "label": "Cheapest on average",
      "description": "The method with the lowest average cost in chromatic orbs: chromatic orbs alone, or a Vorici bench recipe.",
      "format": "text"
    },
    "bestCost": {
      "label": "Its average cost",
      "description": "The average cost of the cheapest method, in chromatic orbs.",
      "format": "number"
    },
    "redChance": {
      "label": "Red socket chance",
      "description": "The chance that one socket rolls red.",
      "format": "percent"
    },
    "greenChance": {
      "label": "Green socket chance",
      "description": "The chance that one socket rolls green.",
      "format": "percent"
    },
    "blueChance": {
      "label": "Blue socket chance",
      "description": "The chance that one socket rolls blue.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "strength": 0,
      "dexterity": 0,
      "intelligence": 0,
      "totalSockets": 6,
      "redSockets": 0,
      "greenSockets": 0,
      "blueSockets": 0,
      "chromaticPrice": 0.5
    },
    "outputs": {
      "chance": 100,
      "chromatics": 0,
      "chromaticCost": 0,
      "best": "Nothing to change",
      "bestCost": 0,
      "redChance": 33.33333333333333,
      "greenChance": 33.33333333333333,
      "blueChance": 33.33333333333333
    },
    "text": "For 0 red, 0 green and 0 blue on a 6-socket item, the average number of chromatic orbs is 0."
  },
  "examples": [
    {
      "given": {
        "strength": 0,
        "dexterity": 0,
        "intelligence": 100,
        "totalSockets": 4,
        "redSockets": 0,
        "greenSockets": 0,
        "blueSockets": 4,
        "chromaticPrice": 0.5
      },
      "expect": {
        "blueChance": 82.5,
        "chance": 46.32503906249999
      },
      "source": "hand calculation in content.mdx from Siveran’s model: blue = 0.9 × (100 + 5 + 5) ÷ (100 + 15 + 5) = 0.825; 0.825⁴ = 46.3%; Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io"
    },
    {
      "given": {
        "strength": 0,
        "dexterity": 0,
        "intelligence": 100,
        "totalSockets": 4,
        "redSockets": 1,
        "greenSockets": 0,
        "blueSockets": 0,
        "chromaticPrice": 0.5
      },
      "expect": {
        "redChance": 8.75,
        "chance": 30.668356933593756,
        "best": "Chromatic orbs"
      },
      "source": "hand calculation in content.mdx: red = 0.1 ÷ 2 + 0.9 × 5 ÷ 120 = 0.0875; at least one red in 4 sockets = 1 − 0.9125⁴ = 30.7%; 1 ÷ 0.307 = 3.26 orbs, cheaper than the 4-orb Vorici 1R recipe; Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io"
    },
    {
      "given": {
        "strength": 50,
        "dexterity": 50,
        "intelligence": 0,
        "totalSockets": 3,
        "redSockets": 0,
        "greenSockets": 0,
        "blueSockets": 3,
        "chromaticPrice": 1
      },
      "expect": {
        "blueChance": 10,
        "chance": 0.1,
        "best": "Vorici 3B",
        "bestCost": 120
      },
      "source": "hand calculation in content.mdx: an off-colour socket on a two-attribute item is 0.1, so 3 blue is 0.1³ = 0.1% (1,000 orbs); the Vorici 3B recipe costs 120; Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io"
    }
  ],
  "sources": [
    "Siveran, Vorici Chromatic Calculator source code (the socket color model and the recipe list in src/Main.ts). https://github.com/Siveran/siveran.github.io"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    },
    {
      "date": "2026-10-01",
      "note": "The answer sentence reads correctly for 1 socket."
    }
  ]
}