# Decision Simulator

> Compare 2–6 choices by expected value, worst case, best case and minimax regret. Give each choice a worst, most likely and best outcome (money, hours, points…). The simulator computes expected values with PERT or triangular weights (or your own probabilities), then applies maximin, maximax, minimax regret and Laplace rules and explains which rule picks which choice.

Part of usefulweb.site (https://usefulweb.site/). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://decisionsimulator.usefulweb.site/ (interactive tool at https://decisionsimulator.usefulweb.site/tool)
- JSON API: POST https://decisionsimulator.usefulweb.site/api/v1/calculate with a JSON object of inputs (schema: https://decisionsimulator.usefulweb.site/api/v1/tool)
- OpenAPI: https://decisionsimulator.usefulweb.site/openapi.json
- MCP (Streamable HTTP): https://decisionsimulator.usefulweb.site/mcp - tool `decision_simulator`

## Inputs
- goal (select): Higher values are
- method (select): Expected value weights
- unit (text): Unit of the values
- choices (table, required): Choices - Worst/likely/best outcome per choice. Probabilities (%) are only used with “My own probabilities” and are normalised to sum to 100.

## Method
- Each choice has three scenario outcomes: worst (W), most likely (M) and best (B).
- PERT expected value = (W + 4M + B) ÷ 6, standard deviation ≈ (B − W) ÷ 6.
- Triangular expected value = (W + M + B) ÷ 3, standard deviation = √((W² + M² + B² − WM − WB − MB) ÷ 18).
- Custom: probabilities are normalised to sum to 1; EV = Σ pᵢ·xᵢ, standard deviation = √(Σ pᵢ·(xᵢ − EV)²).
- Maximin picks the best worst case; maximax the best best case; Laplace the best unweighted average (W + M + B) ÷ 3.
- Minimax regret treats worst / likely / best as three shared states of the world: regret = (best outcome of any choice in that state) − (this choice’s outcome); the choice with the smallest maximum regret wins.
- When lower values are better, “best” means lowest everywhere. Ties go to the choice listed first. The recommendation is the expected-value pick.