The free payoff table calculator.
Enter your alternatives and states of nature, and see what maximax, maximin, minimax regret, Laplace, Hurwicz and expected value with EVPI each pick, with a live chart per rule and the full working shown. Nothing leaves your browser.
1 Your payoff table
Rows are the alternatives you can choose. Columns are the states of nature you cannot choose. Each cell is the result if you pick that row and that state happens. Rename anything by typing over it.
2 State probabilities (optional)
3 Coefficient of optimism
Only the Hurwicz rule uses this dial. Drag it and watch the Hurwicz chart move between pure pessimism and pure optimism.
4 What each decision rule chooses
Maximax (optimistic)
Judge every alternative by its best possible outcome, then take the best of those.
Maximin (pessimistic)
Judge every alternative by its worst possible outcome, then take the best of those.
Minimax regret
Regret is what you gave up by not picking the best alternative for the state that actually happened. This rule keeps your largest possible regret as small as it can be.
Laplace (equally likely)
With no reason to think one state is likelier than another, treat them as equally likely and compare the averages.
Hurwicz (criterion of realism)
A dial between pure optimism and pure pessimism, weighted by the coefficient of optimism alpha from the controls.
Every figure is computed in this browser and reproduced in our published test vectors. Your numbers never leave the page.
Five classical rules, one table.
When you cannot attach probabilities to the future, decision theory still gives you principled ways to choose. Each rule encodes a different attitude to risk.
- Build the table. Rows are your alternatives, columns are the states of nature, each cell is the outcome of that pair. Toggle to cost mode if smaller numbers are better.
- Read the rules. Maximax chases the best case, maximin protects the worst case, minimax regret minimizes what hindsight could cost you, Laplace treats every state as equally likely, and Hurwicz blends optimism and pessimism on a dial.
- Add probabilities when you have them. The calculator then computes each alternative's expected value, the expected value with perfect information, and EVPI - the most any forecast about the future could rationally be worth.
The rules and the worked example follow the classical treatments: Luce and Raiffa's Games and Decisions, Savage's regret criterion, Hurwicz's criterion of realism, and Raiffa and Schlaifer on the value of information. For how each criterion behaves inside a full decision tree, see the decision criteria documentation.
When the decision has more than one stage.
A payoff table compares one round of alternatives. Real decisions branch: choices lead to chances, which lead to more choices. That is what the full software models.
- Build multi-stage decision trees with choices, chances and payoffs
- Switch between these same criteria - expected utility, maximin, maximax, minimax regret, Hurwicz, Laplace - on the whole tree
- Model risk attitude with utility functions, not just raw payoffs
- Value of information analysis on any chance node
- Sensitivity analysis with live charts
- Export thesis-ready reports
- Perpetual license, fully offline, no cloud dependency
Payoff tables and the decision rules, explained.
What is a payoff table?
A payoff table lays out a one-stage decision under uncertainty: each row is an alternative you can choose, each column is a state of nature you cannot choose, and each cell is the result if you pick that row and that state happens. The classical decision rules - maximax, maximin, minimax regret, Laplace and Hurwicz - all read their answer straight off this table.
What is the difference between maximax, maximin and minimax regret?
Maximax is optimistic: judge every alternative by its best possible outcome and take the best of those. Maximin is pessimistic: judge every alternative by its worst outcome and take the best of those. Minimax regret first converts the table to regrets - what you gave up by not picking the best alternative for the state that actually happened - then picks the alternative whose largest possible regret is smallest. On the same table the three rules can each pick a different alternative, which is exactly what this calculator's preloaded example shows.
What is the Hurwicz criterion of realism?
The Hurwicz rule is a dial between pure optimism and pure pessimism. For each alternative it computes alpha × best outcome + (1 - alpha) × worst outcome, where alpha is your coefficient of optimism between 0 and 1. At alpha = 0 it reduces to maximin, at alpha = 1 it reduces to maximax. This calculator has a live slider for alpha, so you can watch the recommended alternative change as your optimism changes.
What is EVPI, the expected value of perfect information?
With state probabilities attached, each alternative has an expected value. EVPI is the expected value with perfect information minus the best expected value: the gap between deciding after you know the state of nature and deciding before. It is the ceiling on what any study, survey or forecast about the state of nature can rationally be worth, and it is never negative.
What if my numbers are costs instead of payoffs?
Switch the calculator to cost mode and every rule is read the other way round: smaller is better, maximax becomes minimin, maximin becomes minimax, regret is measured against the cheapest option in each column, and EVPI becomes the best expected cost minus the expected cost with perfect information. The picks can genuinely change - on the preloaded example, three of the five rules move when the same numbers are read as costs.