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Maximin Strategy Calculator

Enter a payoff matrix with one strategy per row to find the maximin choice.

How it is calculated

Type the payoff matrix with one strategy (action) per line and the payoff in each possible state of the world as the numbers on that line, separated by spaces, commas or semicolons. For each row the tool takes the smallest number, mi = min(row i). It then picks the row with the largest of these minimums, value = max(mi), and reports that value and the row number, counting from 1. If two rows tie, the first one is reported. Blank lines are skipped, rows may have different lengths, and negative numbers are fine. If any entry is not a number, the tool gives no result. The rule looks only at the worst case, so it ignores probabilities and every better outcome.

Worked example

Three strategies, three scenarios: row 1 is 40 25 -10, row 2 is 30 20 15 and row 3 is 60 5 -30. The worst payoff per row is -10, 15 and -30. The largest of these is 15, which belongs to row 2. The tool shows a maximin value of 15.00 and row 2. Row 3 has the biggest possible win at 60 but also the worst loss at -30, so this cautious rule rejects it; a rule based on the best case would choose it.

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Common mistakes

  • Putting the states on the lines and the strategies across. Each line must be one strategy; otherwise the tool compares scenarios, not choices.
  • Entering costs or losses as positive numbers. Maximin picks the largest worst case, which is wrong for costs; enter costs as negatives, or use a minimax rule for costs.
  • Expecting the row number to start at 0. Row 1 is the first line you typed.
  • Leaving text in the box, such as a header or labels like A and B. One non-numeric entry makes the whole result empty.
  • Using maximin when probabilities are known. It ignores them, so a strategy with a tiny chance of a bad result can lose to a safer but lower-paying one.

Sources

About this calculator

The maximin decision rule (Wald's criterion) is a way to choose between strategies when you don't know which future state of the world will occur and you'd rather avoid the worst outcome than chase the best one: for each strategy (row) in a payoff matrix, it finds the minimum payoff across all possible states (columns), then picks the strategy whose minimum is the highest of all the minimums — the "best worst case." It's deliberately pessimistic, which is exactly the point when the downside risk matters more than the upside.

Business strategists use maximin thinking to choose between options — like which market to enter or which supplier to commit to — when the probabilities of different scenarios are unknown or unreliable, game theory students apply it as the classic solution concept for decision-making under uncertainty (as distinct from decision-making under risk, where probabilities are known), and robust engineering and military planners use the same worst-case-optimization logic when a failure mode simply cannot be allowed to happen.

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Comments (1)

  • Editorial team

    Maximin looks only at each row's single worst number, so two strategies can tie even when one is clearly better elsewhere. This tool reports just the first tied row. If you see a tie, compare the tied rows by their next-worst payoffs, or by their averages if you have rough probabilities. Rows are strategies and columns are scenarios, so entering costs as positive figures will flip the logic. What decision are you modelling, and how many scenarios do you have?

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