Maximin
Look only at the worst outcome each option can produce and take the option whose worst outcome is best.
- Time cost
- 20 min
- Output
- A guaranteed floor and its cost in foregone average.
- Steps
- 5
Use when
- The worst case is genuinely unacceptable and must be bounded.
- No probabilities exist and you are unwilling to invent them.
- An adversary, or an unfriendly world, gets to pick which state occurs.
Do not use when
- The worst case is survivable and unlikely. Maximin will reject good options to avoid it.
- You have probabilities and the downside is bounded. This ignores everything except one cell per row.
Inputs required
- Options
- States
- A payoff per cell
Procedure
- 01
Build the payoff table
Same table as minimax regret. Probabilities are not required.
- 02
Find each option’s worst
Across the row, the minimum payoff.
- 03
Choose the best of those
The option with the highest minimum. You have guaranteed a floor.
- 04
Price the floor
Compare the chosen option’s average to the best average available. The difference is what the guarantee costs — make it explicit rather than free.
- 05
Check the floor is real
Maximin only protects against states you listed. A worst case you failed to enumerate is not bounded by anything.
Characteristic failure mode
Worked example
Choosing how much of a modest savings pot to hold in volatile assets.
- 01States: severe downturn, flat, strong growth.
- 02Full-volatile worst case: −38%. Half-and-half worst case: −19%. Cash worst case: −3% real.
- 03Maximin selects cash.
Result
Maximin picks cash, which also has the worst average by a wide margin. That is the method working as designed — and the reason to use it only when the worst case is genuinely unsurvivable.
Where this disagrees with another method
Maximin ignores probability entirely and expected value ignores survivability entirely. Use maximin only on the branches that end the game; use expected value on everything else.
Where to go next