Play safe strategy
This page is about the play safe strategy in a zero sum game.
In this strategy, the player(s) choose the option which minimises the possible loss.
Take this pay off matrix for example:
| Player 2 plays C | Player 2 plays D | Player 2 plays E | Row minima | |
|---|---|---|---|---|
| Player 1 plays A | 2 | -1 | 1 | -1 |
| Player 1 plays B | 1 | -2 4 | -3 | -3 |
| Column maxima | 2 | -1 | 1 |
The numbers in the table represent the benefit to player 1 - play 2 loses that amount.
- The row minima is the worst that can happen for each of player 1’s options.
- The play safe strategy for player 1 is to choose the option with the highest row minima - in this case, option A.
- The column maxima is the best that can happen for each of player 2’s options.
- The play safe strategy for player 2 is to choose the option with the lowest column maxima - in this case, option D.
Value of the game
The value of the game for player 1 is the amount that player 1 can expect to win (or lose) if both players play their play safe strategies.