7 Kez and Lui play a zero-sum game. The game does not have a stable solution.
The game is represented by the following pay-off matrix for Kez.
| Lui | |
| \cline { 2 - 5 } | Strategy | \(\mathbf { L } _ { \mathbf { 1 } }\) | \(\mathbf { L } _ { \mathbf { 2 } }\) | \(\mathbf { L } _ { \mathbf { 3 } }\) |
| \(\mathrm { Kez } \quad \mathbf { K } _ { \mathbf { 1 } }\) | 4 | 1 | - 2 | |
| \(\mathbf { K } _ { \mathbf { 2 } }\) | - 4 | - 2 | 0 | |
| \(\mathbf { K } _ { \mathbf { 3 } }\) | - 2 | - 1 | 2 |
7
- State, with a reason, why Kez should never play strategy \(\mathbf { K } _ { \mathbf { 2 } }\)
7
- \(\quad\) Kez and Lui play the game 20 times.
Kez plays their optimal mixed strategy.
Find the expected number of times that Kez will play strategy \(\mathbf { K } _ { \mathbf { 3 } }\)
Fully justify your answer.