6 Ryan and Casey are playing a card game in which they each have four cards.
- Ryan's cards have the letters A, B, C and D.
- Casey's cards have the letters W, X, Y and Z.
Each player chooses one of their four cards and they simultaneously reveal their choices.
The table shows the number of points won by Ryan for each combination of strategies.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Casey}
| | W | X | Y | Z |
| \cline { 2 - 6 }
Ryan | A | 4 | 0 | 2 | 1 |
| B | 0 | 2 | - 3 | 4 |
| C | 1 | 4 | - 4 | 5 |
| D | 6 | - 1 | 5 | 0 |
\end{table}
For example, if Ryan chooses A and Casey chooses W then Ryan wins 4 points (and Casey loses 4 points).
Both Ryan and Casey are trying to win as many points as possible.
- Use dominance to reduce the \(4 \times 4\) table for the zero-sum game above to a \(4 \times 2\) table.
- Determine an optimal mixed strategy for Casey.