X's Strategy

X will like to divide his play between his rows in such a way that his expected winnings or losses when Y plays the first column will be equal to his expected winnings or losses when Y plays the second column.

Total = Q + 5(1-Q)

Total = 4Q + 3(1-Q)

Therefore, Q + (1-Q)5 = 4Q + 3(1-Q)
Giving Q = 2/5    and    (1-Q)    = 3/5

This means that player X should play his first row 2/5th of the time and his second row 3/5 of the time.

Using the same reasoning Y' Strategy;

1 X R + 4(1-R) =     5R + 3(1-R)
Giving R = 1/5    and    (1-R)    = 4/5

This means that player Y should divide his time between his first and second column in the ratio 1:4

This is shown in the following matrix: