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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 1:4This is shown in the following matrix:
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