Who Dares Wins!

My niece had just one chance to avoid being grounded. She had to play 3 games of chess against her mother and father, who would take turns to be her opponent. If she had to win 2 consecutive games in order to succeed, and her father was a stronger player than her mother, who should she play first and why?

Her father since she can't get two consecutive games against her mother anyway, she should give herself two chances to beat the stronger player. Of course, she better watch out for her mom! One loss and she's out (or maybe I should say, stuck in!)

:-)

Say her chance to win against her father is 0.4 and chance against her mother is 0.7.

So if playing her father first she escapes punishment if she wins the first two games or the last two.

That's 0.4*0.7 + 0.6*0.7*0.4 = 0.448

Now say she plays her mother first:

That's 0.7*0.4 + 0.3*0.4*0.7 = 0.364

Therefore she should play her father twice despite the fact that he is a stronger player.