# Chess tournament

Discrete Mathematics Level 5

You've just made it into the finals of a chess tournament. Your opponent is stronger than you and you are trying to think of a way to beat him. There will be 2 matches, and if it results in a tie, another match will be played to decide the winner. 1 point is awarded for winning, 0.5 for drawing, and 0 for losing. You will beat your opponent if you score more than him in these 2 matches, or if both players score the same, if you win the play-off, you will win the match. You can play a daring game, in which you win 45% and lose 55% of the time, or you can play a defensive game, in which you draw 90% and lose 10% of the time. If you play optimally, the probability that you beat your opponent is $$a/b,$$ where a and b are coprime integers. Find $$a+b.$$

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