Winning the Dice Game

Discrete Mathematics Level 2

Bret and Shawn are playing a game where each turn the players roll a 20-sided die fair and then add the number they get to their score. The winner is the player with the highest score at the end of the game (there may be a tie). Before the last turn, Shawn is ahead by 10 points. The probability that Bret can come back and win the game can be expressed as \( \frac{a}{b}\) where \(a\) and \(b\) are coprime numbers. What is \(a + b\)?

Details and assumptions

Both Shawn and Bret have 1 more roll on the last turn.

If there is a tie, no one won.


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