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## Problem of the Day #17: Starcraft TournamentApril 5, 2011

Posted by Seungln in : potd , trackback

After getting sick of Sreenath’s jokes about spiders on his head, Seungln challenges Sreenath to play a series of Starcraft games against him. The rules are as follows:

• Condition A: If at any time Seungln is ahead of Sreenath by 2 wins, then Seungln wins and Sreenath has to kill all the spiders in the world.
• Condition B: If at any time Sreenath is ahead of SeungIn by 2 wins, then Sreenath wins and Seungln has to be locked up in a room full of spiders.
• Condition C: If neither of A or B happens, then more matches are played until either Condition A or Condition B occurs.

If Seungln has a 60% chance of beating Sreenath, and there is no draw in Starcraft, then the probability that Sreenath will have to kill all the spiders in the world can be expressed as $\frac{m}{n}$, where $m$ and $n$ are relatively prime. Find $n-m$.

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