Problem #88
The Cretan Bull
The story
Animals seem to wreak a lot of havoc in greek myths. The one under consideration is a bull that used to uproot crops and bring down orchard walls in Crete. Hercules is sent to kill it as usual.
The game
The bull is smart however, and it senses that Hercules is after it. It engages in an impromptu game of hide-and-seek (following the same rules as those in Problem 81).
Alas, it only has two choices of hiding places. In the first location, Hercules has a 40% chance to find the bull, if in fact the bull is there. In the second location, Hercules has a 100% chance to find the bull if it is there. The second location is thus a terrible hiding place. But, the bull bets on Hercules dismissing such a location.
If Hercules and the bull play with perfect strategies, what is the expected number of turns it will take for Hercules to capture the bull? The answer is a rational number in lowest terms \frac{p}{q}, and you are to enter p,q.