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Respond to the question: AVERAGE LENGTH OF A GAME?

10/30/2010 12:00 PM by Stuart; AVERAGE LENGTH OF A GAME
Given the following game,

there is a hider and a seeker, each game consists of the hider randomly selecting one of two places to hide that is A with probability p and B with 1 - p, and the seeker randomly choses to search in A with probability q and B with 1 - q. If seeker finds hider then game ends, else both randomly pick again. This continues each time both randomly picking where to hide and search, until seeker finds hider.
I want to know how to formulate the average number of game iterations to expect using theory...that is using p and q, how can i express how long i should expect it to take for seeker to find hider? [Manage messages]