Thread: Struggling with Assignment question

This is the question exactly
Alice: Let's take turns flipping a coin. The first person who gets heads wins. I'll
go first.
Bob: But you might win on the very first throw. Let's compensate by giving me
one extra throw on my first turn.
Alice: Fine.
Bob: And let's use my coin, which comes up heads with probability 'pi' .
Alice: Well, then I had better know 'pi' before I agree.
What value of 'pi' makes the game fair to each player?

I have been stuck on this same problem for so long its embarrassing. I am not asking for the answer I just need someone to point me in the right direction. I thought I was supposed to work out the probability for each player winning in terms of pi assume they are equal, then solve for pi. I went through all my lecture notes and still nothing came to me. Please help!

i haven't worked it through but i would approach the problem like this:

what is the probability of alice winning on turn 1?
what is the probability of the game reaching turn 3 and alice winning on that turn 3?
what is the probability of the game reaching turn 5 and alice winning on that turn 5?
what is the probability of the game reaching turn 7 and alice winning on that turn 7?
....


hence what is the probability of alice winning?

find the value of pi that makes this 0.5.