Risk of ruin

Originally posted by mtthw
As I said, let B = 1. I took one specific case and showed the answer couldn't be 50%. Therefore it can't be 50% in all cases.

PW is 0.5 not 0.1

Originally posted by PBE6
This is a little bit complicated, because not all arrangements are valid (you can't have more than B-1 losses in a row before getting a few wins)

You might be able to use a reflection principle to work out A(m). The number of paths from A to B that hit zero is equal to the number of paths from A to -B.

Originally posted by uzless
PW is 0.5 not 0.1

Pw was unspecified in the question. If Pw is 0.5 then you will hit zero eventually (see the formula I posted for the result).

Originally posted by mtthw
Pw was unspecified in the question. If Pw is 0.5 then you will hit zero eventually (see the formula I posted for the result).

according to your website, you've posted the wrong formula for pw = 0.5

Originally posted by uzless
according to your website, you've posted the wrong formula for pw = 0.5

That's the formula for Pw > 0.5, although you'll notice it equals 1 for Pw = 0.5, so no worries.