Gambler Ruin Expected Duration

Problem

The expected number of steps until ruin or victory from i in a walk to 0 or n is i (n - i) when p = 0.5. For p != 0.5 it is (i - n (1 - r^i) / (1 - r^n)) / (1 - 2p) with r = (1 - p) / p.

Given i, n, and p, return the expected duration.

Hint

The fair-coin case is the parabola i (n - i).

Test cases

case 1

in: [1,5,0.5]

expected: 4

case 2

in: [2,4,0.4]

expected: 3.8461538461538476

case 3

in: [3,6,0.7]

expected: 6.405405405405406

Starter codePython

def gambler_ruin_expected_duration(i, n, p):
    # Your code here
    pass

3 test cases · run your code against them in the editor