St. Petersburg Finite Cutoff EV

Problem

In the St. Petersburg game a fair coin is flipped until the first tail, paying 2^k after k heads, but play is cut off after n rounds. Each of the n rounds contributes 1 to the expectation, so return [expected payoff, maximum payoff] = [n, 2^n].

Return [0.0, 0.0] for n <= 0.

Hint

The k-th round adds 2^k * 2^(-k) = 1 to the expectation.

Test cases

case 1

in: [1]

expected: [1,2]

case 2

in: [3]

expected: [3,8]

case 3

in: [10]

expected: [10,1024]

case 4

in: [0]

expected: [0,0]

Starter codePython

def st_petersburg_finite_ev(n):
    # Your code here
    pass

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