Martingale Betting Expected Profit

Problem

A martingale betting system bets base_bet and doubles after each loss for up to max_bets bets. A win at any point nets base_bet; losing every bet loses base_bet * (2^max_bets - 1). Return the expected profit:

E = base_bet * (1 - (1 - p)^max_bets) - base_bet * (2^max_bets - 1) * (1 - p)^max_bets.

Return 0.0 for max_bets <= 0.

Hint

For a fair game the expected profit stays exactly zero.

Test cases

case 1

in: [1,0.5,3]

expected: 0

case 2

in: [1,0.5,5]

expected: 0

case 3

in: [1,0.4,3]

expected: -0.7279999999999998

case 4

in: [10,0.5,2]

expected: 0

Starter codePython

def martingale_expected_profit(base_bet, p, max_bets):
    # Your code here
    pass

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