Shows that the Martingale strategy has a 50% chance of doubling your money.

MartingaleSimulation.linq

var rand = new Random();

bool Play(ref int bank, int bet)
{
    var win = rand.Next(2) < 1;
    checked
    {
        bank += win ? bet : -bet; // If you win, you gain your bet back AND the winnings.  If you lose, you just lose your bet.
    }

    return win;
}

int Martingale(int bankroll, int target)
{
    var bet = 1;
    while (bankroll > 0 && bankroll < target)
    {
        if (Play(ref bankroll, bet))
        {
            bet = 1; // Reset your bet amount to $1 whenever you win.
        }
        else
        {
            checked
            {
                bet *= 2; // Double your bet if you lose.
            }

            // It is impossible to make a bet larger than your bankroll.
            if (bet > bankroll)
            {
                bet = 1; // A casino will not loan you money. In this case, reset to a bet of $1.
            }
        }
    }

    return bankroll;
}

var start = 100;
Enumerable.Range(0, 100000).Select(_ => (double)Martingale(start, start * 2)).GroupBy(outcome => outcome).ToDictionary(g => g.Key, g => g.Count()).Dump();