[jason1990]

This is a classic mathematical problem, sometimes referred to as the "Gambler's Ruin". However, it is often difficult to dissuade people of their belief once they get set on believing that it works.

First, here's the mathematics: call the minimum bet 1 unit (dollar, euro, chip, whatever). Suppose you have a bankroll of 2^n - 1, exactly enough for n bets. You then apply the strategy until one of two things happens: (A) you lose all your money, (B) RED eventually appears and you are up 1 unit. The probability of RED appearing is 18/38 or 9/19. So the probability of A is (10/19)^n. The probability of B is, therefore, 1 - (10/19)^n. If A occurs, you lose 2^n - 1. If B occurs, you win 1. So you're EV is

-(2^n - 1)*(10/19)^n + 1*(1 - (10/19)^n)
= 1 - (2^n)*(10/19)^n
= 1 - (20/19)^n.

It's easy to see from here that your EV is negative, no matter what n is. For example, suppose you enter the casino with 1,048,575 units. This corresponds to n = 20, giving you an EV of about -1.8.

But looking only at the EV is misleading. What's really happening here (when n = 20) is that you have a 99.999734% chance of winning 1 unit and a 0.000266% chance of losing 1,048,575 units. For some people, when they look at it this way, the strategy looks tempting.

But you should tell your friend's father that, when he uses this strategy, he's effectively playing a "reverse lottery". For example, what if someone offered you a free lottery ticket under the agreement that, if the numbers on the ticket do NOT come up, you win $1. But if they DO come up, you lose everything you own (including the winning lottery ticket). This particular example is actually (for most people and most lotteries) +EV, yet I doubt very many people would be willing to gamble everything they own for a chance to win $1, no matter how good that chance may be.

Side note: I doubt very many people would have the guts to follow this strategy through. If you lose 12 times in a row (which WILL happen if you use this strategy on a regular basis) and you're on a $5 roulette table, you must wager over $40,000 on your next bet! That's going to be a lot of money to anybody who's trying to win $5 using this strategy. Besides which, most casinos have a house limit which determines the maximum size of any particular wager.