2 Progressive roulette betting continued In this question we

2. (Progressive roulette betting: continued) In this question we keep the set up from question 1. Let\'s recall the main conclusions from that question: a round of progressive betting (which we will from now on call a progression, to simplify terminology) always eventually results in a profit of precisely $1, but the average amount of money needed to play a progression is infinite. It is hence reasonable to ask what happens if a bettor tries to play a progression if he only has a finite amount of money, and this question focuses on this more realistic case. Note, of course, that if we are now assuming his money is finite, there is a chance that playing a progression would require the bettor to make a bet he can\'t afford, in which case he simply stops and takes a heavy loss. When this happens, we say a catastrophe took place. (a) (3 points) Suppose the initial funds of the bettor are $M and choose k such that 2^k-1

Solution

Casino players have devised more systems for beating roulette than any other casino game. I believe the reason is because the game is played at a leisurely pace so it allows plenty of time to make bets between spins. System players will use this down time to analyze the data from past results and have enough time to figure out and make the next bet before the ball drops into a pocket. The sheer number of roulette systems is staggering. In an attempt to get a handle on this I decided to select the ten most popular systems that fall into one of the following three categories of roulette systems. Progressive Betting SystemsMost of these systems have been around for a hundred years. Their characteristic is that the amount of your next bet is determined by what happened on previous bets.