# Roulette

• Sep 24th 2008, 09:19 PM
lord12
Roulette
A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets $\1$ on red. If red appears (which has probability $\frac{18}{38}$), then the gambler should take her $\1$ profit and quit. If the gamblers loses the bet (which has probability $\frac{20}{38}$ of occurring), she should make additional $\1$ bets on red on each of the next new spins of the roulette wheel and then quit. Let $X$ denote the gambler's winnings when she quits.

(a) Find $P(X>0)$.
(b) Is this a winning strategy?
(c) Find $E[X]$.

For (a) $P(X>0) = 1 - P(X \leq 0)$. This is the easy way to compute it?
(b) What is the definition of a winning strategy?
(c) $E[X] = \sum x \cdot p(x)$
• Sep 25th 2008, 02:24 AM
mr fantastic
Quote:

Originally Posted by lord12
A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets $\1$ on red. If red appears (which has probability $\frac{18}{38}$), then the gambler should take her $\1$ profit and quit. If the gamblers loses the bet (which has probability $\frac{20}{38}$ of occurring),

she should make additional $\1$ bets on red on each of the next new spins of the roulette wheel and then quit. Mr F asks: What does this mean? Do you mean on the next spin, the next two spins, .....??

Let $X$ denote the gambler's winnings when she quits.

(a) Find $P(X>0)$.
(b) Is this a winning strategy?
(c) Find $E[X]$.

For (a) $P(X>0) = 1 - P(X \leq 0)$. This is the easy way to compute it? Mr F says: It's one way of doing it, I suppose. But it would help to know the answer to my above question.
(b) What is the definition of a winning strategy? Mr F says: E[X] > 0.
(c) $E[X] = \sum x \cdot p(x)$ Mr F asks: And your question is ....?

..
• Sep 25th 2008, 03:24 AM
lord12
next two spins.
• Sep 25th 2008, 03:48 AM
mr fantastic
Quote:

Originally Posted by lord12
next two spins.

Then the only possible value of X that's greater than zero is X = 1. This occurs for either LWW or W. So it's not difficult to calculate Pr(X = 1) ....

The other possible values of X are:

X = -3 which occurs for LLL

X = -1 which occurs for LWL or LLW.

So it's not difficult to calculate Pr(X = -3) and Pr(X = -1).