Results 1 to 4 of 4

Thread: Roulette

  1. #1
    Junior Member
    Joined
    Aug 2007
    Posts
    71

    Roulette

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

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

    For (a) $\displaystyle 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) $\displaystyle E[X] = \sum x \cdot p(x) $
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by lord12 View Post
    A gambling book recommends the following winning strategy for the game of roulette. It recommends that the gambler bets $\displaystyle \$1 $ on red. If red appears (which has probability $\displaystyle \frac{18}{38} $), then the gambler should take her $\displaystyle \$1 $ profit and quit. If the gamblers loses the bet (which has probability $\displaystyle \frac{20}{38} $ of occurring),

    she should make additional $\displaystyle \$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 $\displaystyle X $ denote the gambler's winnings when she quits.

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

    For (a) $\displaystyle 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) $\displaystyle E[X] = \sum x \cdot p(x) $ Mr F asks: And your question is ....?
    ..
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2007
    Posts
    71
    next two spins.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by lord12 View Post
    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).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Expected Value and Roulette
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Feb 3rd 2010, 08:22 PM
  2. Roulette
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Sep 22nd 2009, 03:18 AM
  3. roulette win probability
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 10th 2009, 06:42 AM
  4. Roulette question
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Oct 28th 2008, 07:03 AM
  5. Roulette Strategy
    Posted in the Statistics Forum
    Replies: 29
    Last Post: Sep 30th 2008, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum