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    Roulette probability question




    Hello I have a basic but quite difficult question about roulette probabilities (assuming roulette has 37 numbers 0-36). I need a general formula for calculating the probability of an event, given specific parameters:
    We need to calculate the probability P(e) of the event E = [Bet B appearing X times in N trials(ie. spins) ]
    We know:
    N= the numbers of spins
    X=the number of times a specific bet wins/appears in those N trials (spins)
    P(b) = the probability of bet B for a single spin/trial.
    How do we calculate the probability of [Bet B appearing X times in N trials(spins) ]?

    For example what is the probability of a specific number appearing exactly 1 time in 37 spins, given itís probability is 1/37?
    Whatís the formula?

    Can we in the same way calculate, letís say the probability of 12 specific numbers (probability 12/37) coming 2 times in 5 spins etc.?

    I have tried to devise a formula which you can see here: roulette probability calculation attempt
    P(e) = (n!/(x!(n-x)!)) P(b)^x
    But I think it is incorrect since it gives an extremely low probability of a specific number appearing exactly 1 time in 37 spins.

    Maybe this is the correct formula?
    P(e) = (n!/(x!(n-x)!)) P(b)^x (1-P(b))^n-x
    But this again gives an extremely low probability of a specific number appearing exactly 1 time in 37 spins.

    Thanks in advance.

  2. #2
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    Re: Roulette probability question

    I thought there were 38 possibilities?
    I don't have emotions and sometimes that makes me very sad.

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    Re: Roulette probability question

    Quote Originally Posted by Dason View Post
    I thought there were 38 possibilities?
    Some wheels have both a 0 and 00, some only have a single 0 slot. So sometimes it's 38 possibilities, sometimes 37.

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    Re: Roulette probability question

    You second formula looks alright to me. You're just looking at the binomial distribution. If we assume a probability of 1/37 for a success on a single spin then the probability of getting exactly 1 success in 37 spins is 0.3729305
    I don't have emotions and sometimes that makes me very sad.

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    Re: Roulette probability question


    Hi and thanks for the replies.
    Yes the second formula is correct I believe. I have corrected my article.

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