Results 1 to 11 of 11

Math Help - Dice 7 Odds Theory

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Dice 7 Odds Theory

    Does anyone know how to graph this phenomena on a computer? I graphed with dice how many rolls occur after a 7 before another 7 occurs. I understand that this may not work with computer generated numbers. The odds of 7 is 1 in six but this may be an additional way to predict the odds. The graph by hand showed that the probability after a seven of another 7 on the first roll is 1 in 9 and that proceeds to dip down to 1 in 3 on something like the 5th roll without a 7 and then proceeds exponentially up to approaching 100% after for example 100 rolls without a 7. At this point the dice become unpredictable.
    Attached Thumbnails Attached Thumbnails Dice 7 Odds Theory-7graph.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,792
    Thanks
    1532

    Re: Dice 7 Odds Theory

    Do you understand that "how many rolls occur after a 7 before another 7 occurs" is exactly the same as "how many rolls occur before the first 7 occurs"?
    A 7 can occur on the first roll with probability 1/6 so P(x= 0)= 1/6, NOT "1 in 9".

    Anything other than a 7 on the first roll has probability 5/6 and then a 7 on the second roll has probability 1/6 so P(x= 2)= \frac{5}{6^2}.

    Any thing other than a 7 on the first roll has probability 5/6, anything other than a 7 on the second roll has probablity 5/6, and then a 7 on the third roll has probablity 1/6 so P(x= 3)= \frac{5^2}{3^3}.

    Any thing other than a 7 on the first roll has probability 5/6, anything other than a 7 on the second roll has probablity 5/6, anything other than a 7 on the third roll has probability 5/6, and then a 7 on the fourth roll has probablity 1/6 so P(x= 4)= \frac{5^3}{3^4}.


    See the pattern?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Re: Dice 7 Odds Theory

    You are wrong in a number of ways, first- there are a variety of odds with 2 dice the odds of there being a 7 is how many possibilities with 2 dice, there is: 1/6, 1/5, 1/4, 1/3, 1/2, 1/1, 2/6, 2/5, 2/4, 2/3, 2/2, 2/1, 3/6, 3/5, 3/4, 3/3, 3/2, 3/1, 4/6, 4/5, 4/4 - 21 possibilities. 3 add up to 7, that is 3/21 and 33%. You fail to graph the number of rolls that occur before the first seven. I have a picture of the graph here, it shows how 7 has a probability of more than 33% then dips down to less than 33% then goes back up past 33% and increases exponentially as its asymptote approaches 100% probability of rolling a 7. I lost the actual graph years ago when I figured this out. Everyone drive safely to the Casino and I want a fair cut of the profit!
    Last edited by phillipanthonybiondo; November 29th 2012 at 04:12 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,711
    Thanks
    1640
    Awards
    1

    Re: Dice 7 Odds Theory

    Quote Originally Posted by phillipanthonybiondo View Post
    You are wrong in a number of ways, first- there are a variety of odds with 2 dice the odds of there being a 7 is how many possibilities with 2 dice,

    If indeed you think that, then you are seriously uninformed.
    Here is your first posting:
    Quote Originally Posted by phillipanthonybiondo View Post
    Does anyone know how to graph this phenomena on a computer? I graphed with dice how many rolls occur after a 7 before another 7 occurs.
    Rolling two dice. There are six ways of getting a sum of seven.

    So \mathcal{P}(S=7)=\frac{1}{6}.

    If X is the number of 'rolls' on which the first seven appears then
    \mathcal{P}(X=k)=\left( {\frac{5}{6}} \right)^{k - 1} \left( {\frac{1}{6}} \right) = \frac{{5^{k - 1} }}{{6^k }}.

    Now assume that it takes K rolls to get the first seven, how many more to get the next seven?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Re: Dice 7 Odds Theory

    6 ways? How? 1/6, 3/4, 5/2, what else?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,711
    Thanks
    1640
    Awards
    1

    Re: Dice 7 Odds Theory

    Quote Originally Posted by phillipanthonybiondo View Post
    6 ways? How? 1/6, 3/4, 5/2, what else?
    This question shows how poorly informed you are.
    Look at the web calculation.

    The coefficient of x^k is the number of ways that the sum of two dice is equal k~.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Re: Dice 7 Odds Theory

    You fail to tell me how there are more than 3 possibilities to roll a 7.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: Dice 7 Odds Theory

    6-1, 1-6, 5-2, 2-5, 4-3, 3-4.
    There are 36 possible outcomes with two dice. Six possibilities with the first to go with six possiblities for the second.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Re: Dice 7 Odds Theory

    you are repeating a six and a one, it doesn't matter which dice has the 6 or 1 and I only found 25 possible combinations so 3/25 is 12%.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

    Re: Dice 7 Odds Theory

    Try thinking it out with dice of different colours, say one red one and one blue one.
    There are two ways of throwing 6-1.
    6 with the red die and 1 with the blue die or,
    6 with the blue die and 1 with the red die.
    There is only one way of throwing, say, double one.
    1 with the red die and 1 with the blue die.
    6-1 is twice as likely as 1-1.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Nov 2012
    From
    Marlinton, wv
    Posts
    6

    Re: Dice 7 Odds Theory

    Yes I figured that out.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Odds with 2 normal dice and 1 unusual?
    Posted in the Statistics Forum
    Replies: 3
    Last Post: April 24th 2011, 01:56 PM
  2. bookies odds vs real odds
    Posted in the Statistics Forum
    Replies: 10
    Last Post: February 18th 2011, 04:49 PM
  3. Replies: 0
    Last Post: December 29th 2009, 08:08 PM
  4. Help, Dice odds with Risk.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: December 4th 2007, 10:43 PM
  5. Dice odds. Risk style.
    Posted in the Statistics Forum
    Replies: 0
    Last Post: November 29th 2007, 03:16 AM

Search Tags


/mathhelpforum @mathhelpforum