Page 1 of 2 12 LastLast
Results 1 to 15 of 16

Math Help - Dice probability and the casino

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    5

    Dice probability and the casino

    Hi

    A dice has 3 sides A B C

    It is thrown twice and lands as A A
    then what is the probability that next to land will be B or C?

    That is A A B or A A C

    The dice has no memory of what was thrown before but surely the probability can't be 2/3.

    It is rare to see say B B B B B B B B to land consecutively so surely there is less probility that B will land again than an A or C? The A and the C have their '1/3 probability of landing destiny' to fullfill and the B has landed more than its fair share of occassions so surely A or C are more likely to land next?

    What are the probabilty calculations?

    Thankyou
    Last edited by AceHero; December 24th 2009 at 10:11 AM. Reason: Did not write question properly first time
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by AceHero View Post
    Hi

    A dice has 3 sides A B C

    It is thrown twice and lands as A A
    then what is the probability that next to land will be B or C?

    That is A A B or A A C

    The dice has no memory of what was thrown before but surely the probability can't be 2/3.

    It is rare to see say B B B B B B B B to land consecutively so surely there is less probility that B will land again than an A or C?

    What are the probabilty calculations?

    Thankyou
    It is 2/3. There are three outcomes, two of which are desirable, hence the chance is 2/3

    No, it is equally likely to land on B as A or C.

    As the die has no memory each event is independent of the previous event and hence all outcomes are equally likely
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jun 2009
    Posts
    220
    Thanks
    1
    Quote Originally Posted by AceHero View Post
    Hi

    A dice has 3 sides A B C

    It is thrown twice and lands as A A
    then what is the probability that next to land will be B or C?

    That is A A B or A A C

    The dice has no memory of what was thrown before but surely the probability can't be 2/3.

    It is rare to see say B B B B B B B B to land consecutively so surely there is less probility that B will land again than an A or C?

    What are the probabilty calculations?

    Thankyou
    You were right when you said that the die 'has no memory' . It's what's known in probability as independence.

    All earlier rolls have no effect what so ever on the next roll, so the probability of getting, say, B OR C is ALWAYS 2/3 . Why would it change? Nothing has physically happened to the die, so long as it's a 'fair' die.

    Also, all strings (of equal length) of rolls are equally likely. For example BBBBBBBB is just as likely as ABABCBCC.
    Last edited by pomp; December 24th 2009 at 10:02 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2009
    Posts
    5
    Quote Originally Posted by pomp View Post

    For example BBBBBBBB is just as likely as ABABCBCC.
    I get this, but surely if you were sitting in a casino and the dice rolled BBBBBBB then surely you would feel confident that A or C may land next.

    In an infinite time period you would see BBBBBBBB land as often as ABABCBCC but in the 1 hour (time limit) you may be sitting in the casino you won't see BBBBBBBB that often and you will expect the letters to be assorted.

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jun 2009
    Posts
    220
    Thanks
    1
    Quote Originally Posted by AceHero View Post
    I get this, but surely if you were sitting in a casino and the dice rolled BBBBBBB then surely you would feel confident that A or C may land next.

    In an infinite time period you would see BBBBBBBB land as often as ABABCBCC but in the 1 hour (time limit) you may be sitting in the casino you won't see BBBBBBBB that often and you will expect the letters to be assorted.

    I don't recommend going to a casino any time soon.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Dec 2009
    Posts
    5
    Quote Originally Posted by pomp View Post
    I don't recommend going to a casino any time soon.
    I know what you say makes sense mathematically ..... but I'm sure that I'm correct in some deep parallel universe sort of way ..... and there are plenty of casino dwellers sitting there on the slot machines that know I'm correct.

    If AAAAAAAAA land so many times in a row .... all the gamblers I've seen will put down a B or C on their bet.


    Thanks Pomp ... (deep down know you're telling the truth but I can't admit it to myself)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by AceHero View Post
    I get this, but surely if you were sitting in a casino and the dice rolled BBBBBBB then surely you would feel confident that A or C may land next.

    In an infinite time period you would see BBBBBBBB land as often as ABABCBCC but in the 1 hour (time limit) you may be sitting in the casino you won't see BBBBBBBB that often and you will expect the letters to be assorted.

    That's because the human mind doesn't comprehend random chance - it tries to make order out of something. It's a major reason why casinos rake in the money

    BBBBBBBB is as likely as ABABCACA or any other sequence. A simple tree diagram will show this

    Admittedly if you were not picky about the order they came in but the actual number it would be different. For the above sequence you're more likely to get 4 As, 2Bs and 2Cs than 8 B's
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Dec 2009
    Posts
    5
    Quote Originally Posted by e^(i*pi) View Post
    That's because the human mind doesn't comprehend random chance - it tries to make order out of something. It's a major reason why casinos rake in the money
    I thought that I was going to make a break through in casino science .... but guess not then Will just have to keep doing the 9-5 shift
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by AceHero View Post
    I know what you say makes sense mathematically ..... but I'm sure that I'm correct in some deep parallel universe sort of way ..... and there are plenty of casino dwellers sitting there on the slot machines that know I'm correct.
    And yet the casinos make a profit and the punter who knows what you say they know make a loss.

    CB
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Dec 2009
    Posts
    5
    What about my probability destiny theory.

    If AAAAAAAAA does fall in this sequence then in a 1 hour time frame B and C have yet to fulfill their 1/3 probability destiny. So surely they will have an increased theorectical probability to be next.

    Lets forget that the dice does not have a memory for a moment .... because that just spoils it.

    How do you calculate the probability of B landing after A?
    Is it 1/3+1/3 or 1/3x1/3 or something else?



    Deep down I know you're all correct but I have a feeling that there is something in what I am saying?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by AceHero View Post

    Deep down I know you're all correct but I have a feeling that there is something in what I am saying?
    Deep down you know we are right, but you still think we're wrong!?

    CB
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by AceHero View Post
    I get this, but surely if you were sitting in a casino and the dice rolled BBBBBBB then surely you would feel confident that A or C may land next.

    In an infinite time period you would see BBBBBBBB land as often as ABABCBCC but in the 1 hour (time limit) you may be sitting in the casino you won't see BBBBBBBB that often and you will expect the letters to be assorted.

    It may well be that you decide to do a Bayesian analyis of the situation ....
    Follow Math Help Forum on Facebook and Google+

  13. #13
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Hi AceHero,

    and Happy Christmas!

    You stated "a dice has 3 sides A, B, C".

    Is this a standard dice of 6 sides, with only 3 of them marked,
    or is this a 6-sided dice with two A sides, two B sides and two C sides?

    From the discussion, I can "safely" assume it has 6 sides.
    Also, each side is equally likely if we are rolling an unbiased dice.

    On "any" throw, the probability of an A is 1/3, B is 1/3, C is 1/3.
    As the throws are independent, it does not matter that the first two throws
    were A followed by A.
    Previous throws do not alter the probability for subsequent throws.

    Hence, on "any" throw, the probabilities remain the same.

    A few of us did an experiment once...
    The probability of achieving an unbroken series of 10 heads by tossing a coin is very small, practically impossible according to our maths lecturer.
    We threw 13 heads in a row and if you work out that
    probabilty, it's quite small.
    Yet, the probability of any alternative sequence of 13 is equal to it.
    However, if you ask what is the probability of 6 heads and 7 tails, you are summing together the probability of all the different sequences that give
    rise to 6 heads and  7 tails.

    The moral of the story is..

    The probability of a B or C landing "next" is the probability
    of a B or C landing on "any" throw for this case.
    This is 2/3.

    The probability of B landing after A is equal to the probabilty of A landing after A,
    which equals the probability of C landing after A, which equals the probability of B after any of A, B, C etc,
    which is 1/3.

    If A keeps occuring, B and C have "increased expectations of occuring in our minds".
    According to quantum physics, this may bias the outcome !!
    However, if there is never any bias, the probabilities never change.
    This of course is saying that the outcome of the next throw is completely random.
    There is a tiny probability that A will keep occuring for our lifetime.

    However, I feel that what you are really asking here is....
    Is not the probability of a sequence containing a B or C much greater than
    AAAAAAAAAAAAA ?
    and is not the probability of a sequence with a B or C even greater still than
    AAAAAAAAAAAAAAAAAAAA ?

    Absolutely!
    Last edited by Archie Meade; December 25th 2009 at 02:01 PM.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Hi\ Sharonk868,

    AceHero\ posted\ a\ good\ question.\

    The\ probability\ of\ AAB\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}

    The\ probability\ of\ AAC\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}

    The\ probability\ of\ AAA\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}


    However,\ the\ probability\ of\ a\ B\ or\ C\ landing\ next\

    at\ any\ stage\ is\ \frac{2}{3}
    Follow Math Help Forum on Facebook and Google+

  15. #15
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Archie Meade View Post
    Hi\ Sharonk868,

    AceHero\ posted\ a\ good\ question.\

    The\ probability\ of\ AAB\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}

    The\ probability\ of\ AAC\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}

    The\ probability\ of\ AAA\ is\ \frac{1}{3}\frac{1}{3}\frac{1}{3}=\frac{1}{27}


    However,\ the\ probability\ of\ a\ B\ or\ C\ landing\ next\

    at\ any\ stage\ is\ \frac{2}{3}
    You are wasting your breath, sharonk... is a spammer and no longer with us.

    CB
    Follow Math Help Forum on Facebook and Google+

Page 1 of 2 12 LastLast

Similar Math Help Forum Discussions

  1. Dice Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 7th 2011, 02:16 AM
  2. Dice Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 29th 2010, 06:20 PM
  3. dice probability
    Posted in the Statistics Forum
    Replies: 6
    Last Post: January 16th 2010, 10:58 AM
  4. Dice probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 10th 2009, 11:19 PM
  5. Dice Probability
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: August 8th 2009, 03:32 PM

Search Tags


/mathhelpforum @mathhelpforum