Page 1 of 18 1234511 ... LastLast
Results 1 to 20 of 342

Thread: Question for Math/Gambling/Craps Experts

  1. #1
    I got into a rather heated exchange over on the Wizard's forum on this question:

    You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

    What is the probability that both dice are showing a 2?


    My answer was 1/6 or one out of 6. The Wizard had a different answer and so did just about everyone else.

    What's your answer?

  2. #2
    Alan: When I first looked at your question I also instinctively thought, "1-in-6 chance".

    After reviewing the thread you mentioned, however, I'm convinced it's really a 1/11 chance.

    They are right in that it all boils down to whether a specific die is selected or not.

    I won't argue the point with you, myself, as it appears Wizard's forum has already done that sort of work.

  3. #3
    Well, I think the answer of 1/11 is not correct because the question was not worded properly.

    Let me offer this and then tell me your answer:

    I throw two dice on a craps table. One die immediately comes to rest showing a 2, but the second die hits the wall and starts spinning like a top. While spinning you ask yourself, what are the chances it will settle showing another two?

    Is your answer still 1/11 or is it 1/6 ??

    Now, going back to the question on the Wizard's forum: we were also told that one of the two dice shows a 2. There are only two dice involved in this "puzzle." Do you still think the answer is 1/11 or do you also think it's 1/6 ? Does it matter which of the two dice already shows a 2 when there are only two dice to begin with?

  4. #4
    Originally Posted by Alan Mendelson View Post
    Let me offer this and then tell me your answer:

    I throw two dice on a craps table. One die immediately comes to rest showing a 2, but the second die hits the wall and starts spinning like a top. While spinning you ask yourself, what are the chances it will settle showing another two?

    Is your answer still 1/11 or is it 1/6 ??
    In the case of the craps table, the odds become 1/6 for you because you can see exactly which one of the dice has landed with a "2" with definite finality. When you cannot see either of the dice the odds become 1/11. It's exactly why your original problem with both dice hidden was presented that way. Actually seeing the dice and/or not seeing them makes all the difference.

    Analogy: If I am playing heads-up hold'em with pocket KK, my odds of winning the pot are much greater not seeing my opponent's hand than when I actually see his pocket AA.

    EDIT: I have a bad feeling I'm going to enter an argumentative quicksand with Alan if I continue, LOL.

    I do totally appreciate the deceptive nature of this problem, though!
    Last edited by Count Room; 04-16-2015 at 03:42 PM.

  5. #5
    You're not reading the question properly. You are told that at least one of the dice is a 2. That's the same thing as seeing the dice rolled on the table. It is not a lie that at least one of the dice is a two according to the original question.

    Are you reading the question? Do you see where it says Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

    Because the "partner" truthfully says at least one of the dice is a 2, it is the same thing as rolling two dice on a craps table with one die coming to rest as a 2 and the second die spinning.

    By the way, on the Wizard's forum there are now two others who understand that we are now talking about only one die -- the unseen die.

  6. #6
    Originally Posted by Alan Mendelson View Post

    Because the "partner" truthfully says at least one of the dice is a 2, it is the same thing as rolling two dice on a craps table with one die coming to rest as a 2 and the second die spinning....
    Alan: I respectfully submit to you that, no, the partner telling you that one of the dice is a "2" (even with ironclad truthfulness & integrity), is not the same thing as rolling two dice on a craps table with one die coming to rest on a 2 as the second one still spins....

    You have more information available to you at that moment on the craps table (because you can see which of the two dice is definitely a "2") than when both dice are hidden from you. For all practical purposes, only one die is "hidden" from you at the craps table (the one still spinning).

    I assure you I have read and understand everything about these two different settings you described. Again, we will have to respectfully agree to disagree.

    ...And, again, I fully appreciate how mind-blowingly deceptive this problem can be!

    There's not much more I can say. I hope Dan Druff can stop by soon and provide his input on the matter.

    EDIT: If it would help matters any, think of what that one poster said on Wizard's site: Picture the two dice having different colors (such as blue and yellow). You know whether it was the blue die or the yellow die having a "2" at the craps table, yet in the original scenario with your truthful partner you still don't know which color die has the "2".
    Last edited by Count Room; 04-16-2015 at 08:45 PM.

  7. #7
    There is new information that I just discovered and it appears that for the last several years that the information existed on the Wizard's site and no one else saw it. This info makes me wonder if the whole thing was a joke and the forum members fell for it.

    Here is the link to the thread:
    http://wizardofvegas.com/forum/quest...o-dice-puzzle/

    Click on the "spoiler tag" in the original post and read what is hidden in the "spoiler." It makes me wonder if he wrote the question as he did to poke fun at the whole forum.

    In the meantime, is it really more complicated than saying this:

    One die is a 2, what are the chances that another die is also a 2? Does it really matter if there are only two dice but you don't know which of the two dice is the one with the 2?

    Read the original post, the way the question is actually worded, and then click on the "spoiler". It might give you a different idea.

  8. #8
    I am amazed that this debate continues. As Alan continually points out, one die was already identified as having landed on 2. Therefore, there is only one remaining die in question which has a 1 in 6 chance of also being a 2.

    The question was not "what are the odds of rolling two 2's". The question was "....one die is a 2, what are the odds of the second die also being a 2...". Obviously--1 of 6.

    What if his friend had peeked and said both dies are on 2. What would you say the odds are that one of them is a 2? I hope you don't tell me 1 of 11.

  9. #9
    Thank you Regnis. It also amazes me that over on the Wizard's forum there is such a lack of reading comprehension. Clearly the question makes it known that at least one die has a 2. It says that in the question, yet they ignore it. Even the Wizard ignored it. What is their problem?

    However there is a glimmer of hope. Several others now have started to say the same thing: one die is known. The odds pertain to the second die. And since there are only two dice in the problem, it doesn't matter which is the second die. And believe it or not, those who believe in the 1/11 answer maintain that both dice must still be considered.

    It's crazy. There must be a language problem.

  10. #10
    Originally Posted by Alan Mendelson View Post
    Thank you Regnis. It also amazes me that over on the Wizard's forum there is such a lack of reading comprehension. Clearly the question makes it known that at least one die has a 2. It says that in the question, yet they ignore it. Even the Wizard ignored it. What is their problem?

    However there is a glimmer of hope. Several others now have started to say the same thing: one die is known. The odds pertain to the second die. And since there are only two dice in the problem, it doesn't matter which is the second die. And believe it or not, those who believe in the 1/11 answer maintain that both dice must still be considered.

    It's crazy. There must be a language problem.
    I'd suggest putting an end to this with an actual field trial. Could someone grab a friend or partner and have him/her quietly roll dice in the background until a "2" shows up? Just simply repeat the exercise over many trials and tabulate actual results to make sure of this?

    EDIT: Alan, take those guys' wagers on Wizard's forum. You're being offered 7:1 odds, apparently. If you are correct, it's a huge overlay for you.
    Last edited by Count Room; 04-17-2015 at 01:48 PM. Reason: EDIT: I still think it's an 11/1 shot for a second "2"

  11. #11
    I've asked them to take two dice. Set one showing a 2 and then using the other die to count the faces and figure it's 1/6 but that has been deemed wrong because it's a two dice problem not a one die problem. I'm stunned.

  12. #12
    Originally Posted by Alan Mendelson View Post
    I've asked them to take two dice. Set one showing a 2 and then using the other die to count the faces and figure it's 1/6 but that has been deemed wrong because it's a two dice problem not a one die problem. I'm stunned.
    That's not what needs to be done at all!

    Have them do exactly as the original problem says: Have a partner roll both dice in secret. When at least one "2" shows up, s/he truthfully tells you so. Then both dice are revealed. Checkmark "YES" when both are 2's, "NO" when there is only one 2.

    Tabulate a bunch of sample trials and see what happens..

  13. #13
    Count Room that is NOT what was asked in the original post. And this "test" that you suggest doesn't answer whether or not you just need to look at one dice and if the answer is 1/6. I am sorry, but what you are suggesting is more "static."

    Look, everyone who has ever played craps and sees one die comes to rest on a 6 knows that the second die must avoid a 7 so there won't be a 7-out. What every craps player has gone through is a simple application of what answers the question on the forum.

    Frankly, I think the math guys on the Wizard's forum just never played craps.

    By the way, in Rob Singer's new article he mentions it: http://alanbestbuys.com/id362.html

    To answer your suggestion, specifically, Count Room, why don't you do this:

    Take two dice. Set one as a 2. (Because we are told in the original post on the Wizard's site that at least one die is a 2.) Now pick up the second die and look at it. As you look at the second die ask yourself: what are the chances that when the second die is viewed it is also showing a 2? As you look at that second die count how many faces it has. Does it have 6 or does it have Eleven?

  14. #14
    (I am basically reposting how this thread began for placeholder purposes.)

    Alan, your original post in this thread said:

    "You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

    What is the probability that both dice are showing a 2?"


    You, Rob Singer, and regnis all say 1/6 (when done EXACTLY how it is described above in bold lettering).

    I say 1/11 (when done EXACTLY how it is described above in bold lettering).

    I do think it's time to have an exact simulation of what is written above so this matter can be laid to rest.

    We'll just be blowing hot air and never getting anywhere otherwise...forever in pointless disagreement when it can truly be resolved once and for all.

    Also, Frank Scoblete has been notably absent from this discussion...

  15. #15
    Count Room and others, I just posted this on the Wizard's forum:

    Do any of you play craps?

    When the dice are thrown on the table and the first one comes to rest on a 4 don't you say to yourself as you watch the other die "no 3, no 3"?

    Of course, you will say that is not relevant to the original post. But let's once again examine the question in the original post:

    Quote: Dween
    You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

    What is the probability that both dice are showing a 2?



    Now, you tell me why looking at just ONE DIE would not be the right way to answer THIS QUESTION ??

    Let me give you a hint:

    THE QUESTION: Dice in a cup are shaken and come to rest under a cup on the table.
    REAL CRAPS: Dice are thrown on a table and come to rest.

    THE QUESTION: The friend looks and says that at least one of the dice is a 2.
    REAL CRAPS: One of the dice is visible and shows a 2. But the second die is behind a stack of player's chips. The stickman calls out "well one of them is a two, Rob (a base dealer) you call it!"

    THE QUESTION: What is the probability that both dice are showing a 2?
    REAL CRAPS: The die behind the stack of chips has only six sides. The probability is that 1/6 is another 2, and 1/6 is a 5 for a 7-out.

    How do you get 1/11 ???

  16. #16
    Maybe it would be more obvious with two coins. Same process only this time your partner tells you if there is one head. Does that mean there a 1 in 2 chance that the other coin is a head? No. Look at the 4 possibilities .... HH, HT, TH and TT. Your partner will find one head in the first three cases. However, as you cam clearly see there's only a 1 in 3 chance that both coins are heads. You can lay out all the possibilities with the dice as well and see the same basic logic.

  17. #17
    Originally Posted by Alan Mendelson View Post

    Now, you tell me why looking at just ONE DIE would not be the right way to answer THIS QUESTION ??

    ....................

    How do you get 1/11 ???
    This has to be my final post for a while on this matter. I have other things I need to do!

    You have a GREEN die and a BLUE die at the craps table.

    You shoot the dice, the GREEN die stops at a "2" while the BLUE die keeps spinning.

    I agree from this standpoint your odds are 1/6 for the BLUE die to land on "2".

    `````````````````````````````````````````````````` ```````

    Now the craps dealer puts a screen in front of both the GREEN and BLUE dice.

    Another player rolls the dice behind the screen, and the stickman truthfully says, "At least one of these dice is a 2."

    The possibilities here with both dice unseen?

    GREEN BLUE
    2 1 <---MISS
    2 2 <---(((((((HIT)))))))))
    2 3 <---MISS
    2 4 <---MISS
    2 5 <---MISS
    2 6 <---MISS
    1 2 <---MISS
    3 2 <---MISS
    4 2 <---MISS
    5 2 <---MISS
    6 2 <---MISS

    10 Misses, 1 Hit......

    1/11

    Does this help at all? I gotta run for now..

  18. #18
    No Arc, it's not about coins which is why there is such a bunch of craziness over on the Wizard's forum. They are using the "coin problem" to address the dice question. That is a big mistake.

    Count Room you are also changing the original question when you talk about two dice unseen. In the original question the dice have been seen and at least one of them is a 2. Therefore it is the other die that answers the question.

    Look what was just posted on the Wizard's forum in response to my question about two dice thrown on a craps table (posted above):

    Quote: Dalex64

    On the craps table, if you throw two dice, one of them lands on a two where you can see it, and one of them lands out of sight - the odds of the one out of sight being a two is 1/11


    And my response:

    Are you serious?

    Hey buddy, there are only six sides on a die, and the six sides are numbered: 1, 2, 3, 4, 5, 6. That die that's out of sight can be ONE of those SIX numbers.

    Get real.


    They have really lost it.

  19. #19
    With the bad rolls and even worse results lately in craps, I think they have been using 11 sided dice. But if not, the odds of any number on 1 die is 1 of 6.

    If you rephrase the question to what are the odds of rolling 2-2, then the answer is not 1 of 6. But if 1 die is already a 2, there is a 1 in 6 chance the other will be a 2.

    Plain and simple--not that hard.

  20. #20
    Regnis it is so funny how they tried to deny that 1/6 is the proper answer. The most prominent was "but you don't know which dice is showing a 2." Like that is supposed to matter?

    I really think the whole thing stems from:

    a. they misunderstood the question
    b. they got mixed up with the coin problem and used the methodology for solving the coin problem to solve the dice problem

    But the Wizard also got it wrong. How? Did he also misread the question?

    By the way, it's not over. There are still those claiming that the answer is 1/11 for the craps table example with one die hidden.

    And to all the craps players out there who are not members of the forum: thank you for your emails of support. Please join the forum.

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •