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Thread: Question for your Christmas Dinner Guests

  1. #41
    RS you will have to explain. You were one of those who said the odds are 1/11. Why won't you take this bet?

  2. #42
    Originally Posted by mickeycrimm View Post

    Red 2 Green 1
    Red 2 Green 2
    Red 2 Green 3
    Red 2 Green 4
    Red 2 Green 5
    Red 2 Green 6
    Green 2 Red 1
    Green 2 Red 3
    Green 2 Red 4
    Green 2 Red 5
    Green 2 Red 6
    .
    The above are the 11 combinations where at least one of the dice is showing a 2. The question was proposed "if a person looks under the cup and announces to someone else that at least one of the dice is showing a 2 what is the chance the other die is also a 2? Here's the dirty little secret to that question. It doesn't matter if someone peeks under the cup or rolls the dice out of the cup so both people are looking at both dice as they land. If at least one of the dice is a 2 then the chance of both die's being a 2 is 1 in 11. You simply can't get past the fact that there are 11 combinations that include at least one 2....and only one of them is 2-2.

    Now, I've been mulling over contacting the manufacturer of Bubble Craps. I think I have a new bet for them to include on their machines. The bet would be independent of whether the dice pass or 7 out.

    "On the next roll where at least one of the dice is a 2; when the other die is a 2 pays 10 for 1."

    Per the average the house will take in 11 bets and pay out 10 bets per every 11 decisions. A house edge of 9.1%. That bet would fit right in with a lot of the other craps bets. AND ONE HELL OF A LOT OF PEOPLE WOULD FALL FOR IT!
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  3. #43
    No mickeycrimm. What I can't get past is that when one die lands on two there are only six possible numbers on the second die. That's what I can't get past.

  4. #44
    Yitgadal v’yitkadash. Alan-I thought this subject was dead and buried.

  5. #45
    DIE 1. DIE 2.
    1. 1.
    2.* 2.
    3. 3.
    4. 4.
    5. 5.
    6. 6.

    When Die 1 lands on a 2, there are six possible outcomes on Die 2.

    Not sure which die is showing a 2?

    Okay then. If Die 2 is showing a 2 there are six possible outcomes on Die 1.

    This had nothing to do with the ELEVEN combinations of dice showing a 2. Absolutely nothing.

    It's not a math problem. It's a common sense problem.

  6. #46
    Originally Posted by regnis View Post
    Yitgadal v’yitkadash. Alan-I thought this subject was dead and buried.
    It came up at a craps table, when there was a spinner. The shooter said "I only have a 1/6 chance of losing."

    LOL

  7. #47
    Originally Posted by Alan Mendelson View Post
    No mickeycrimm. What I can't get past is that when one die lands on two there are only six possible numbers on the second die. That's what I can't get past.
    You are not taking into account that the 2 can be on either die.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  8. #48
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    No mickeycrimm. What I can't get past is that when one die lands on two there are only six possible numbers on the second die. That's what I can't get past.
    You are not taking into account that the 2 can be on either die.
    It doesn't matter if there's a two on one die or both dice, or the red one or the green one. Read again what I wrote above. It goes like this:

    If you have two dice and there's a 2 on one of them there are six faces on the other die. It doesn't matter. There are only two dice. Your answer is always 1/6.

    BUT if you ask me how many dice combinations have a two the answer is 11. And then if you ask me how many of those combinations is 2-2 the answer is one. And if you ask me what are the chances of rolling 2-2 the answer is 1/36.

  9. #49
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    No mickeycrimm. What I can't get past is that when one die lands on two there are only six possible numbers on the second die. That's what I can't get past.
    You are not taking into account that the 2 can be on either die.
    Just ignore him. Problem: Solved.

  10. #50
    Originally Posted by RS__ View Post
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    No mickeycrimm. What I can't get past is that when one die lands on two there are only six possible numbers on the second die. That's what I can't get past.
    You are not taking into account that the 2 can be on either die.
    Just ignore him. Problem: Solved.
    AMEN BROTHER!!
    Take off that stupid mask you big baby.

  11. #51
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    This is what I don't understand. And I'm not alone. But explain this: if I can see which die is a 2 the answer is 1/6. But if I am told one die is a 2 but don't see it myself the answer is 1/11?????
    If you see both dice but can't distinguish between the two the answer is 1 in 11. If you are rolling two white dice out of a cup do you know exactly which one the 2 is on? It's not good enough to say the die on the left is on a 2 or the die on the right is on a 2. If the dice are color coded it's easy. There are 11 combinations where at least one of the dice is showing a two. If the red die is on two then this is what is possible:

    Red 2 Green 1
    Red 2 Green 2
    Red 2 Green 3
    Red 2 Green 4
    Red 2 Green 5
    Red 2 Green 6

    These are the combinations that are not possible when the red die is on a 2:

    Green 2 Red 1
    Green 2 Red 3
    Green 2 Red 4
    Green 2 Red 5
    Green 2 Red 6

    It's being able to eliminate these 5 combinations that gives the answer 1 in 6. If you don't have enough information to eliminate them then the answer is 1 in 11.
    Using mickey's colour scheme...

    Alan you maintain the answer is 1/6 to this, the original 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?

    You seem to like to change the wording of the original question, so please look at how I've changed it here:

    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, "The green die is a 2."
    What is the probability that both dice are showing a 2?


    The answer to this is 1/6. Do you see why? Do you think there is no difference between the way both problems are posed?
    Last edited by a2a3dseddie; 12-27-2017 at 03:53 PM.

  12. #52
    There are only two dice. If one is already a two the other die has a 1/6 chance of also being a two. I don't care what color they are because there are only two dice.

    In other words they are interchangeable.

    What amazes me is how you guys come up with 1/11 when using real, physical dice?

    When this came up at the craps table NO ONE came up with a 1/11 answer when I repeated the original question. Maybe it's because the eight people there were just stupid dealers and players and a boxman. What do we know about math? We just look at two dice and count pips.
    Last edited by Alan Mendelson; 12-27-2017 at 06:12 PM.

  13. #53
    Question: if you are the PEEKER how do you answer this question? (Remember you are the PEEKER.)

    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?

    Remember you are the PEEKER.

    Do you say to yourself "I know the answer is 1/6" or do you say to yourself "the answer is 1/11"?

    Remember you are the PEEKER.

    Next. If you are the peeker and you say the answer is 1/6 what will you say to your friend when he says 1/11?

  14. #54
    Originally Posted by Alan Mendelson View Post
    Originally Posted by regnis View Post
    Yitgadal v’yitkadash. Alan-I thought this subject was dead and buried.
    It came up at a craps table, when there was a spinner. The shooter said "I only have a 1/6 chance of losing." LOL
    If one die is still spinning then in effect you have only rolled one die.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  15. #55
    Alan, if it doesn't matter which die it is, and it's always 1 in 6 that the other die will be a 2, then adding them together would be 12 combinations. I've already listed the first 11 combinations. Can you tell us what the 12th combination is?
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  16. #56
    Originally Posted by mickeycrimm View Post
    Alan, if it doesn't matter which die it is, and it's always 1 in 6 that the other die will be a 2, then adding them together would be 12 combinations. I've already listed the first 11 combinations. Can you tell us what the 12th combination is?
    Wow is your math bad. If you already have a 2 on one die you can't count that die as having six possible faces: you have it as a TWO. You can't count the same die twice.

    Now the second die has six possible faces, one of which is a two.

    Are you starting to understand that charts of possible combinations are only that-- charts of combinations? But when you use real, physical dice the chart of combinations no longer can apply.

  17. #57
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    Originally Posted by regnis View Post
    Yitgadal v’yitkadash. Alan-I thought this subject was dead and buried.
    It came up at a craps table, when there was a spinner. The shooter said "I only have a 1/6 chance of losing." LOL
    If one die is still spinning then in effect you have only rolled one die.
    And so it is with the two dice in the cup. The die known to be a two is like the die that has come to rest on the table. The unknown die is the spinner which has six sides and one of which is a two.

    Please don't tell me the issue is we don't know which die is the spinner BECAUSE IT DOES NOT MATTER.

  18. #58
    I'm going to ask this question again because NO ONE has responded:

    If the guy who peeks under the cup CORRECTLY knows that the answer is 1/6, how do you justify the "non peeker" saying the answer is 1/11 ?? Can there be two answers to the same question with the same information?

    By the way, even my critics have agreed that the peeker knows the correct answer is 1/6.

  19. #59
    Originally Posted by Alan Mendelson View Post
    I'm going to ask this question again because NO ONE has responded:

    If the guy who peeks under the cup CORRECTLY knows that the answer is 1/6, how do you justify the "non peeker" saying the answer is 1/11 ?? Can there be two answers to the same question with the same information?

    By the way, even my critics have agreed that the peeker knows the correct answer is 1/6.
    The peeker can only know that the answer is 1 in 6 if he knows exactly which die is on the 2.
    "More importantly, mickey thought 8-4 was two games over .500. Argued about it. C'mon, man. Nothing can top that for math expertise. If GWAE ever has you on again, you can be sure I'll be calling in with that gem.'Nuff said." REDIETZ

  20. #60
    Originally Posted by mickeycrimm View Post
    Originally Posted by Alan Mendelson View Post
    I'm going to ask this question again because NO ONE has responded:

    If the guy who peeks under the cup CORRECTLY knows that the answer is 1/6, how do you justify the "non peeker" saying the answer is 1/11 ?? Can there be two answers to the same question with the same information?

    By the way, even my critics have agreed that the peeker knows the correct answer is 1/6.
    The peeker can only know that the answer is 1 in 6 if he knows exactly which die is on the 2.
    Because the damn peeker has MORE information than the non peeker has!! You're just too damn block headed to understand this.

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