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An old bar bet

Posted By: Timothy Chow
Date: Tuesday, 6 September 2011, at 2:28 p.m.

In Response To: Average number of rolls to roll 66 (falafel)

You might be thinking about the question that Ray Kershaw mentioned, which was, how many times do you need to roll the dice before you have a 50/50 chance of rolling 66? This is considerably less than 36. On the other hand, it's also more than 18—as Ray mentioned, it's between 24 and 25.

The subtle difference here is the source of an old bar bet. Some people can be tricked into thinking that because the probability of 66 is 1/36, they should have a 50/50 chance of seeing a 66 after 18 rolls. But you can bet them even odds that they won't roll a 66 even after, say, 21 attempts, and still come out ahead.

Messages In This Thread

• Average number of rolls to roll 66
  Raj Jansari -- Tuesday, 6 September 2011, at 9:20 a.m.
  • Average number of rolls to roll 66
    Stick -- Tuesday, 6 September 2011, at 9:25 a.m.
    • Average number of rolls to roll 66
      Raj Jansari -- Tuesday, 6 September 2011, at 9:27 a.m.
      • Average number of rolls to roll 66
        falafel -- Tuesday, 6 September 2011, at 9:33 a.m.
        • Average number of rolls to roll 66
          Art Grater -- Tuesday, 6 September 2011, at 9:57 a.m.
          • Average number of rolls to roll 66
            Raj Jansari -- Tuesday, 6 September 2011, at 10:01 a.m.
            • Average number of rolls to roll 66
              Bob Koca -- Tuesday, 6 September 2011, at 11:06 a.m.
              • No hand waving - Bob gave proof
                Taper_Mike -- Tuesday, 6 September 2011, at 7:52 p.m.
              • Average number of rolls to roll 66
                Jason Lee -- Friday, 9 September 2011, at 12:39 a.m.
                • Average number of rolls to roll 66
                  Joe Russell -- Friday, 9 September 2011, at 2:31 p.m.
                  • Average number of rolls to roll 66
                    Jason Lee -- Saturday, 10 September 2011, at 12:57 a.m.
                    • Average number of rolls to roll 66
                      Bob Koca -- Saturday, 10 September 2011, at 3:02 a.m.
                      • Average number of rolls to roll 66
                        Casper van der Tak -- Saturday, 10 September 2011, at 7:51 a.m.
                    • Average number of rolls to roll 66
                      Joe Russell -- Saturday, 10 September 2011, at 4:33 a.m.
                • Average number of rolls to roll 66
                  Daniel Murphy -- Saturday, 10 September 2011, at 12:14 a.m.
            • Average number of rolls to roll 66
              Ray Kershaw -- Tuesday, 6 September 2011, at 12:44 p.m.
              • Average number of rolls to roll 66
                Raj Jansari -- Tuesday, 6 September 2011, at 1:06 p.m.
                • Average number of rolls to roll 66
                  Ray Kershaw -- Tuesday, 6 September 2011, at 1:37 p.m.
                  • Average number of rolls to roll 66
                    Raj Jansari -- Tuesday, 6 September 2011, at 2:02 p.m.
                  • Average number of rolls to roll 66
                    leobueno -- Tuesday, 6 September 2011, at 9:22 p.m.
                    • Average number of rolls to roll 66
                      Ray Kershaw -- Wednesday, 7 September 2011, at 9:15 a.m.
                      • How many rolls before you are better than 50% to... Ray gave the formula!
                        Taper_Mike -- Thursday, 8 September 2011, at 11:39 p.m.
          • Average number of rolls to roll 66
            Art Grater -- Tuesday, 6 September 2011, at 10:05 a.m.
        • An old bar bet
          Timothy Chow -- Tuesday, 6 September 2011, at 2:28 p.m.
    • Average number of rolls to roll 66
      John O'Hagan -- Tuesday, 6 September 2011, at 3:48 p.m.