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Average number of rolls to roll 66

Posted By: leobueno
Date: Tuesday, 6 September 2011, at 9:22 p.m.

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

Is the analysis that follows correct?

Instead of asking what the probability of rolling a 66 in one roll (P = 1/36), ask what is the probability of NOT rolling a 66 in one roll (p = 35/36 = 0.97222...)

Then, the probability of NOT rolling a 66 in 2 rolls is p*p.

The probability of NOT rolling a 66 in 3 rolls is p*p*p, and so on, so that the probability of NOT rolling a 66 after n rolls is p^n.

The probability of NOT rolling a 66 drops below 0.5 somewhere between the 24th and 25th rolls, so that must be the point at which we can expect to get a 66.

Here is the series of p^n, where n = number of rolls:

1 0.9722

2 0.9452

3 0.9190

4 0.8934

5 0.8686

6 0.8445

7 0.8210

8 0.7982

9 0.7761

10 0.7545

11 0.7335

12 0.7132

13 0.6933

14 0.6741

15 0.6554

16 0.6372

17 0.6195

18 0.6023

19 0.5855

20 0.5693

21 0.5534

22 0.5381

23 0.5231

24 0.5086

25 0.4945

26 0.4807

27 0.4674

28 0.4544

29 0.4418

30 0.4295

31 0.4176

32 0.4060

33 0.3947

34 0.3837

35 0.3731

36 0.3627

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.