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Average number of rolls to roll 66

Posted By: Jason Lee
Date: Friday, 9 September 2011, at 12:39 a.m.

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

UBK: Here is another way.

Consider what happens on the first roll. If the event occurs then you are done after one trial. If it does not then you have used up one trial and then it is like starting over again. So if E is the expected number of tosses needed and p is the probability of success we have that

E = (p)(1) + (1-p) (1+E)

Solving for E gives E = 1/p.

Consider the following game: A fair coin is flipped until a tail is flipped.

• If tails appears for the first time on the first flip, you pay me $1.
• If tails appears for the first time on the second flip, I pay you $2.
• If tails appears for the first time on the third flip, you pay me $4.
• If tails appears for the first time on the fourth flip, I pay you $8.
• ...

How much should I pay to play this game?

JLee

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.