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An educated guess (Posted on 2016-04-18) Difficulty: 3 of 5
You throw a perfect die (digits 1 to 6), adding up the results until the total score is over N.

What’s your estimate of the most likely final sum?

Please write down your guess prior to analytical evaluation or simulation.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts preliminary simulation | Comment 2 of 7 |
A simulation shows that as n gets larger, the expected total seems to approach something like n + 2+2/3, after having reached a low of about n+2.5.

1 4.0717
2 4.7447
3 5.5517
4 6.4966
5 7.5902
6 8.8285
7 9.7051
8 10.6587
9 11.6438
10 12.6341

10 12.6727
20 22.6734
30 32.6407
40 42.6718
50 52.667
60 62.6828
70 72.6808
80 82.6777
90 92.694
100 102.6474


DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 tr0 = 10000
 
 For n = 1 To 10
  tosses = 0: overtot = 0
  For tr = 1 To tr0
    tot = 0
    Do
      tot = tot + Int(6 * Rnd(1) + 1)
    Loop Until tot > n
    overtot = overtot + tot
  Next tr
  avrg = overtot / tr0
  Text1.Text = Text1.Text & n & Str(avrg) & crlf
 Next n
 
  Text1.Text = Text1.Text & crlf
 
 For n = 10 To 100 Step 10
  tosses = 0: overtot = 0
  For tr = 1 To tr0
    tot = 0
    Do
      tot = tot + Int(6 * Rnd(1) + 1)
    Loop Until tot > n
    overtot = overtot + tot
  Next tr
  avrg = overtot / tr0
  Text1.Text = Text1.Text & n & Str(avrg) & crlf
 Next n
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2016-04-18 09:01:29
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