Probability question: names in hats

[robvalue]

OK, interesting.

I have coded the problem.

I am getting the following results, over a series of 5000 games:

3 players: around 25%
4 players: around 14%
10 players: around 8%

This would tentatively place Aractus's solution as wrong, although I haven't looked through it properly yet.

The first two there line up with my calculations: 1/4 and 5/36 for 3 and 4 players respectively

Here is the code, in microsoft small basic:

---

done=0

While done=0


ok=0
While ok=0
 TextWindow.WriteLine("")
 TextWindow.WriteLine("Enter number of players (at least 3)")
 TextWindow.WriteLine("")
 players=TextWindow.ReadNumber()
 For i = 3 To 10
   If players = i Then
     ok=1
   EndIf
 EndFor
EndWhile

TextWindow.WriteLine("")
TextWindow.WriteLine("Enter index for number of times to run")
TextWindow.WriteLine("")
times=TextWindow.ReadNumber()

wins=0

For i = 1 To times
 left=players
 For j = 1 to players
   ticket[j] = j
 EndFor
 
 
 
 For j = 1 to players-1
   
   ok=0
   While ok=0
   
   b = left
   random()
   If ticket[a] <> j Then
     ok=1
   EndIf
   
   endwhile
   
   choice[j] = ticket[a]
   
   If a < left Then
     For k = a to left
     ticket[k] = ticket[k+1]
   EndFor
   
   EndIf
   
 left = left - 1
   
 EndFor
 
 choice[players]=ticket[1]
 
 If choice[players] = players then
 wins = wins + 1
endif

 
 EndFor
 
 
 TextWindow.Write("Wins ")
 TextWindow.WriteLine(wins)
 TextWindow.WriteLine("")
 TextWindow.Write("Win % ")
 TextWindow.WriteLine(Math.Round((100*wins / times)))
 TextWindow.WriteLine("")

endwhile


Sub random
 a = Math.GetRandomNumber(b)

EndSub

 
 

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