If I put nine pieces of paper, with a digit from 1-9 written on each one, into a hat, and pull 3 out without replacement, what is the likelihood that I will select three numbers that result in a winning tic-tac-toe?

 1 | 2 | 3 
---+---+---
 4 | 5 | 6 
---+---+---
 7 | 8 | 9 

The odds of winning are between .094 and .095 out of 1.0

Here is the Visual Basic program I used to swat this fly:

Imports System
Imports System.IO
Imports System.Text
Imports System.Runtime.InteropServices
Imports System.Math
Module Module1
    Sub Main()
        Randomize()
        Dim strgoagain As String
        Dim intwinning(8, 3) As Integer
        intwinning(0, 0) = 1
        intwinning(0, 1) = 2
        intwinning(0, 2) = 3
        intwinning(1, 0) = 4
        intwinning(1, 1) = 5
        intwinning(1, 2) = 6
        intwinning(2, 0) = 7
        intwinning(2, 1) = 8
        intwinning(2, 2) = 9
        intwinning(3, 0) = 1
        intwinning(3, 1) = 4
        intwinning(3, 2) = 7
        intwinning(4, 0) = 2
        intwinning(4, 1) = 5
        intwinning(4, 2) = 8
        intwinning(5, 0) = 3
        intwinning(5, 1) = 6
        intwinning(5, 2) = 9
        intwinning(6, 0) = 1
        intwinning(6, 1) = 5
        intwinning(6, 2) = 9
        intwinning(7, 0) = 3
        intwinning(7, 1) = 5
        intwinning(7, 2) = 7
        strgoagain = "?"
        While strgoagain <> "N"
            mainline(intwinning)
            Console.WriteLine("Again ? (Y/N)")
            strgoagain = UCase(Console.ReadLine())
        End While
    End Sub

    Sub mainline(ByRef intwinning)
        Dim dblwins As Double
        Dim dblloop As Double
        Dim dblgamessofar As Double
        Dim intcounter As Integer
        dblwins = 0
        dblgamessofar = 0
        dblloop = 0
        intcounter = 0
        While dblloop <= 0
            Console.WriteLine("How many times shall we play?")
            dblloop = Int(Console.ReadLine())
        End While
        For index1 As Double = 0 To dblloop
            playthegame(intwinning, dblwins, dblgamessofar)
            intcounter += 1
            If intcounter > 9999 Then
                intcounter = 0
                Console.WriteLine(Str(dblgamessofar) & _
                " games so far...")
                Console.WriteLine("Winning odds so far are " & _
                Str(dblwins / dblgamessofar))
            End If
        Next
        Console.WriteLine(" ")
        Console.WriteLine("Odds of winning are " & _
        Str(dblwins / dblloop))
    End Sub

    Sub playthegame(ByRef intwinning, ByRef dblwins, _
    ByRef dblgamessofar)
        Dim intwork1(9) As Integer
        Dim intgame(3) As Integer
        Dim intrandom1 As Integer
        Dim intrandom2 As Integer
        dblgamessofar += 1
        intwork1(0) = 1
        intwork1(1) = 2
        intwork1(2) = 3
        intwork1(3) = 4
        intwork1(4) = 5
        intwork1(5) = 6
        intwork1(6) = 7
        intwork1(7) = 8
        intwork1(8) = 9
        intrandom1 = 8
        For index1 As Integer = 0 To 2
            intrandom2 = Int((intrandom1 - 0 + 1) * Rnd()) + 0
            intrandom1 -= 1
            intgame(index1) = intwork1(intrandom2)
            intwork1(intrandom2) = 0
            If intrandom2 < 9 Then
                For index2 As Integer = intrandom2 To 8
                    intwork1(index2) = intwork1(index2 + 1)
                    intwork1(index2 + 1) = 0
                Next
            End If
        Next
        For index1 As Integer = 0 To 7
            If intwinning(index1, 0) = intgame(0) And _
                intwinning(index1, 1) = intgame(1) And _
                intwinning(index1, 2) = intgame(2) Then
                dblwins += 1
                Exit Sub
            End If
            If intwinning(index1, 0) = intgame(0) And _
                intwinning(index1, 1) = intgame(2) And _
                intwinning(index1, 2) = intgame(1) Then
                dblwins += 1
                Exit Sub
            End If
            If intwinning(index1, 0) = intgame(1) And _
                intwinning(index1, 1) = intgame(0) And _
                intwinning(index1, 2) = intgame(2) Then
                dblwins += 1
                Exit Sub
            End If
            If intwinning(index1, 0) = intgame(1) And _
                intwinning(index1, 1) = intgame(2) And _
                intwinning(index1, 2) = intgame(0) Then
                dblwins += 1
                Exit Sub
            End If
            If intwinning(index1, 0) = intgame(2) And _
                intwinning(index1, 1) = intgame(0) And _
                intwinning(index1, 2) = intgame(1) Then
                dblwins += 1
                Exit Sub
            End If
            If intwinning(index1, 0) = intgame(2) And _
                intwinning(index1, 1) = intgame(1) And _
                intwinning(index1, 2) = intgame(0) Then
                dblwins += 1
                Exit Sub
            End If
        Next
    End Sub
End Module

 

Posted by Penny on 2004-07-30 18:05:43