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A Simple Wheel Generator Source.Prev TopicNext Topic
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That is really neat and user friendly too!
Thanks a bunch!
-
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineWe're reposting the WheelGenerator Class with some comments only.
We removed the update fluff to clear the clutter.
So if you copy and paste this code, you will see very limited updating when running the program.
If there is an error, just review the previous post and compare, or just copy and paste back the previous posted code.
We are working on explaining the logic behind the code.
WheelGenerator.vb
_____________________________________________________
Public Class WheelGenerator
'Class for creating a conduit between this descendant thread and the progenitor thread.
Public Class StatusUpdate
Public ProgressPercentagePer1000 As Integer
Public ProgressInformation As String
Public WheelInformation As String
End Class
'WheelGenerator Class Variables and Constant Definitions
'N - Wheel Pool size
'R - Draw size
'X - Quantity of Draw Numbers Matching Pool Numbers
'Y - Minimum Winning Numbers in a Play Line
'IncludeIndexNumbers - Setting that Adds an Index Number to the Play Lines
'IndexMax - Maximum Allowed Combinations that can be stored
'Numbers() - Place to store Combinations as bits within a byte array (set of bytes).
Public N, R, X, Y As Integer
Public IncludeIndexNumbers As Boolean
Const IndexMax As Integer = 13983816
Private Numbers(IndexMax, 12) As Byte
Public Sub GenerateWheel(ByVal worker As System.ComponentModel.BackgroundWorker, ByVal e As System.ComponentModel.DoWorkEventArgs)
'Variable Definitions
'T - Total combinations of N Pool numbers taken R Draw Size at a time.
'Z - Total matching combinations of N Pool numbers taken X Matching Size at a time.
'Zs - Random selection point in Z total matching combinations.
'Zremain - Remaining total Z matching combinations after a Zs random selection.
'Pos - A position within a set of combinations, usually incremented by 1 to the next combination.
'Count - A tracking counter for matching conditions between two combinations.
'Index - A play line tracking variable, usually incremented by 1.
'MissingNumbers - Missing pool numbers not selected by the Building Win Condition algorithm.
'MissingSelection - A randomly selected combination that has some or all the missing pool numbers.
'MissingIndex - A position within the Z set of matching combinations used to find a randomly selected MissingSelection, usually incremented by 1.
'RandNumReamin - A random selection point of the remaining set of possible Z total matching combinations or missing pool number combinations.
'NumRemain - A string set of remaing numbers not randomly selected.
'TempWheel - A string for holding wheel information and the generated wheel itself.
'UpdateStatus - A conduit variable for relaying wheel generator information back to the progenitor thread.
Dim T, Z, Zs, Zremain, Pos, Count, Index, MissingNumbers, MissingSelection, MissingIndex, RandNumRemain As Integer
Dim NumRemain As String = ""
Dim tempWheel As String = ""
Dim UpdateStatus As New StatusUpdate
T = Comb(N, R)
Z = Comb(N, X)
Randomize(Microsoft.VisualBasic.Timer)
tempWheel = "Condition" & vbCrLf
If X > 1 Then
tempWheel &= "- If " & X.ToString & " Drawn Numbers are in the Set of " & N.ToString & " Numbers," & vbCrLf
Else
tempWheel &= "- If " & X.ToString & " Drawn Number is in the Set of " & N.ToString & " Numbers," & vbCrLf
End If
If Y > 1 Then
tempWheel &= "- Then at least 1 Combination has " & Y.ToString & " Winning Numbers." & vbCrLf
Else
tempWheel &= "- Then at least 1 Combination has " & Y.ToString & " Winning Number." & vbCrLf
End If
tempWheel &= "____________________________________________" & vbCrLf
UpdateStatus.ProgressInformation = "Clearing Combination Set..."
worker.ReportProgress(0, UpdateStatus)
'Clears the place where the numbers are stored for the total possible combinations
'for the Matching condition of N taken X at a time.
For a = 0 To Z
For b As Integer = 0 To 12
Numbers(a, b) = &H0
Next
Next
'Is the Win Condition Y less than the Draw Size?
'If it is, run the Match / Win algorithm.
'If it is not, generate all the possible combinations for N pool numbers taken R at a time.
If Y < R Then
UpdateStatus.ProgressInformation = "Building Match Condition..."
worker.ReportProgress(0, UpdateStatus)
'Store all the possible Matching combinations of N pool numbers taken X matching draw numbers at a time.
For a As Integer = 1 To Z
WriteCombination(a, Index2Combin(N, X, a), WriteCombin.Add)
Next
UpdateStatus.ProgressInformation = "Building Win Condition..."
worker.ReportProgress(0, UpdateStatus)
'Algorithm for randomly selecting the matching combination.
'Mark it as an inclusion by setting a bit in the Numbers() byte array, Byte = 12, Bit = 4.
'Eliminate by exclusion the other matching combinations not selected that have
' at least the same quantity of Y matching pool numbers or better and set the exclusion bit in the Numbers() array, Byte = 12, Bit = 5.
'Complete the matching combination by randomly selecting any other pool numbers not selected to fill out the combiantion
' to the Draw size R.
'And again Eliminate by exclusion the other matching combinations not selected that have
' at least the same quantity of Y matching pool numbers or better and set the exclusion bit in the Numbers() array, Byte = 12, Bit = 5.
'Check to see if the Alogrithm missed any pool numbers.
'Randomly add any combinations that may have been eliminated and also have the missing pool numbers to complete the wheel.
'Toggle the inclusion and exclusion bits.
'Fill the selected missing matching combination to complete the combination out to the R draw size and add to the wheel.
Zremain = Z
Index = 0
Do
'Random matching combination selection.
Zs = RandomLowerUpper(1, Zremain)
Pos = 0
Count = 0
Do
Pos += 1
If (CSTEBit(BitState.ExmBit, Numbers(Pos, 12), 4) = &H0) And (CSTEBit(BitState.ExmBit, Numbers(Pos, 12), 5) = &H0) Then
Count += 1
End If
Loop Until Count = Zs
Numbers(Pos, 12) = CSTEBit(BitState.SetBit, Numbers(Pos, 12), 4)
Zremain -= 1
'Mark for inclusion.
For a = 1 To Z
If (CSTEBit(BitState.ExmBit, Numbers(a, 12), 4) = &H0) And (CSTEBit(BitState.ExmBit, Numbers(a, 12), 5) = &H0) Then
If CompareCombination(a, ReadCombination(Pos, N, ReadCombin.GetStoredNumbers)) >= Y Then
Numbers(a, 12) = CSTEBit(BitState.SetBit, Numbers(a, 12), 5)
Zremain -= 1
End If
End If
Next
'Mark for exclusion.
If X < R Then
For a = X + 1 To R
NumRemain = ReadCombination(Pos, N, ReadCombin.GetNotStoredNumbers)
RandNumRemain = RandomLowerUpper(1, Int(Len(NumRemain) / 3))
WriteCombination(Pos, ReadCombination(Pos, N, ReadCombin.GetStoredNumbers) & Mid(NumRemain, 3 * RandNumRemain - 2, 3), WriteCombin.Add)
Next
For a = 1 To Z
If (CSTEBit(BitState.ExmBit, Numbers(a, 12), 4) = &H0) And (CSTEBit(BitState.ExmBit, Numbers(a, 12), 5) = &H0) Then
If CompareCombination(a, ReadCombination(Pos, N, ReadCombin.GetStoredNumbers)) >= Y Then
Numbers(a, 12) = CSTEBit(BitState.SetBit, Numbers(a, 12), 5)
Zremain -= 1
End If
End If
Next
End If
'Increment Index, Store selected win combination, Add to wheel information.
Index += 1
WriteCombination(0, ReadCombination(Pos, N, ReadCombin.GetStoredNumbers), WriteCombin.Add)
If IncludeIndexNumbers Then
tempWheel &= Format(Index, "00000000 - ") & ReadCombination(Pos, N, ReadCombin.GetStoredNumbers) & vbCrLf
Else
tempWheel &= ReadCombination(Pos, N, ReadCombin.GetStoredNumbers) & vbCrLf
End If
Loop Until Zremain = 0
'Check for missing pool numbers.
If Len(ReadCombination(0, N, ReadCombin.GetNotStoredNumbers)) / 3 <> 0 Then
'Establish how many missing pool numbers and count how many possible eliminated matching combinations there are.
MissingNumbers = Len(ReadCombination(0, N, ReadCombin.GetNotStoredNumbers)) / 3
Count = 0
For a = 1 To Z
If (CompareCombination(a, ReadCombination(0, N, ReadCombin.GetNotStoredNumbers)) = MissingNumbers) And (CSTEBit(BitState.ExmBit, Numbers(a, 12), 5) = &H1) Then
Count += 1
End If
Next
'Randomly select one of the eliminated matching combinations.
MissingSelection = RandomLowerUpper(1, Count)
Count = 0
MissingIndex = 0
Do
MissingIndex += 1
If (CompareCombination(MissingIndex, ReadCombination(0, N, ReadCombin.GetNotStoredNumbers)) = MissingNumbers) And (CSTEBit(BitState.ExmBit, Numbers(MissingIndex, 12), 5) = &H1) Then
Count += 1
End If
Loop Until Count = MissingSelection
'Toggle the inclusion and exclusion bits.
Numbers(MissingIndex, 12) = CSTEBit(BitState.TogBit, Numbers(MissingIndex, 12), 4)
Numbers(MissingIndex, 12) = CSTEBit(BitState.TogBit, Numbers(MissingIndex, 12), 5)
'Fill out the selected mathcing combination to the R draw size and store the combination.
If X < R Then
For a = X + 1 To R
NumRemain = ReadCombination(MissingIndex, N, ReadCombin.GetNotStoredNumbers)
RandNumRemain = RandomLowerUpper(1, Int(Len(NumRemain) / 3))
WriteCombination(MissingIndex, ReadCombination(MissingIndex, N, ReadCombin.GetStoredNumbers) & Mid(NumRemain, 3 * RandNumRemain - 2, 3), WriteCombin.Add)
Next
End If
'Increment the Index and add the the wheel information.
Index += 1
If IncludeIndexNumbers Then
tempWheel &= Format(Index, "00000000 - ") & ReadCombination(MissingIndex, N, ReadCombin.GetStoredNumbers) & vbCrLf
Else
tempWheel &= ReadCombination(MissingIndex, N, ReadCombin.GetStoredNumbers) & vbCrLf
End If
End If
Else
'Generate all the combinations for N pool numbers taken R draw at a time and add to the wheel information.
For a = 1 To T
If IncludeIndexNumbers Then
tempWheel &= Format(a, "00000000 - ") & Index2Combin(N, R, a) & vbCrLf
Else
tempWheel &= Index2Combin(N, R, a) & vbCrLf
End If
Next
Index = T
End If
'Complete the wheel information and send the update back through the conduit variable.
tempWheel &= "____________________________________________" & vbCrLf
If Index > 1 Then
UpdateStatus.WheelInformation = "Wheel" & vbCrLf & _
"- Pick " & R.ToString & vbCrLf & _
"- " & N.ToString & " Numbers" & vbCrLf & _
"- " & Format(Index, "##,###,###") & " Combinations" & vbCrLf & _
"- " & Format((Index / T), "##0.######% ") & "Coverage of " & Format(T, "##,###,### ") & "Combinations" & vbCrLf & vbCrLf & tempWheel
Else
UpdateStatus.WheelInformation = "Wheel" & vbCrLf & _
"- Pick " & R.ToString & vbCrLf & _
"- " & N.ToString & " Numbers" & vbCrLf & _
"- " & Format(Index, "##,###,###") & " Combination" & vbCrLf & _
"- " & Format((Index / T), "##0.######% ") & "Coverage of " & Format(T, "##,###,### ") & "Combinations" & vbCrLf & vbCrLf & tempWheel
End If
worker.ReportProgress(0, UpdateStatus)
End Sub
Enum WriteCombin
Add = True
Remove = False
End Enum
Enum ReadCombin
GetStoredNumbers = True
GetNotStoredNumbers = False
End Enum
Enum BitState As Byte
ClrBit = 0
SetBit = 1
TogBit = 2
ExmBit = 3
End Enum
Function Modulus(ByVal a As Double, ByVal b As Double) As Long
Modulus = a - b * Int(a / b)
End Function
Function RandomLowerUpper(ByVal L As Long, ByVal U As Long) As Long
RandomLowerUpper = Int(Rnd() * (U - (L - 1))) + L
End Function
Function Fact(ByVal N As Integer) As Double
If (N <= 1) Then
Fact = 1
Else
Fact = N * Fact(N - 1)
End If
End Function
Function Perm(ByVal N As Integer, ByVal R As Integer) As Double
Dim a As Integer
Dim b As Double
b = 1
If (N < R) Then
Perm = 0
Else
For a = (N - (R - 1)) To N
b = b * a
Next a
Perm = b
End If
End Function
Function Comb(ByVal N As Integer, ByVal R As Integer) As Long
If (N < R) Then
Comb = 0
Else
Comb = Perm(N, R) / Fact(R)
End If
End Function
Function Cdist(ByVal N As Integer, ByVal R As Integer, ByVal C As Integer, ByVal Z As Integer) As Long
If ((Z < C) Or (Z > (N - (R - C))) Or (Z > N) Or (C > R) Or (N < 1) Or (R < 1) Or (C < 1) Or (Z < 1)) Then
Cdist = 0
Else
Cdist = Comb((Z - 1), (C - 1)) * Comb((N - Z), (R - C))
End If
End Function
Function fColumnSum(ByVal N As Integer, ByVal R As Integer, ByVal Z As Integer) As Long
Dim a As Integer
Dim ColumnSum As Double
If (Z < 1) Then
fColumnSum = 0
ElseIf ((Z >= 1) And (Z < (N - (R - 1)))) Then
ColumnSum = 0
For a = 1 To Z
ColumnSum = ColumnSum + Cdist(N, R, 1, a)
Next a
fColumnSum = ColumnSum
ElseIf (Z >= (N - (R - 1))) Then
fColumnSum = Comb(N, R)
End If
End Function
Function Index2Combin(ByVal N As Integer, ByVal R As Integer, ByVal I As Long) As String
Dim a, Combination(), Z As Integer
Dim J As Double
ReDim Combination(R)
Dim tmpString As String
Dim NumberFound As Boolean
tmpString = ""
J = I
J = J - 1
Z = 0
For a = 1 To R
If ((I >= 1) And (I <= Comb(N, R))) Then
If (a = 1) Then
Combination(a) = 1
Else
Combination(a) = Combination(a - 1) + 1
End If
NumberFound = False
Do
Select Case (J - fColumnSum((N - Z), (R - (a - 1)), (Combination(a) - (Z + 1))))
Case Is < 0
Combination(a) = Combination(a) - 1
NumberFound = True
Case Is = 0
NumberFound = True
Case Is > 0
Combination(a) = Combination(a) + 1
End Select
Loop Until NumberFound
J = J - fColumnSum((N - Z), (R - (a - 1)), (Combination(a) - (Z + 1)))
Z = Combination(a)
Else
Combination(a) = 0
End If
tmpString = tmpString & Format(Combination(a), "00 ")
Next a
Index2Combin = tmpString
End Function
Function Combin2Index(ByVal N As Integer, ByVal R As Integer, ByVal Combination As String) As Long
Dim a As Integer
Dim fSum As Double
fSum = 1
For a = 1 To R
If (a = 1) Then
fSum = fSum + fColumnSum(N, R, (Val(Mid(Combination, 3 * a - 2, 2)) - 1))
Else
fSum = fSum + fColumnSum((N - Val(Mid(Combination, 3 * (a - 1) - 2, 2))), (R - (a - 1)), (Val(Mid(Combination, 3 * a - 2, 2)) - (Val(Mid(Combination, 3 * (a - 1) - 2, 2)) + 1)))
End If
Next a
Combin2Index = fSum
End Function
Sub WriteCombination(ByVal I As Integer, ByVal Combination As String, ByVal Add As Boolean)
Dim bytPos As Integer
Dim bitPos As Byte
Dim R As Integer
Dim Z As Integer
R = Int(Len(Combination) / 3)
If R <> 0 Then
For a As Integer = 1 To R
Z = CInt(Val(Mid(Combination, 3 * a - 2, 2)))
bytPos = CInt(IntPart(CDbl(Z) / 8))
bitPos = CByte(8 * DecPart(CDbl(Z) / 8))
If Add Then
Numbers(I, bytPos) = CSTEBit(BitState.SetBit, Numbers(I, bytPos), bitPos)
Else
Numbers(I, bytPos) = CSTEBit(BitState.ClrBit, Numbers(I, bytPos), bitPos)
End If
Next
End If
End Sub
Function ReadCombination(ByVal I As Integer, ByVal N As Integer, ByVal GetStoredValues As Boolean) As String
Dim tmpText As String = ""
Dim bytPos As Integer
Dim bitPos As Byte
For a As Byte = 1 To N
bytPos = CInt(IntPart(CDbl(a) / 8))
bitPos = CByte(8 * DecPart(CDbl(a) / 8))
If GetStoredValues Then
If CSTEBit(BitState.ExmBit, Numbers(I, bytPos), bitPos) = 1 Then
tmpText &= Format(a, "00 ")
End If
Else
If CSTEBit(BitState.ExmBit, Numbers(I, bytPos), bitPos) = 0 Then
tmpText &= Format(a, "00 ")
End If
End If
Next
ReadCombination = tmpText
End Function
Function CompareCombination(ByVal I As Integer, ByVal Combination As String) As Integer
Dim T As Integer = 0
Dim bytPos As Integer
Dim bitPos As Byte
For a As Integer = 1 To Int(Len(Combination) / 3)
bytPos = CInt(IntPart(CDbl(Val(Mid(Combination, 3 * a - 2, 2))) / 8))
bitPos = CByte(8 * DecPart(CDbl(Val(Mid(Combination, 3 * a - 2, 2))) / 8))
T += CSTEBit(BitState.ExmBit, Numbers(I, bytPos), bitPos)
Next
CompareCombination = T
End Function
Public Function CSTEBit(ByVal CSTE As Byte, ByVal Byt As Byte, ByVal Bit As Byte) As Byte
If Bit < 8 Then
Dim Mask As Byte = 2 ^ Bit
Select Case CSTE
Case BitState.ClrBit
Return Byt And Not Mask
Case BitState.SetBit
Return Byt Or Mask
Case BitState.TogBit
Return Byt Xor Mask
Case BitState.ExmBit
If ((Byt And Mask) > 0) Then
Return 1
Else
Return 0
End If
Case Else
Return Byt
End Select
Else
Return Byt
End If
End Function
Function IntPart(ByVal n As Double) As Integer
Select Case Math.Sign(n)
Case -1
Return Math.Ceiling(n)
Case 0
Return 0
Case 1
Return Math.Floor(n)
End Select
End Function
Function DecPart(ByVal n As Double) As Double
Select Case Math.Sign(n)
Case -1
Return (n - Math.Ceiling(n))
Case 0
Return 0
Case 1
Return (n - Math.Floor(n))
End Select
End Function
End Class
_____________________________________________________
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineOk, we're going handle this in a few different posts, so, try to hold on to any questions till complete.
We will work a small example of a wheel generation using the settings of: Set = 9, Pick = 5, Match = 4, Win = 3.
If you decide to use these setting on your own copy of the wheel generator, keep in mind your resultant wheel may be different than the example we are posting here.
This is due to the random nature of the algorithm process.
Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThere are three things we need to complete the algorithm process.
1 - Track the pool numbers selected.
2 - Track the wheel combinations generated.
3 - Create the total combinations that are possible for the matching condition.
From those three things we can start selection of matching combinations and make a playable combo for our wheel.
The process works well, but it has a interesting problem that may occur and is handled by checking for any missing pool numbers not selected.
Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineBelow is the basic setup.
As we go along, when we make selections and mark what we selected, we will Gray out what was selected.
Pool Numbers 01 02 03 04 05 06 07 08 09 Wheel Random Selection from
Matching Condition CombinationsMatching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineNext, Randomly select a Matching Condition Combination and mark the combination.
Then, mark the Pool Numbers that are the same as the Random Selection.
Pool Numbers 01 02 03 04 05 06 07 08 09 Wheel Random Selection from
Matching Condition Combinations05 07 08 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineNow, go through the Matching Condition Combinations and mark any combinations that have at least 3 or more of our Randomly Selected combination numbers.
The 3 or more is the Winning Condtition we are looking for as well.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel
Random Selection from
Matching Condition Combinations05 07 08 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineNext, Complete the randomly selected matching combo by randomly selecting any pool number not already selected.
Mark the randomly selected pool number.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel
Random Selection from
Matching Condition Combinations05 06 07 08 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineBefore we add the completed combo to the wheel, go through the Matching Condition Combinations and mark those combos that have not been makred with at least 3 or more numbers from our completed randomly selected combo.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel
Random Selection from
Matching Condition Combinations05 06 07 08 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineNow, add the combo to the Wheel.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel 05 06 07 08 09
Random Selection from
Matching Condition CombinationsMatching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineNow, repeat the process.
For simplicity, we will do eveything all at once.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel 05 06 07 08 09
01 03 04 06 09
Random Selection from
Matching Condition Combinations01 03 04 06 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineIn this repeated process you'll notice we have covered all the Pool Numbers, but we have not selected all the Matching Condition Combinations.
We must keep repeating the process until all of the Matching Condition Combinations have been either selected (included) or marked as covered by the initial random selection (excluded).
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel 05 06 07 08 09
01 03 04 06 09
02 03 04 08 09
Random Selection from
Matching Condition Combinations02 03 04 08 09 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineOne more after this.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel 05 06 07 08 09
01 03 04 06 09
02 03 04 08 09
01 02 06 07 08
Random Selection from
Matching Condition Combinations01 02 06 07 08 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineFinally, we have the Wheel.
Pool Numbers 01 02 03 04 05 06 07 08 09
Wheel 05 06 07 08 09
01 03 04 06 09
02 03 04 08 09
01 02 06 07 08
01 02 03 04 05
Random Selection from
Matching Condition Combinations01 02 03 04 05 Matching Condition Combinations 01 02 03 04 01 02 03 05 01 02 03 06 01 02 03 07 01 02 03 08 01 02 03 09 01 02 04 05 01 02 04 06 01 02 04 07 01 02 04 08 01 02 04 09 01 02 05 06 01 02 05 07 01 02 05 08 01 02 05 09 01 02 06 07 01 02 06 08 01 02 06 09 01 02 07 08 01 02 07 09 01 02 08 09 01 03 04 05 01 03 04 06 01 03 04 07 01 03 04 08 01 03 04 09 01 03 05 06 01 03 05 07 01 03 05 08 01 03 05 09 01 03 06 07 01 03 06 08 01 03 06 09 01 03 07 08 01 03 07 09 01 03 08 09 01 04 05 06 01 04 05 07 01 04 05 08 01 04 05 09 01 04 06 07 01 04 06 08 01 04 06 09 01 04 07 08 01 04 07 09 01 04 08 09 01 05 06 07 01 05 06 08 01 05 06 09 01 05 07 08 01 05 07 09 01 05 08 09 01 06 07 08 01 06 07 09 01 06 08 09 01 07 08 09 02 03 04 05 02 03 04 06 02 03 04 07 02 03 04 08 02 03 04 09 02 03 05 06 02 03 05 07 02 03 05 08 02 03 05 09 02 03 06 07 02 03 06 08 02 03 06 09 02 03 07 08 02 03 07 09 02 03 08 09 02 04 05 06 02 04 05 07 02 04 05 08 02 04 05 09 02 04 06 07 02 04 06 08 02 04 06 09 02 04 07 08 02 04 07 09 02 04 08 09 02 05 06 07 02 05 06 08 02 05 06 09 02 05 07 08 02 05 07 09 02 05 08 09 02 06 07 08 02 06 07 09 02 06 08 09 02 07 08 09 03 04 05 06 03 04 05 07 03 04 05 08 03 04 05 09 03 04 06 07 03 04 06 08 03 04 06 09 03 04 07 08 03 04 07 09 03 04 08 09 03 05 06 07 03 05 06 08 03 05 06 09 03 05 07 08 03 05 07 09 03 05 08 09 03 06 07 08 03 06 07 09 03 06 08 09 03 07 08 09 04 05 06 07 04 05 06 08 04 05 06 09 04 05 07 08 04 05 07 09 04 05 08 09 04 06 07 08 04 06 07 09 04 06 08 09 04 07 08 09 05 06 07 08 05 06 07 09 05 06 08 09 05 07 08 09 06 07 08 09 Continues...
The One Over None
I Know... -
Native American Eagle SunMN
United States
Member #21
December 7, 2001
4,811 Posts
OfflineThis is an actual Wheel that was built with the code.
Wheel
- Pick 5
- 9 Numbers
- 5 Combinations
- 3.968254% Coverage of 126 Combinations
Condition
- If 4 Drawn Numbers are in the Set of 9 Numbers,
- Then at least 1 Combination has 3 Winning Numbers.
____________________________________________
05 06 07 08 09
01 03 04 06 09
02 03 04 08 09
01 02 06 07 08
01 02 03 04 05
____________________________________________Continues...
The One Over None
I Know...