Powerball numbers statisticsPrev TopicNext Topic

• Tucker Black

  

  Colorado
  United States
  Member #173,294
  February 25, 2016
  1,134 Posts
  Offline
  Apr 24, 2025, 10:59 am

  ▲▼

  In this thread I will discuss a few statistics for Powerball drawing numbers -- not the past drawings, but the probability of various results for any future drawing.

  I am only dealing with the five white balls from 1 to 69, not the Powerball. The Powerball number is a different range, 1 to 26, and is drawn from a different ballset.

  There are 11,238,513 different ways to draw 5 numbers from 1 to 69 without replacement. I wrote a computer program to go through all those combinations to measure a few different things.

   

  Even/odd

  There are 35 odd numbers from 1 to 69 and 34 even numbers. The probability distribution for the number of drawn numbers that will be odd or even is as follows:

  odd	even	percentage
  0	5	2.48%
  1	4	14.44%
  2	3	31.68%
  3	2	32.67%
  4	1	15.84%
  5	0	2.89%

   

  As you can see, the least likely outcome is all even numbers at 2.48%. This is closely followed by all odd numbers at 2.89%, since there is one more odd number than even in the matrix.

  The most likely outcome is 3 odd numbers and 2 even, almost 1/3 of the time, closely followed by 3 even numbers and 2 odd.

   

  Range from lowest to highest

  The minimum range is 4 (e.g. 35,36,37,38,39) and the maximum range is 68 (e.g. 1, 11, 17, 43, 69). The average range is 46.6667.

   

  Spacing between numbers

  When the drawn numbers are written in ascending order (similar to how a QP is printed), let us define "spacing" as the difference between two adjacent numbers. For example, with 9, 11, 17, 45, 59, the spacings are 2, 6, 28 and 14.

  The average spacing between numbers is 11.6667.

   

  Smallest number

  The average smallest number is 11.6667. This is somewhat interesting in that it is exactly the same as the average spacing.

   

  Largest number

  The average largest number is 58.3333. Note that 69, the largest possible number, minus 58.3333 is the same as 11.6667 minus 1, the smallest possible number. This is not surprising since the numbers are uniformly distributed between 1 and 69.

   

  Average number

  The average number drawn is 35. This one should be obvious, since it is exactly halfway between 1 and 69.

   

  Summary

  If we start with the smallest average number and add the average spacing to it and continue to the fifth number, we get:

  11.6667

  23.3333

  34.9999

  46.6667

  58.3333

  Then round off each one to the nearest integer:

  12

  23

  35

  47

  58

   

  Three of these five numbers are odd and two are even, which is the most likely outcome for odd/even. It ends with the average largest number. It includes the average number of 35. The range is 46, which is 46.6667 rounded down to the nearest integer, because the rounding took the first number up to 12 and the last number down to 58. 

  This ticket, 12-23-35-47-58, is the most average result of picking 5 numbers from 1 to 69. It doesn't means it's a winning bet, but I found this interesting.

  When I have some more time, I will compare MegaMillions (new rules) with Powerball in a different thread.
• rcbbuckeye

  

  100

  Texas
  United States
  Member #55,887
  October 23, 2007
  22,271 Posts
  Offline
  Apr 24, 2025, 12:14 pm

  ▲▼
  In response to Tucker Black

  Quote: Originally posted by Tucker Black on Apr 24, 2025

  In this thread I will discuss a few statistics for Powerball drawing numbers -- not the past drawings, but the probability of various results for any future drawing.

  I am only dealing with the five white balls from 1 to 69, not the Powerball. The Powerball number is a different range, 1 to 26, and is drawn from a different ballset.

  There are 11,238,513 different ways to draw 5 numbers from 1 to 69 without replacement. I wrote a computer program to go through all those combinations to measure a few different things.

   

  Even/odd

  There are 35 odd numbers from 1 to 69 and 34 even numbers. The probability distribution for the number of drawn numbers that will be odd or even is as follows:

  odd	even	percentage
  0	5	2.48%
  1	4	14.44%
  2	3	31.68%
  3	2	32.67%
  4	1	15.84%
  5	0	2.89%

   

  As you can see, the least likely outcome is all even numbers at 2.48%. This is closely followed by all odd numbers at 2.89%, since there is one more odd number than even in the matrix.

  The most likely outcome is 3 odd numbers and 2 even, almost 1/3 of the time, closely followed by 3 even numbers and 2 odd.

   

  Range from lowest to highest

  The minimum range is 4 (e.g. 35,36,37,38,39) and the maximum range is 68 (e.g. 1, 11, 17, 43, 69). The average range is 46.6667.

   

  Spacing between numbers

  When the drawn numbers are written in ascending order (similar to how a QP is printed), let us define "spacing" as the difference between two adjacent numbers. For example, with 9, 11, 17, 45, 59, the spacings are 2, 6, 28 and 14.

  The average spacing between numbers is 11.6667.

   

  Smallest number

  The average smallest number is 11.6667. This is somewhat interesting in that it is exactly the same as the average spacing.

   

  Largest number

  The average largest number is 58.3333. Note that 69, the largest possible number, minus 58.3333 is the same as 11.6667 minus 1, the smallest possible number. This is not surprising since the numbers are uniformly distributed between 1 and 69.

   

  Average number

  The average number drawn is 35. This one should be obvious, since it is exactly halfway between 1 and 69.

   

  Summary

  If we start with the smallest average number and add the average spacing to it and continue to the fifth number, we get:

  11.6667

  23.3333

  34.9999

  46.6667

  58.3333

  Then round off each one to the nearest integer:

  12

  23

  35

  47

  58

   

  Three of these five numbers are odd and two are even, which is the most likely outcome for odd/even. It ends with the average largest number. It includes the average number of 35. The range is 46, which is 46.6667 rounded down to the nearest integer, because the rounding took the first number up to 12 and the last number down to 58. 

  This ticket, 12-23-35-47-58, is the most average result of picking 5 numbers from 1 to 69. It doesn't means it's a winning bet, but I found this interesting.

  When I have some more time, I will compare MegaMillions (new rules) with Powerball in a different thread.

  That is pretty interesting info Tucker. Appreciate this info!

  JUST LOOK AT THE ODDS OF ANY JACKPOT GAME, THAT WILL TELL YOU EVERYTHING YOU NEED TO KNOW
• KY Floyd

  

  NY
  United States
  Member #23,834
  October 16, 2005
  5,128 Posts
  Offline
  Apr 24, 2025, 3:17 pm

  ▲▼

  "As you can see, the least likely outcome is all even numbers at 2.48%. "

  So about 7 million times as likely as any single combination that could win the jackpot? So what are you going to do with it?
• ethanl

  

  Australia
  Member #218,237
  October 24, 2021
  137 Posts
  Offline
  Apr 25, 2025, 9:03 am

  ▲▼

  is this like your program 

  This script performs a comprehensive analysis of all possible 5-number combinations from 1-69, which is 11,238,513 combinations. It measures:

  1. Even/Odd Distribution: How many combinations have 0, 1, 2, 3, 4, or 5 even numbers
  2. Range Analysis: The difference between highest and lowest number in each combination
  3. Spacing Metrics: The gaps between consecutive numbers and their averages
  4. Smallest Number Statistics: Distribution and average of the smallest number in combinations
  5. Largest Number Statistics: Distribution and average of the largest number in combinations
  6. Average Number: The mean value of numbers in each combination

  The script uses a recursive approach to generate combinations efficiently. Since there are over 11 million combinations, I've included progress tracking that displays updates every 10 million combinations processed.

  the script 

   

  function Analyze-Combinations {
      # Function to calculate combinations using a memory-efficient approach
      # This avoids generating all combinations at once which would cause memory issues

      # Initialize counters and variables for our metrics
      $totalCombinations = 0
      $evenCount = @{0 = 0; 1 = 0; 2 = 0; 3 = 0; 4 = 0; 5 = 0}  # Count of combinations with 0,1,2,3,4,5 even numbers
      $rangeStats = @{
          "Sum" = 0
          "Count" = 0
          "Min" = [int]::MaxValue
          "Max" = 0
          "Buckets" = @{}  # For range distribution (10-unit buckets)
      }
      $spacingStats = @{
          "Sum" = 0
          "Count" = 0
          "Min" = [int]::MaxValue
          "Max" = 0
          "AverageSpacings" = @{}  # For average spacing distribution
      }
      $smallestStats = @{
          "Sum" = 0
          "Counts" = @{}  # Frequency of each smallest number
      }
      $largestStats = @{
          "Sum" = 0
          "Counts" = @{}  # Frequency of each largest number
      }
      $averageStats = @{
          "Sum" = 0
          "Buckets" = @{}  # For average value distribution (5-unit buckets)
      }

      # Helper function to process a single combination
      function Process-Combination {
          param (
              [array]$combo
          )
         
          $totalCombinations++
         
          # Count even numbers
          $evenNumbers = ($combo | Where-Object { $_ % 2 -eq 0 }).Count
          $evenCount[$evenNumbers]++
         
          # Calculate range (highest - lowest)
          $range = $combo[-1] - $combo[0]
          $rangeBucket = [Math]::Floor($range / 10) * 10
          $rangeStats["Sum"] += $range
          $rangeStats["Count"]++
          $rangeStats["Min"] = [Math]::Min($rangeStats["Min"], $range)
          $rangeStats["Max"] = [Math]::Max($rangeStats["Max"], $range)
          if (-not $rangeStats["Buckets"].ContainsKey($rangeBucket)) {
              $rangeStats["Buckets"][$rangeBucket] = 0
          }
          $rangeStats["Buckets"][$rangeBucket]++
         
          # Calculate spacing metrics
          $totalSpacing = 0
          $minSpacing = [int]::MaxValue
          $maxSpacing = 0
         
          for ($i = 0; $i -lt 4; $i++) {
              $spacing = $combo[$i+1] - $combo[$i]
              $totalSpacing += $spacing
              $minSpacing = [Math]::Min($minSpacing, $spacing)
              $maxSpacing = [Math]::Max($maxSpacing, $spacing)
          }
         
          $avgSpacing = $totalSpacing / 4
          $avgSpacingRounded = [Math]::Round($avgSpacing, 1)
         
          $spacingStats["Sum"] += $avgSpacing
          $spacingStats["Count"]++
          $spacingStats["Min"] = [Math]::Min($spacingStats["Min"], $minSpacing)
          $spacingStats["Max"] = [Math]::Max($spacingStats["Max"], $maxSpacing)
         
          if (-not $spacingStats["AverageSpacings"].ContainsKey($avgSpacingRounded)) {
              $spacingStats["AverageSpacings"][$avgSpacingRounded] = 0
          }
          $spacingStats["AverageSpacings"][$avgSpacingRounded]++
         
          # Smallest number
          $smallest = $combo[0]
          $smallestStats["Sum"] += $smallest
          if (-not $smallestStats["Counts"].ContainsKey($smallest)) {
              $smallestStats["Counts"][$smallest] = 0
          }
          $smallestStats["Counts"][$smallest]++
         
          # Largest number
          $largest = $combo[-1]
          $largestStats["Sum"] += $largest
          if (-not $largestStats["Counts"].ContainsKey($largest)) {
              $largestStats["Counts"][$largest] = 0
          }
          $largestStats["Counts"][$largest]++
         
          # Average number
          $avg = ($combo | Measure-Object -Average).Average
          $avgBucket = [Math]::Floor($avg / 5) * 5
          $averageStats["Sum"] += $avg
          if (-not $averageStats["Buckets"].ContainsKey($avgBucket)) {
              $averageStats["Buckets"][$avgBucket] = 0
          }
          $averageStats["Buckets"][$avgBucket]++
         
          # Show progress every 10 million combinations
          if ($totalCombinations % 10000000 -eq 0) {
              Write-Progress -Activity "Analyzing Combinations" -Status "Processed $totalCombinations combinations" -PercentComplete (($totalCombinations / 11238513) * 100)
          }
      }

      # Generate combinations using a recursive algorithm
      function Generate-Combinations {
          param (
              [int]$start,
              [int]$k,
              [array]$current
          )
         
          if ($k -eq 0) {
              Process-Combination -combo $current
              return
          }
         
          for ($i = $start; $i -le 69 - $k + 1; $i++) {
              $newCurrent = $current + $i
              Generate-Combinations -start ($i + 1) -k ($k - 1) -current $newCurrent
          }
      }

      # Start the recursive generation with an empty array
      Write-Host "Starting analysis of all 5-number combinations from 1-69..."
      $startTime = Get-Date
      Generate-Combinations -start 1 -k 5 -current @()
      $endTime = Get-Date
     
      # Calculate and format results
      $results = [PSCustomObject]@{
          TotalCombinations = $totalCombinations
          ProcessingTime = ($endTime - $startTime).TotalSeconds
         
          EvenOddDistribution = $evenCount
          EvenOddPercentages = @{}
         
          RangeStats = [PSCustomObject]@{
              Average = $rangeStats["Sum"] / $rangeStats["Count"]
              Min = $rangeStats["Min"]
              Max = $rangeStats["Max"]
              Distribution = $rangeStats["Buckets"]
          }
         
          SpacingStats = [PSCustomObject]@{
              AverageSpacing = $spacingStats["Sum"] / $spacingStats["Count"]
              MinSpacing = $spacingStats["Min"]
              MaxSpacing = $spacingStats["Max"]
              SpacingDistribution = $spacingStats["AverageSpacings"]
          }
         
          SmallestNumberStats = [PSCustomObject]@{
              Average = $smallestStats["Sum"] / $totalCombinations
              Distribution = $smallestStats["Counts"]
          }
         
          LargestNumberStats = [PSCustomObject]@{
              Average = $largestStats["Sum"] / $totalCombinations
              Distribution = $largestStats["Counts"]
          }
         
          AverageNumberStats = [PSCustomObject]@{
              Average = $averageStats["Sum"] / $totalCombinations
              Distribution = $averageStats["Buckets"]
          }
      }
     
      # Calculate percentages for even/odd distribution
      foreach ($key in $evenCount.Keys) {
          $results.EvenOddPercentages[$key] = [Math]::Round(($evenCount[$key] / $totalCombinations) * 100, 2)
      }
     
      return $results
  }

  # Run the analysis
  $analysisResults = Analyze-Combinations

  # Display the results in a formatted way
  Write-Host "=========== COMBINATION ANALYSIS RESULTS ==========="
  Write-Host "Total combinations analyzed: $($analysisResults.TotalCombinations)"
  Write-Host "Processing time: $([Math]::Round($analysisResults.ProcessingTime, 2)) seconds"
  Write-Host ""

  Write-Host "---------- Even/Odd Distribution ----------"
  foreach ($key in $analysisResults.EvenOddDistribution.Keys | Sort-Object) {
      Write-Host "$key even numbers: $($analysisResults.EvenOddDistribution[$key]) combinations ($($analysisResults.EvenOddPercentages[$key])%)"
  }
  Write-Host ""

  Write-Host "---------- Range Statistics ----------"
  Write-Host "Average range: $([Math]::Round($analysisResults.RangeStats.Average, 2))"
  Write-Host "Min range: $($analysisResults.RangeStats.Min)"
  Write-Host "Max range: $($analysisResults.RangeStats.Max)"
  Write-Host "Range distribution (top 5):"
  $analysisResults.RangeStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Range $($_.Key)-$($_.Key+9): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Spacing Statistics ----------"
  Write-Host "Average spacing between consecutive numbers: $([Math]::Round($analysisResults.SpacingStats.AverageSpacing, 2))"
  Write-Host "Min spacing: $($analysisResults.SpacingStats.MinSpacing)"
  Write-Host "Max spacing: $($analysisResults.SpacingStats.MaxSpacing)"
  Write-Host "Average spacing distribution (top 5):"
  $analysisResults.SpacingStats.SpacingDistribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Spacing $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Smallest Number Statistics ----------"
  Write-Host "Average smallest number: $([Math]::Round($analysisResults.SmallestNumberStats.Average, 2))"
  Write-Host "Distribution (top 5):"
  $analysisResults.SmallestNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Smallest number $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Largest Number Statistics ----------"
  Write-Host "Average largest number: $([Math]::Round($analysisResults.LargestNumberStats.Average, 2))"
  Write-Host "Distribution (top 5):"
  $analysisResults.LargestNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Largest number $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Average Number Statistics ----------"
  Write-Host "Average of all numbers in combinations: $([Math]::Round($analysisResults.AverageNumberStats.Average, 2))"
  Write-Host "Distribution by 5-unit buckets (top 5):"
  $analysisResults.AverageNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Average $($_.Key)-$($_.Key+4): $($_.Value) combinations"
      }
  Write-Host ""

  # Export detailed results to CSV files if needed
  $analysisResults.EvenOddDistribution.GetEnumerator() | 
      Select-Object @{N='EvenNumbers';E={$_.Key}}, @{N='Count';E={$_.Value}}, @{N='Percentage';E={$analysisResults.EvenOddPercentages[$_.Key]}} | 
      Export-Csv -Path "even_odd_distribution.csv" -NoTypeInformation

  $analysisResults.RangeStats.Distribution.GetEnumerator() | 
      Select-Object @{N='RangeBucket';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "range_distribution.csv" -NoTypeInformation

  $analysisResults.SmallestNumberStats.Distribution.GetEnumerator() | 
      Select-Object @{N='SmallestNumber';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "smallest_number_distribution.csv" -NoTypeInformation

  $analysisResults.LargestNumberStats.Distribution.GetEnumerator() | 
      Select-Object @{N='LargestNumber';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "largest_number_distribution.csv" -NoTypeInformation

  Write-Host "Detailed results exported to CSV files."
• JustMaybe

  

  us
  Member #228,334
  January 2, 2023
  1,493 Posts
  Offline
  Apr 25, 2025, 9:55 am

  ▲▼
  In response to Tucker Black

  Quote: Originally posted by Tucker Black on Apr 24, 2025

  In this thread I will discuss a few statistics for Powerball drawing numbers -- not the past drawings, but the probability of various results for any future drawing.

  I am only dealing with the five white balls from 1 to 69, not the Powerball. The Powerball number is a different range, 1 to 26, and is drawn from a different ballset.

  There are 11,238,513 different ways to draw 5 numbers from 1 to 69 without replacement. I wrote a computer program to go through all those combinations to measure a few different things.

   

  Even/odd

  There are 35 odd numbers from 1 to 69 and 34 even numbers. The probability distribution for the number of drawn numbers that will be odd or even is as follows:

  odd	even	percentage
  0	5	2.48%
  1	4	14.44%
  2	3	31.68%
  3	2	32.67%
  4	1	15.84%
  5	0	2.89%

   

  As you can see, the least likely outcome is all even numbers at 2.48%. This is closely followed by all odd numbers at 2.89%, since there is one more odd number than even in the matrix.

  The most likely outcome is 3 odd numbers and 2 even, almost 1/3 of the time, closely followed by 3 even numbers and 2 odd.

   

  Range from lowest to highest

  The minimum range is 4 (e.g. 35,36,37,38,39) and the maximum range is 68 (e.g. 1, 11, 17, 43, 69). The average range is 46.6667.

   

  Spacing between numbers

  When the drawn numbers are written in ascending order (similar to how a QP is printed), let us define "spacing" as the difference between two adjacent numbers. For example, with 9, 11, 17, 45, 59, the spacings are 2, 6, 28 and 14.

  The average spacing between numbers is 11.6667.

   

  Smallest number

  The average smallest number is 11.6667. This is somewhat interesting in that it is exactly the same as the average spacing.

   

  Largest number

  The average largest number is 58.3333. Note that 69, the largest possible number, minus 58.3333 is the same as 11.6667 minus 1, the smallest possible number. This is not surprising since the numbers are uniformly distributed between 1 and 69.

   

  Average number

  The average number drawn is 35. This one should be obvious, since it is exactly halfway between 1 and 69.

   

  Summary

  If we start with the smallest average number and add the average spacing to it and continue to the fifth number, we get:

  11.6667

  23.3333

  34.9999

  46.6667

  58.3333

  Then round off each one to the nearest integer:

  12

  23

  35

  47

  58

   

  Three of these five numbers are odd and two are even, which is the most likely outcome for odd/even. It ends with the average largest number. It includes the average number of 35. The range is 46, which is 46.6667 rounded down to the nearest integer, because the rounding took the first number up to 12 and the last number down to 58. 

  This ticket, 12-23-35-47-58, is the most average result of picking 5 numbers from 1 to 69. It doesn't means it's a winning bet, but I found this interesting.

  When I have some more time, I will compare MegaMillions (new rules) with Powerball in a different thread.

  Let's assume that one day these numbers (12-23-35-47-58) hit, either winning the second prize or the jackpot.

  Will the system reset to produce a different set of numbers going into the future?

  I believe winning the lottery jackpot is a 💯 % factor of luck.

  May Fortuna, goddess of chance or lot vindicate me.
• Tucker Black

  

  Colorado
  United States
  Member #173,294
  February 25, 2016
  1,134 Posts
  Offline
  Apr 25, 2025, 1:19 pm

  ▲▼
  In response to JustMaybe

  Quote: Originally posted by JustMaybe on Apr 25, 2025

  Let's assume that one day these numbers (12-23-35-47-58) hit, either winning the second prize or the jackpot.

  Will the system reset to produce a different set of numbers going into the future?

  It's not a system. There is no reliable system for predicting numbers that are randomly drawn with replacement. It doesn't matter if 12-23-35-47-58 gets chosen or not, as all the numbered balls are put back in the hopper after every drawing.

  The same happens with live keno, where the casino picks 20 numbers out of 80, then dumps the balls back in the hopper for the next drawing.

  An RNG game is, in theory, the same thing, but it is not as much fun.
• Tucker Black

  

  Colorado
  United States
  Member #173,294
  February 25, 2016
  1,134 Posts
  Offline
  Apr 25, 2025, 1:21 pm

  ▲▼
  In response to ethanl

  Quote: Originally posted by ethanl on Apr 25, 2025

  is this like your program 

  This script performs a comprehensive analysis of all possible 5-number combinations from 1-69, which is 11,238,513 combinations. It measures:

  1. Even/Odd Distribution: How many combinations have 0, 1, 2, 3, 4, or 5 even numbers
  2. Range Analysis: The difference between highest and lowest number in each combination
  3. Spacing Metrics: The gaps between consecutive numbers and their averages
  4. Smallest Number Statistics: Distribution and average of the smallest number in combinations
  5. Largest Number Statistics: Distribution and average of the largest number in combinations
  6. Average Number: The mean value of numbers in each combination

  The script uses a recursive approach to generate combinations efficiently. Since there are over 11 million combinations, I've included progress tracking that displays updates every 10 million combinations processed.

  the script 

   

  function Analyze-Combinations {
      # Function to calculate combinations using a memory-efficient approach
      # This avoids generating all combinations at once which would cause memory issues

      # Initialize counters and variables for our metrics
      $totalCombinations = 0
      $evenCount = @{0 = 0; 1 = 0; 2 = 0; 3 = 0; 4 = 0; 5 = 0}  # Count of combinations with 0,1,2,3,4,5 even numbers
      $rangeStats = @{
          "Sum" = 0
          "Count" = 0
          "Min" = [int]::MaxValue
          "Max" = 0
          "Buckets" = @{}  # For range distribution (10-unit buckets)
      }
      $spacingStats = @{
          "Sum" = 0
          "Count" = 0
          "Min" = [int]::MaxValue
          "Max" = 0
          "AverageSpacings" = @{}  # For average spacing distribution
      }
      $smallestStats = @{
          "Sum" = 0
          "Counts" = @{}  # Frequency of each smallest number
      }
      $largestStats = @{
          "Sum" = 0
          "Counts" = @{}  # Frequency of each largest number
      }
      $averageStats = @{
          "Sum" = 0
          "Buckets" = @{}  # For average value distribution (5-unit buckets)
      }

      # Helper function to process a single combination
      function Process-Combination {
          param (
              [array]$combo
          )
         
          $totalCombinations++
         
          # Count even numbers
          $evenNumbers = ($combo | Where-Object { $_ % 2 -eq 0 }).Count
          $evenCount[$evenNumbers]++
         
          # Calculate range (highest - lowest)
          $range = $combo[-1] - $combo[0]
          $rangeBucket = [Math]::Floor($range / 10) * 10
          $rangeStats["Sum"] += $range
          $rangeStats["Count"]++
          $rangeStats["Min"] = [Math]::Min($rangeStats["Min"], $range)
          $rangeStats["Max"] = [Math]::Max($rangeStats["Max"], $range)
          if (-not $rangeStats["Buckets"].ContainsKey($rangeBucket)) {
              $rangeStats["Buckets"][$rangeBucket] = 0
          }
          $rangeStats["Buckets"][$rangeBucket]++
         
          # Calculate spacing metrics
          $totalSpacing = 0
          $minSpacing = [int]::MaxValue
          $maxSpacing = 0
         
          for ($i = 0; $i -lt 4; $i++) {
              $spacing = $combo[$i+1] - $combo[$i]
              $totalSpacing += $spacing
              $minSpacing = [Math]::Min($minSpacing, $spacing)
              $maxSpacing = [Math]::Max($maxSpacing, $spacing)
          }
         
          $avgSpacing = $totalSpacing / 4
          $avgSpacingRounded = [Math]::Round($avgSpacing, 1)
         
          $spacingStats["Sum"] += $avgSpacing
          $spacingStats["Count"]++
          $spacingStats["Min"] = [Math]::Min($spacingStats["Min"], $minSpacing)
          $spacingStats["Max"] = [Math]::Max($spacingStats["Max"], $maxSpacing)
         
          if (-not $spacingStats["AverageSpacings"].ContainsKey($avgSpacingRounded)) {
              $spacingStats["AverageSpacings"][$avgSpacingRounded] = 0
          }
          $spacingStats["AverageSpacings"][$avgSpacingRounded]++
         
          # Smallest number
          $smallest = $combo[0]
          $smallestStats["Sum"] += $smallest
          if (-not $smallestStats["Counts"].ContainsKey($smallest)) {
              $smallestStats["Counts"][$smallest] = 0
          }
          $smallestStats["Counts"][$smallest]++
         
          # Largest number
          $largest = $combo[-1]
          $largestStats["Sum"] += $largest
          if (-not $largestStats["Counts"].ContainsKey($largest)) {
              $largestStats["Counts"][$largest] = 0
          }
          $largestStats["Counts"][$largest]++
         
          # Average number
          $avg = ($combo | Measure-Object -Average).Average
          $avgBucket = [Math]::Floor($avg / 5) * 5
          $averageStats["Sum"] += $avg
          if (-not $averageStats["Buckets"].ContainsKey($avgBucket)) {
              $averageStats["Buckets"][$avgBucket] = 0
          }
          $averageStats["Buckets"][$avgBucket]++
         
          # Show progress every 10 million combinations
          if ($totalCombinations % 10000000 -eq 0) {
              Write-Progress -Activity "Analyzing Combinations" -Status "Processed $totalCombinations combinations" -PercentComplete (($totalCombinations / 11238513) * 100)
          }
      }

      # Generate combinations using a recursive algorithm
      function Generate-Combinations {
          param (
              [int]$start,
              [int]$k,
              [array]$current
          )
         
          if ($k -eq 0) {
              Process-Combination -combo $current
              return
          }
         
          for ($i = $start; $i -le 69 - $k + 1; $i++) {
              $newCurrent = $current + $i
              Generate-Combinations -start ($i + 1) -k ($k - 1) -current $newCurrent
          }
      }

      # Start the recursive generation with an empty array
      Write-Host "Starting analysis of all 5-number combinations from 1-69..."
      $startTime = Get-Date
      Generate-Combinations -start 1 -k 5 -current @()
      $endTime = Get-Date
     
      # Calculate and format results
      $results = [PSCustomObject]@{
          TotalCombinations = $totalCombinations
          ProcessingTime = ($endTime - $startTime).TotalSeconds
         
          EvenOddDistribution = $evenCount
          EvenOddPercentages = @{}
         
          RangeStats = [PSCustomObject]@{
              Average = $rangeStats["Sum"] / $rangeStats["Count"]
              Min = $rangeStats["Min"]
              Max = $rangeStats["Max"]
              Distribution = $rangeStats["Buckets"]
          }
         
          SpacingStats = [PSCustomObject]@{
              AverageSpacing = $spacingStats["Sum"] / $spacingStats["Count"]
              MinSpacing = $spacingStats["Min"]
              MaxSpacing = $spacingStats["Max"]
              SpacingDistribution = $spacingStats["AverageSpacings"]
          }
         
          SmallestNumberStats = [PSCustomObject]@{
              Average = $smallestStats["Sum"] / $totalCombinations
              Distribution = $smallestStats["Counts"]
          }
         
          LargestNumberStats = [PSCustomObject]@{
              Average = $largestStats["Sum"] / $totalCombinations
              Distribution = $largestStats["Counts"]
          }
         
          AverageNumberStats = [PSCustomObject]@{
              Average = $averageStats["Sum"] / $totalCombinations
              Distribution = $averageStats["Buckets"]
          }
      }
     
      # Calculate percentages for even/odd distribution
      foreach ($key in $evenCount.Keys) {
          $results.EvenOddPercentages[$key] = [Math]::Round(($evenCount[$key] / $totalCombinations) * 100, 2)
      }
     
      return $results
  }

  # Run the analysis
  $analysisResults = Analyze-Combinations

  # Display the results in a formatted way
  Write-Host "=========== COMBINATION ANALYSIS RESULTS ==========="
  Write-Host "Total combinations analyzed: $($analysisResults.TotalCombinations)"
  Write-Host "Processing time: $([Math]::Round($analysisResults.ProcessingTime, 2)) seconds"
  Write-Host ""

  Write-Host "---------- Even/Odd Distribution ----------"
  foreach ($key in $analysisResults.EvenOddDistribution.Keys | Sort-Object) {
      Write-Host "$key even numbers: $($analysisResults.EvenOddDistribution[$key]) combinations ($($analysisResults.EvenOddPercentages[$key])%)"
  }
  Write-Host ""

  Write-Host "---------- Range Statistics ----------"
  Write-Host "Average range: $([Math]::Round($analysisResults.RangeStats.Average, 2))"
  Write-Host "Min range: $($analysisResults.RangeStats.Min)"
  Write-Host "Max range: $($analysisResults.RangeStats.Max)"
  Write-Host "Range distribution (top 5):"
  $analysisResults.RangeStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Range $($_.Key)-$($_.Key+9): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Spacing Statistics ----------"
  Write-Host "Average spacing between consecutive numbers: $([Math]::Round($analysisResults.SpacingStats.AverageSpacing, 2))"
  Write-Host "Min spacing: $($analysisResults.SpacingStats.MinSpacing)"
  Write-Host "Max spacing: $($analysisResults.SpacingStats.MaxSpacing)"
  Write-Host "Average spacing distribution (top 5):"
  $analysisResults.SpacingStats.SpacingDistribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Spacing $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Smallest Number Statistics ----------"
  Write-Host "Average smallest number: $([Math]::Round($analysisResults.SmallestNumberStats.Average, 2))"
  Write-Host "Distribution (top 5):"
  $analysisResults.SmallestNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Smallest number $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Largest Number Statistics ----------"
  Write-Host "Average largest number: $([Math]::Round($analysisResults.LargestNumberStats.Average, 2))"
  Write-Host "Distribution (top 5):"
  $analysisResults.LargestNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Largest number $($_.Key): $($_.Value) combinations"
      }
  Write-Host ""

  Write-Host "---------- Average Number Statistics ----------"
  Write-Host "Average of all numbers in combinations: $([Math]::Round($analysisResults.AverageNumberStats.Average, 2))"
  Write-Host "Distribution by 5-unit buckets (top 5):"
  $analysisResults.AverageNumberStats.Distribution.GetEnumerator() | 
      Sort-Object -Property Value -Descending | 
      Select-Object -First 5 | 
      ForEach-Object {
          Write-Host "  Average $($_.Key)-$($_.Key+4): $($_.Value) combinations"
      }
  Write-Host ""

  # Export detailed results to CSV files if needed
  $analysisResults.EvenOddDistribution.GetEnumerator() | 
      Select-Object @{N='EvenNumbers';E={$_.Key}}, @{N='Count';E={$_.Value}}, @{N='Percentage';E={$analysisResults.EvenOddPercentages[$_.Key]}} | 
      Export-Csv -Path "even_odd_distribution.csv" -NoTypeInformation

  $analysisResults.RangeStats.Distribution.GetEnumerator() | 
      Select-Object @{N='RangeBucket';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "range_distribution.csv" -NoTypeInformation

  $analysisResults.SmallestNumberStats.Distribution.GetEnumerator() | 
      Select-Object @{N='SmallestNumber';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "smallest_number_distribution.csv" -NoTypeInformation

  $analysisResults.LargestNumberStats.Distribution.GetEnumerator() | 
      Select-Object @{N='LargestNumber';E={$_.Key}}, @{N='Count';E={$_.Value}} | 
      Export-Csv -Path "largest_number_distribution.csv" -NoTypeInformation

  Write-Host "Detailed results exported to CSV files."

  I wrote mine in Visual Basic.

  Did you get the same results?
• ethanl

  

  Australia
  Member #218,237
  October 24, 2021
  137 Posts
  Offline
  Apr 25, 2025, 4:26 pm

  ▲▼

  no as  my pc crashed as running 11 million combinations it take significant time  and my computer's processing power and didnt have enough memory available for my pc run my script
• jaom

  

  The Region, Indiana
  us
  Member #247,519
  November 18, 2024
  3 Posts
  Offline
  May 5, 2025, 7:18 pm

  ▲▼

  Here's a python version of your program (excluding exporting results to CSV files).  I got similar results as above.

  import time
  import math
  import itertools

  def analyze_combinations():
      start_time = time.time()

      total_combinations = 0

      # Even‐odd counts: keys 0–5
      even_count = {i: 0 for i in range(6)}

      # Range stats
      range_stats = {
          "Sum": 0,
          "Count": 0,
          "Min": None,
          "Max": None,
          "Buckets": {}
      }

      # Spacing stats
      spacing_stats = {
          "Sum": 0.0,
          "Count": 0,
          "Min": None,
          "Max": None,
          "AverageSpacings": {}
      }

      # Smallest‐number stats
      smallest_stats = {
          "Sum": 0,
          "Counts": {}
      }

      # Largest‐number stats
      largest_stats = {
          "Sum": 0,
          "Counts": {}
      }

      # Average‐number stats
      average_stats = {
          "Sum": 0.0,
          "Buckets": {}
      }

      # Generate all combinations of 5 out of 1..69
      for comb in itertools.combinations(range(1, 70), 5):
          total_combinations += 1

          # Even‐odd
          evens = sum(1 for x in comb if x % 2 == 0)
          even_count[evens] += 1

          # Smallest & largest
          smallest = comb[0]
          largest = comb[-1]

          smallest_stats["Sum"] += smallest
          smallest_stats["Counts"][smallest] = smallest_stats["Counts"].get(smallest, 0) + 1

          largest_stats["Sum"] += largest
          largest_stats["Counts"][largest] = largest_stats["Counts"].get(largest, 0) + 1

          # Average of the five numbers
          avg_num = sum(comb) / 5.0
          average_stats["Sum"] += avg_num
          avg_bucket = int(avg_num)            # bucket by integer part
          average_stats["Buckets"][avg_bucket] = average_stats["Buckets"].get(avg_bucket, 0) + 1

          # Range = max − min
          r = largest - smallest
          range_stats["Sum"] += r
          range_stats["Count"] += 1
          if range_stats["Min"] is None or r < range_stats["Min"]:
              range_stats["Min"] = r
          if range_stats["Max"] is None or r > range_stats["Max"]:
              range_stats["Max"] = r
          rbucket = (r // 10) * 10              # 0–9→0, 10–19→10, etc.
          range_stats["Buckets"][rbucket] = range_stats["Buckets"].get(rbucket, 0) + 1

          # Spacings between consecutive numbers
          spacings = [comb[i+1] - comb[i] for i in range(4)]
          avg_spacing = sum(spacings) / 4.0
          spacing_stats["Sum"] += avg_spacing
          spacing_stats["Count"] += 1
          if spacing_stats["Min"] is None or avg_spacing < spacing_stats["Min"]:
              spacing_stats["Min"] = avg_spacing
          if spacing_stats["Max"] is None or avg_spacing > spacing_stats["Max"]:
              spacing_stats["Max"] = avg_spacing
          s_bucket = round(avg_spacing, 2)      # bucket by two‐decimal average
          spacing_stats["AverageSpacings"][s_bucket] = spacing_stats["AverageSpacings"].get(s_bucket, 0) + 1

      end_time = time.time()

      # Even‐odd percentages
      even_percentages = {
          k: round((even_count[k] / total_combinations) * 100, 2)
          for k in even_count
      }

      results = {
          "TotalCombinations": total_combinations,
          "ProcessingTime": end_time - start_time,
          "EvenOddDistribution": even_count,
          "EvenOddPercentages": even_percentages,
          "RangeStats": {
              "Average": range_stats["Sum"] / range_stats["Count"] if range_stats["Count"] else 0,
              "Min": range_stats["Min"],
              "Max": range_stats["Max"],
              "Distribution": range_stats["Buckets"]
          },
          "SpacingStats": {
              "AverageSpacing": spacing_stats["Sum"] / spacing_stats["Count"] if spacing_stats["Count"] else 0,
              "MinSpacing": spacing_stats["Min"],
              "MaxSpacing": spacing_stats["Max"],
              "SpacingDistribution": spacing_stats["AverageSpacings"]
          },
          "SmallestNumberStats": {
              "Average": smallest_stats["Sum"] / total_combinations,
              "Distribution": smallest_stats["Counts"]
          },
          "LargestNumberStats": {
              "Average": largest_stats["Sum"] / total_combinations,
              "Distribution": largest_stats["Counts"]
          },
          "AverageNumberStats": {
              "Average": average_stats["Sum"] / total_combinations,
              "Distribution": average_stats["Buckets"]
          }
      }

      return results

  
  def main():
      res = analyze_combinations()

      # Print exactly as in your PowerShell snippet
      print("=========== COMBINATION ANALYSIS RESULTS ===========")
      print(f"Total combinations analyzed: {res['TotalCombinations']}")
      print(f"Processing time: {round(res['ProcessingTime'], 2)} seconds\n")

      print("---------- Even/Odd Distribution ----------")
      for k in sorted(res["EvenOddDistribution"].keys()):
          cnt = res["EvenOddDistribution"][k]
          pct = res["EvenOddPercentages"][k]
          print(f"{k} even numbers: {cnt} combinations ({pct}%)")
      print()

      print("---------- Range Statistics ----------")
      print(f"Average range: {round(res['RangeStats']['Average'], 2)}")
      print(f"Min range: {res['RangeStats']['Min']}")
      print(f"Max range: {res['RangeStats']['Max']}")
      print("Range distribution (sorted):")
      top_ranges = sorted(res["RangeStats"]["Distribution"].items(),
                          key=lambda x: x[1], reverse=True)[:7]
      for bucket, cnt in top_ranges:
          print(f"  Range {bucket}-{bucket+9}: {cnt} combinations")
      print()

      print("---------- Spacing Statistics ----------")
      print(f"Average spacing between consecutive numbers: {round(res['SpacingStats']['AverageSpacing'], 2)}")
      print(f"Min spacing: {res['SpacingStats']['MinSpacing']}")
      print(f"Max spacing: {res['SpacingStats']['MaxSpacing']}")
      print("Average spacing distribution (top 5):")
      top_spacings = sorted(res["SpacingStats"]["SpacingDistribution"].items(),
                            key=lambda x: x[1], reverse=True)[:5]
      for bucket, cnt in top_spacings:
          print(f"  Spacing {bucket}: {cnt} combinations")
      print()

      print("---------- Smallest Number Statistics ----------")
      print(f"Average smallest number: {round(res['SmallestNumberStats']['Average'], 2)}")
      print("Distribution (top 5):")
      top_smallest = sorted(res["SmallestNumberStats"]["Distribution"].items(),
                            key=lambda x: x[1], reverse=True)[:5]
      for num, cnt in top_smallest:
          print(f"  Smallest number {num}: {cnt} combinations")
      print()

      print("---------- Largest Number Statistics ----------")
      print(f"Average largest number: {round(res['LargestNumberStats']['Average'], 2)}")
      print("Distribution (top 5):")
      top_largest = sorted(res["LargestNumberStats"]["Distribution"].items(),
                            key=lambda x: x[1], reverse=True)[:5]
      for num, cnt in top_largest:
          print(f"  Largest number {num}: {cnt} combinations")
      print()

      print("---------- Average Number Statistics ----------")
      print(f"Average average number: {round(res['AverageNumberStats']['Average'], 2)}")
      print("Distribution (top 5):")
      top_average = sorted(res["AverageNumberStats"]["Distribution"].items(),
                            key=lambda x: x[1], reverse=True)[:5]
      for num, cnt in top_average:
          print(f"  Average number {num}: {cnt} combinations")
      print()

  
  if __name__ == "__main__":
      main()

   

  My Results:

  =========== COMBINATION ANALYSIS RESULTS ===========
  Total combinations analyzed: 11238513
  Processing time: 70.92 seconds

  ---------- Even/Odd Distribution ----------
  0 even numbers: 324632 combinations (2.89%)
  1 even numbers: 1780240 combinations (15.84%)
  2 even numbers: 3671745 combinations (32.67%)
  3 even numbers: 3560480 combinations (31.68%)
  4 even numbers: 1623160 combinations (14.44%)
  5 even numbers: 278256 combinations (2.48%)

  ---------- Range Statistics ----------
  Average range: 46.67
  Min range: 4
  Max range: 68
  Range distribution (sorted):
    Range 50-59: 3413242 combinations
    Range 40-49: 3101117 combinations
    Range 30-39: 1974492 combinations
    Range 60-69: 1680867 combinations
    Range 20-29: 863367 combinations
    Range 10-19: 197742 combinations
    Range 0-9: 7686 combinations

  ---------- Spacing Statistics ----------
  Average spacing between consecutive numbers: 11.67
  Min spacing: 1.0
  Max spacing: 17.0
  Average spacing distribution (top 5):
    Spacing 13.0: 354025 combinations
    Spacing 13.25: 353600 combinations
    Spacing 12.75: 352800 combinations
    Spacing 13.5: 351390 combinations
    Spacing 12.5: 350056 combinations

  ---------- Smallest Number Statistics ----------
  Average smallest number: 11.67
  Distribution (top 5):
    Smallest number 1: 814385 combinations
    Smallest number 2: 766480 combinations
    Smallest number 3: 720720 combinations
    Smallest number 4: 677040 combinations
    Smallest number 5: 635376 combinations

  ---------- Largest Number Statistics ----------
  Average largest number: 58.33
  Distribution (top 5):
    Largest number 69: 814385 combinations
    Largest number 68: 766480 combinations
    Largest number 67: 720720 combinations
    Largest number 66: 677040 combinations
    Largest number 65: 635376 combinations

  ---------- Average Number Statistics ----------
  Average average number: 35.0
  Distribution (top 5):
    Average number 35: 502040 combinations
    Average number 34: 501450 combinations
    Average number 36: 496800 combinations
    Average number 33: 495071 combinations
    Average number 37: 485896 combinations