probability of getting a pair in poker in excel

I'm working on a probability problem related to poker, and I could really use some help with figuring out how to calculate it in Excel. Here’s the scenario:


In a game of poker, you're dealt 5 cards from a standard deck of 52 cards. I want to determine the probability of getting at least one pair (i.e., two cards of the same rank) in my hand.


I understand that this involves some combinatorial calculations, but I'm not sure how to set it up properly in Excel. I've been playing poker online and this question came up because I'm interested in evaluating my chances of winning. Could someone help me verify if this approach is correct and guide me on how to properly set up these calculations in Excel?

Attachment 31692

Kind of bored tonight so.... is this a different version?

Code:

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' Function to calculate combinations (nCr)
Function Combinations(n As Integer, r As Integer) As Double
    ' Handle cases where r is invalid
    If r < 0 Or r > n Then
        Combinations = 0
        ' Handle base cases for combinations
    ElseIf
        r = 0 Or r = n Then
        Combinations = 1
        ' Optimize calculation by choosing the smaller 'r'
    ElseIf
        r > n / 2 Then
        Combinations = Combinations(n, n - r)
        ' Calculate the combination iteratively
    Else
        Dim result As Double
        result = 1
        For i = 1 To r
            result = result * (n - i + 1) / i
        Next i
        Combinations = result
    End If
End Function

Sub CalculatePairProbability()
    ' Declare variables to store the calculated values
    Dim totalPossibleHands As Double
    Dim handsWithNoPair As Double
    Dim probabilityOfNoPair As Double
    Dim probabilityOfAtLeastOnePair As Double
    ' 1. Calculate the total number of possible 5-card hands
    totalPossibleHands = Combinations(52, 5)
    ' 2. Calculate the number of 5-card hands with NO pairs
    '    a) Choose 5 distinct ranks from 13 available ranks
    Dim numberOfRankCombinations As Double
    numberOfRankCombinations = Combinations(13, 5)
    '    b) For each of these 5 ranks, choose 1 of the 4 suits
    Dim numberOfSuitCombinations As Double
    numberOfSuitCombinations = 4 ^ 5 ' 4 choices for each of the 5 cards 
    '    c) Total number of "no pair" hands
    handsWithNoPair = numberOfRankCombinations * numberOfSuitCombinations
    ' 3. Calculate the probability of getting NO pairs
    probabilityOfNoPair = handsWithNoPair / totalPossibleHands
    ' 4. Calculate the probability of getting AT LEAST ONE pair
    '    This is 1 minus the probability of getting no pairs
    probabilityOfAtLeastOnePair = 1 - probabilityOfNoPair
    ' Display the result to the user
    MsgBox "The probability of getting at least one pair in a 5-card hand is approximately: " & Format(probabilityOfAtLeastOnePair, "0.00%")
End Sub'

' --- End of Module Level Code ---

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