Using the Binomial Distribution function in excel

I don't think this can be calculated in closed-form solution.

Function pWin(p As Double, nH As Long, nT As Long) As Variant
    ' Returns the probability that a coin with
    ' probability p of heads will accumulate
    ' nH excess heads before nT excess tails
    Dim q       As Double   ' 1-p
    Dim adPrb() As Double  ' array of probabilities
    Dim i       As Long     ' index to array
    Dim pH      As Double   ' probability of Heads winning
    Dim pT      As Double   ' probability of Tails winning
    
    Dim dH      As Double   ' rate at which pH is increasing
    Dim dT      As Double   ' rate at which pT is increasing
    
    Dim dPrb    As Double   ' temporary variable
    Dim iOdd    As Long     ' odd/even roll
    Dim nToss   As Long     ' tosses made
    
    If nH < 1 Then Exit Function
    If nT < 1 Then Exit Function

    q = 1# - p
    ReDim adPrb(-nT To nH)
    adPrb(0) = 1#

    ' loop until the sum of probabilities is close to 1
    Do While pH + pT < 0.99999
        iOdd = (iOdd + 1) Mod 2
        For i = -nT + ((nT + iOdd) And 1) To nH Step 2
            dPrb = 0#
            If i > 1 - nT Then dPrb = p * adPrb(i - 1)
            If i < nH - 1 Then dPrb = q * adPrb(i + 1) + dPrb
            adPrb(i) = dPrb
            If i = -nT Then pT = pT + dPrb
            If i = nH Then pH = pH + dPrb
        Next i
        nToss = nToss + 1
    Loop
    ' scale result to 100%
    pWin = Array(pH / (pH + pT), nToss)
End Function

For your example on the other board (with a coin biased to flip heads 65% of the time, what's the probability of accumulating 7 heads before 9 tails?),

=pWin(65%, 7, 9) returns 99.62%.

Thought you'd died ...

To be clear, the posted code computes the probability of flipping (for the example) 7 more heads than tails.

The probability of flipping 7 heads before 9 tails would require changing the code -- you only need to simulate 16 flips total.

1. Copy the code from the post
2. Press Alt+F11 to open the Visual Basic Editor (VBE)
3. From the menu bar in the VBE window, do Insert > Module
4. Paste the code in the window that opens
5. Close the VBE to return to Excel

See the example usage in post #3.