How do you calculate %xHKO?

Well, I wrote a new program to calculate this stuff. (Written in Excel VBA because almost everyone has Excel.) Inputs are taken from cells B1, B2, B3. (B1 = min damage, B2= max damage, B3 = Monster HP.)

To use this code, open Excel > open Visual Basic Editor (Alt+F11) > Insert > Module > Copy/Paste code into Module. Input values for min, max, monster hp in cells B1, B2, B3. Execute the code by Alt+F8 in main Excel window or by F5 in Visual Basic Editor. Output is spit out in column F.

Code:

Sub Test()

Dim min As Double
Dim max As Double
Dim monhp As Double
Dim n As Integer
Dim max_n As Integer
Dim damage As Double

Dim hko() As Double
Dim hkotemp() As Double

Dim sum As Double
Dim poss As Double
Dim prob As Double

min = ActiveSheet.Cells(1, 2)
max = ActiveSheet.Cells(2, 2)
monhp = ActiveSheet.Cells(3, 2)
max_n = Int(monhp / min)
If (max_n * min) < monhp Then
    max_n = max_n + 1
End If

For a = 1 To (max_n + 1)
    ActiveSheet.Cells(a, 6).Value = ""
Next a

ReDim hko(min To max)
For a = min To max
    hko(a) = 1
Next a

sum = 0
poss = (max - min) + 1
For i = min To max
    If i >= monhp Then
        sum = sum + hko(i)
    End If
Next i
prob = sum / poss * 100
ActiveSheet.Cells(1, 6).Value = prob

n = 1
Do While n < max_n
    For x = 1 To n
    
        Erase hkotemp()
        ReDim hkotemp(((x * min) + min) To ((x * max) + max))
        
        For y = min To max
            For z = x * min To x * max
                damage = y + z
                If x = 1 Then
                    Erase hko()
                    ReDim hko(min To max)
                    For a = min To max
                        hko(a) = 1
                    Next a
                    hkotemp(damage) = hkotemp(damage) + hko(z)
                Else
                    hkotemp(damage) = hkotemp(damage) + hko(z)
                End If
            Next z
        Next y
        
        Erase hko()
        ReDim hko(((x * min) + min) To ((x * max) + max))
        For g = ((x * min) + min) To ((x * max) + max)
            hko(g) = hkotemp(g)
        Next g
        
    Next x
    
    n = n + 1
    
    sum = 0
    For h = (n * min) To (n * max)
        If h >= monhp Then
            sum = sum + hko(h)
        End If
    Next h
    poss = ((max - min) + 1) ^ n
    prob = sum / poss * 100
    
    ActiveSheet.Cells(n, 6).Value = prob
Loop

End Sub

For reference, this webpage has tables of probabilities when rolling 1 to 25 (6-sided) dice:
http://wizardofodds.com/gambling/dice2.html

If you set the min/max to match dice, the output of this program matches what you would expect from those tables. However, when you change the values to numbers similar to in-game damage numbers (i.e., min/max are over 10000), the calculation takes way too long. Or actually, it starts to have problems when min/max get over 500 or so.

So the way to go is to generate a sample and calculate probability using the sample. The result is not going to be completely accurate, but it should be very close as long as you have a large enough sample size.