I am trying to write a little application that calculates the odds of getting a user defined result (or greater) on a user defined number of dice with user defined number of sides.

Example:

"What is the chance of rolling a five or a six three times or more, when rolling 5d6?"

The code below is what I have come up with, but I seem to get an unexpected result when I use values as in the example.

The correct result would be 0.002743484

What I get is 0.041152263.

A more complete overview of the results scenario can be found:

http://www.staff.ncl.ac.uk/nikolas.lloyd/wargames/crossfire/cfdiceeg.html. Many thanks to the site authour for the mathematical explanation.

I realise that my code is more than likely not optimised and that I have probably overstated the data types (hey, it stopped the ByRef Type mismatch errors), but I am a bit of a novice user.

Any advice would be greatly appreciated.

Thanks,

-John

Code:

```
Option Explicit
Dim n, x, p, r As Double
Private Sub cmdCalculate_Click()
'Reset Variables
'hold the factorial result
f = 0
'number of dice being rolled
n = 0
'probability of success on a single die
p = 0
'minimum value required on a dice
r = 0
'numbr of sides on a die
s = 0
'number of successes required to meet (r) where x<=n
x = 0
'Start Calculations
All
End Sub
Private Sub All()
'store cumualtive calculation of odds
Dim result As Double
'Fetch User inputs
n = CDbl((frmDice.txtTotalDice.Value))
r = CDbl(frmDice.txtRequiredRoll.Value)
s = CDbl(frmDice.txtDiceSize.Value)
x = CDbl((frmDice.txtHits.Value))
'calculate odds of success on a single die
p = CDbl((((d - r) + 1) / d))
'Loop, summing odds of desired results. Rolling 5 dice with
'_at least_ three favourable results required means summing
' odds of 3 results, 4 results and 5 results.
'Remember, n is the number of dice (ie 5) and x is the number of successes
Do While x <= n
result = result + Individual(n, x, p)
x = x + 1
Loop
'Display Result on Form
frmDice.txtResult.Text = 100 * r & " %"
End Sub
Public Function Individual(n, x, p)
'Calculate the odds of acheiving (x) successes rolling (n) dice given single
'die probabiltiy of (p).
'THanks to
f = (Factorial(n) / (Factorial(x) * Factorial((n - x)))) _
* (p ^ x) * ((1 - p) ^ (n - x))
End Function
Function Factorial(ByVal x As Double) As Double
'perform required factorial calculation
Dim i As Integer
Factorial = 1
For i = 1 To x
Factorial = Factorial * i
Next i
End Function
```