Monte Carlo Simulation in VBA consistently underestimates the true value

Question

I have a weird problem with a Monte Carlo Simulation that I built. It is a nested loop to calculate the expected value of investments (actually Poker Tournaments). To demonstrat

Answer 1

It looks like you are repeatedly calling Randomize, presumably as part of a tight loop. Every time this is called, it reseeds the random number generator from the system clock. Doing so with each pass through the loop introduces autocorrelations (though exactly how isn't quite clear).

Consider the following experiment:

Sub Test()
    Dim i As Long, A As Variant
    Dim count1 As Long, count2 As Long
    ReDim A(1 To 10000)

    For i = 1 To 10000
        Randomize
        A(i) = IIf(Rnd() < 0.5, 0, 1)
    Next i

    'count how often A(i) = A(i+1)
    For i = 1 To 9999
        If A(i) = A(i + 1) Then count1 = count1 + 1
    Next i

    For i = 1 To 10000
        A(i) = IIf(Rnd() < 0.5, 0, 1)
    Next i

    'count how often A(i) = A(i+1)
    For i = 1 To 9999
        If A(i) = A(i + 1) Then count2 = count2 + 1
    Next i

   Debug.Print "First Loop: " & count1
   Debug.Print "Second Loop: " & count2 & vbCrLf

End Sub

Typical output:

First Loop: 5452
Second Loop: 4996

I have run it several times. The first loop almost always produces a number which differs from 5000 by a large amount whereas the second loop almost always produces a number fairly close to 5000 (the expected value is 4999.5 if successive calls to Rnd correspond to independent random variables -- hence there is a distinct lack of independence when repeatedly reseeding).

Moral of the story: call Randomize just once in the simulation, say as the first line of the main sub. Alternatively, use Application.WorksheetFunction.RandBetween(0,1) and let Excel worry about the seeding.

If this autocorrelation doesn't explain the error, the problem lies in the code that you haven't shown, so you would need to include that code.