Function Beta(nToss As Long, run As Long, pHeads As Double) As Double
    ' shg 2011
    ' http://arxiv.org/PS_cache/math/pdf/0511/0511652v1.pdf
    Dim k      As Double
    Dim l           As Long
 
    k = (1 - pHeads) * pHeads ^ run
 
    With WorksheetFunction
        For l = nToss \ (run + 1) To 0 Step -1
            Beta = Beta + .Combin(nToss - l * run, l) * (-k) ^ l
        Next l
    End With
End Function

###### Perl Code #####


$p = 1/2083; # Probability of event
$m = 2; # Length of streak
$n = 1000000; # Length of series

print "calculating....\n";

$iter = int( $n/($m+1) ); #ceiling( ($n-$m)/($m+1) )
$last = $n - ($iter-1)*($m+1) - $m - 1;

$c = (1-$p)*$p**$m;

$prob[$m] = $p**$m;

for ($j = 1; $j <= $iter; $j++) {

$prob[0] = $prob[$m] + (1-$prob[0])*$c;
for ($i = 1; $i <= $m; $i++) {
$prob[$i] = $prob[$i-1] + (1-$prob[$i])*$c; 
}

}

print "Probability of ", $m, " events of probability ", $p, " in a row in ", $n, " trials = ", $prob[$last], " \nor ", 1/$prob[$last]-1, " to 1";


###### End Perl Code #####

function calcStreakProb(lSeries, lStreak, dProb) {
	lSeries = lSeries.replace(/,/g, "")
	lStreak = lStreak.replace(/,/g, "")
	lSeries = parseInt(lSeries);
	lStreak = parseInt(lStreak);
	if(dProb.indexOf('%') > -1) {
		dProb = dProb.replace(/%/g, '');
		dProb = parseFloat(0+dProb/100);
	} else {
		dProb = parseFloat(0+dProb);
	}
	if (dProb < 0 || dProb > 1) {
		alert("Probability must be between 0 and 1");
		return;
	}
	if (lStreak > lSeries) {
		return 0;
	}
	var dTotProb = new Array(lSeries);
	dTotProb[lStreak] = Math.pow(dProb, lStreak);
	for (var i = lStreak+1; i<= lSeries; i++) {
		dTotProb[i] = dTotProb[i-1] + Math.pow(dProb, lStreak) * (1-dProb) * (dTotProb[i-lStreak-1] != undefined ? 1-dTotProb[i-lStreak-1] : 1);
	}
	return fmtPercent(dTotProb[lSeries]);

Option Explicit

Function ProbRun(n As Long, r As Long, p As Double)
    ' shg 2011
    ' http://arxiv.org/PS_cache/math/pdf/0511/0511652v1.pdf

    ' Probability of a r or more consecutive heads in n tosses
    ' of a coin having probability p of heads
    ProbRun = 1 - (Beta(n, r, p) - p ^ r * Beta(n - r, r, p))
End Function

Function Beta(n As Long, r As Long, p As Double) As Double
    ' shg 2011
    ' http://arxiv.org/PS_cache/math/pdf/0511/0511652v1.pdf

    Dim q           As Double
    Dim l           As Long
    
    q = 1 - p   ' = probability of tails

    With WorksheetFunction
        For l = 0 To n \ (r + 1)
            Beta = Beta + (-1) ^ l * .Combin(n - l * r, l) * (q * p ^ r) ^ l
        Next l
    End With
End Function

Sub MonteCarlo()
    Dim rCal        As Range    ' area to calculate on MC sheet based on # trades
    Dim rTry        As Range    ' results each trial
    Dim rInp        As Range    ' range with run calculations
    Dim rOut        As Range    ' cumulative results of trials
    Dim nTry        As Long     ' number of trials
    Dim iTry        As Long     ' index to trials

    With Application
        .Calculation = xlCalculationManual
        .ScreenUpdating = False

        nTry = Sheet1.Range("Trials").Value
        Set rCal = Sheet2.Range("rgnCalc")
        Set rInp = Sheet2.Range("rgnInp")
        Set rOut = Sheet1.Range("rgnOut")
        rOut.ClearContents

        For iTry = 1 To nTry
            rCal.Calculate
            rInp.Copy
            rOut.PasteSpecial Paste:=xlPasteValues, _
                              Operation:=xlPasteSpecialOperationAdd, _
                              Transpose:=True
        Next iTry

        Sheet1.Range("Trials").Copy
        rOut.PasteSpecial Paste:=xlPasteValues, _
                          Operation:=xlPasteSpecialOperationDivide

        .CutCopyMode = False
        .Calculation = xlCalculationAutomatic
        .ScreenUpdating = True
    End With

    Beep
End Sub

Function ProbRun(n As Long, r As Long, p As Double)

' Probability of a r or more consecutive heads in n tosses
' of a coin having probability p of heads

    Dim prob(100)           As Double   'size of max r
    Dim c                   As Double
    Dim iter                As Long
    Dim last                As Long
    Dim i                   As Long
    Dim j                   As Long
    
    iter = n \ (r + 1)
    last = n - iter * (r + 1)

    c = (1 - p) * p ^ r

    prob(r) = p ^ r
    For j = 1 To iter
        prob(0) = prob(r) + (1 - prob(0)) * c
        For i = 1 To r
            prob(i) = prob(i - 1) + (1 - prob(i)) * c
        Next i
    Next j
    
    ProbRun = prob(last)
End Function

I'm familiar with that paper. The formula is correct, but it is starting to look
like it's an ill-conditioned calculation. The roundoff error is inherent to the calculation, not to Excel or VB.

[=0]"0 %";[=1]"100 %";0.0%