P(getting Pi correct to n digits after x trials)?

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moonman239
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I would like to know how confident I can be in my Monte Carlo estimate of Pi, plus/minus a specified margin of error. I know the locations of the "pins" are uniformly distributed, thus P(pin being within circle's radius) = P(x <= radius) * P(y <= radius)
 

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Here are four links:

1) http://answers.yahoo.com/question/index?qid=20080107132917AAxtMth", Yahoo Answers
If you take N=100 dots you get an approximate value for pi, e.g. 3.241. Repeat this e.g. 20 times and have 20 approximate values for pi. For these 20 values you can calculate the standard deviation.

2) "www.evsis.org/docs/tdpp2_chap1.pdf"[/URL]
On page 4 to 6 of the document you will find a pseudo-code to calculate the variance and standard deviation.

3) [PLAIN]http://www.physics.sc.edu/~yar/phys309_2010/calculating_Pi/Pi_report.htm" )
This website talks about how many dots you need to ensure a certain number of correct digits.

4) http://mathforum.org/library/drmath/view/51909.html", Math Forum
This article discusses the standard deviation and confidence interval.
 
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I just gave myself a dopeslap for not thinking about using the standard deviation formula.