[DougOzzzz]

I haven't tried to understand your post yet explaining your method for solving the problem

I can speak for Excel's RNG being crappy though. There are some very obvious patterns if you analyze a large sequence of randomly generated numbers. I almost always get incorrect answers when I write simulations in Excel even with millions of trials.

Still, it seems a bit strange that BruceZ's method could be so far off. I understood his method, and it makes sense. The flaw in the method also makes sense, and logically I concluded that the error would cause the odds to increase.

However the difference still seems large. I'll try to understand your method at a later time. I don't have as much mathematical training as most of you here so sometimes it's difficult for me to translate these formulas into something that makes sense to me.

I do appreciate the effort that everyone put into answering my question, though.