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To not match 52 times would therefore just be (12/13)^52, or 0.01557 (1.557% chance you make it through the deck). That works out to approximately 1 in 64.214, or 63.214:1.

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This is only an approximation. I believe you'll need the inclusion/exclusion method to get an exact count...and I'm not sure that's all that's involved, or that it's even remotely as simple as that.

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Yes, that person was incorrect on nearly all of their statements including parts you didn't quote.

LetYouDown, did you just come up with that problem or did you see it somewhere? Also, what do you do for a living (if that's not too personal)? I've noticed that you seem to answer many of the people's questions.

By the way, I'm still interested in the analytical solution. If anyone could show it to me I would be impressed.