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Old 08-15-2005, 08:15 PM
elitegimp elitegimp is offline
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Join Date: Apr 2004
Location: boulder, CO
Posts: 14
Default Re: Another Boredom Filler

I don't know if you can actually claim independence, but for any specific point in your count, there are 48 cards that don't match and 52 that do... so there's a 12/13 chance you don't match a specific time. 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.

The other thing I was gonna do was to just count the possible deck combinations, but that seems like a lot more work.

edit: what I want to know is what the expected number of cards you get through before the card = count... I've tried 5 times (sample size warning!!!) and didn't get past the 22 card any of those times.

edit 2: If my probability calculation is right, then
P(count = card i | no match in first i-1 cards) = (12/13)^(i-1) * (1/13) => P(get through the deck) = 1 - Sum (from i = 1 to 52) (12/13)^(i-1)*1/13 = 0.01557 as above

So EV = Sum (from i=1 to infinity... assuming an infinite deck so that eventually count = card) i*(12/13)^(i-1)*(1/13) = 12

So in the long run, you should average going through 12 cards per time (if I'm right, which is a big assumption)
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