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Old 01-06-2005, 05:43 PM
Grendel Grendel is offline
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Join Date: Oct 2004
Location: Chasing flooshes
Posts: 94
Default Re: Help with the math, or do I get an aluminum hat

Well, the probability of pairing at least one of two random cards on the flop is
1-(44/50)*(43/49)*(42/48) = 32.4%

Your results certainly are tainted because of the reasons you mentioned, especially because if you hold two high cards (and likely raise), you're more likely to see the flop if someone else also has high cards. That is, your chances of pairing AQ is less than 32% when someone else has KQ. Also, does your 30/170 stat include the times you flopped two pair or trips? Just to make the math easier, I'll assume that it does, but you might want to check that.

Given that the probability of flopping a pair is 32.4%, the probability of pairing exactly N times out of 170 tries is:

nCr(170,N) * (.324)^N * (1-.324)^(170-N)

Now if we sum up the results from N=0 to N=30, we get... 0.0012%. Wow, that's 1-in-83,000 aluminum foil hat time. Help me, did I do something wrong here?

Yikes. Now if we assume that one of your opponents always has one of your two cards, the odds of your flopping a pair drop to
1-(44/49)*(43/48)*(42/47) = 28.1%

And summing N=0..30 of
nCr(170,N) * (.281)^N * (1-.281)^(170-N)
Is 0.1077%. There's your 1-in-1000 streak.

Before I run out and buy a roll of aluminum foil myself, how often did you flop two pair, trips, or quads with your hands?

-Grendel
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