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Originally Posted by AaronT
I'm saying those things do significantly impact card removal effects of broadway cards, yes. Just consider heads up vs. full ring. Think for a moment about how many hole cards ARE there heads up vs. a family pot into the flop full ring...
When I first started learning this game, I had a common conceptual problem shared by many beginners. When someone would count the outs after a flop for, say, a flush draw, they would say something like, "Okay, you have 9 outs so your probability of hitting on the turn is 9/47," and I would always think, "Wait a minute! What about everybody ELSE'S cards? There are 8 other people at the table and they each have two cards, so there are only 31 cards left in the deck, not 47."
But every reference I found used 9/47 no matter how many people were at the table. It finally penetrated into my brain that it wasn't the remaining cards in the deck we cared about. What we really wanted to know was the probability that, of all the unknown cards, one of the ones I needed happened to be sitting on top of the remaining deck. Since the unknown cards included everybody else's hole cards, then it really didn't matter how many people were at the table. There could be so many people at the table that the deck only had 2 or 3 cards left, and the probability would still be 9/47, just like always.
Spadebidder seems to have discovered that there is a real, though extremely small, card removal effect for high cards. But I'm having a hard time seeing how that's related to the number of people at the table.
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For full discloser my degrees are in computer science and economics. I'm close to a math degree as well (as well as physics.) So I can dabble in the maths. My lack of qualification in answering your question comes from the fact that your question was how STRONG the card removal effect should be. That's a poker question, not a math question.
Well, you're plenty qualified in my book.
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I think maybe what suprised you about the standard deviation fall between the use of all pocket pairs and just 9's or below had more to do with the fact that the smaller sample size is going to reduce the number of standard deviations of its own accord EVEN IF THERE WAS NO CARD REMOVAL EFFECT. If some other pheonomon explains it the smaller sample size has it explaining it over a smaller "time frame" so it's less "bizzare."
My only intention in originally replying to you was to help point out to you some of you possible source of error.
For which I am thankful. I would rather have my errors pointed out to me than to go on making erroneous conclusions because of them.