[PairTheBoard]

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BillC --
The infinite and infinitesimal often lead to paradoxes

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What paradoxes?


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BillC --
(Aside: in a one-dimensional random walk, you will return to zero with probability one. This also true for a 2-dim random walk; but it fails for higher dimensions. (The probability of return to origin is called the Polya number) So maybe it is better to keep >2 independent bankrolls...).


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What do 2 or higher diminsional random walks have to do with the subject at hand and where in the world do you come up with the idea of 2 or more independent bankrolls? Are you trying to clarify things or obfuscate them?



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BillC --
Just to recap: In games of great skew, you need to use a more precise calculation to determine ROR and bankroll. It would seem apt to ask what BR would be needed to enter a big poker tournament, e.g WSOP, assuming you are a somewhat above average player. It has to be huge.


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What are you recapping? You are now introducing something new. Why are you talking about Skew? The applicable principle in tournament poker affecting ROR is Variance.



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BillC --
The question of applying the Central Limit Theorem always dogs these sort of applied random walk models. It seems that the way out are error bounds involving higher moments as in the article by Stu Ethier (et. al) (thanks for the link BruceZ). Unfortunely the math gets way beyond the ken of most. They just have to trust us. The normal approximation is OK for poker.


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Evidently the math is a bit beyond your ken as well or you would not have used the word "seems" in this sentence,

"It seems that the way out are error bounds involving higher moments as in the article by Stu Ethier (et. al)"



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BillC --
Sileo's derivation was just an explanation for the gambling conference of math that is really old, almost as old as stochastic analysis itself. The gambling conference proceedings are not refereed and are below the standards of academic math journals. You can say anything. They have published pure bunk. That is not to say that Sileo is wrong, he just reivented the wheel, and explained it for non-math people like Don Schlesinger and the BlackJack community.


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So even though Sileo's work is correct you find it relevant to point out that it's not original and take the opportunity to blast the gambling conference of math for being academically substandard, with the hyperbole that "You can say anything" there. Really.



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BillC --
Final note: if you bet more than 2 times Kelly, your win rate will be negative.

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Interesting. If you're playing with an edge and you bet more than 2 times Kelly, your win rate suddenly becomes negative. Maybe you should present that at the next gambling conference of math. They'll probably go for it. I hear you can say anything there.

PairTheBoard