Am I stupid? I can't fit these two concepts into any type of harmony. - Page 5

xniNja · #41 08-27-2005, 04:29 AM

Well, my take on this topic is I feel once you claim you are playing infinitely, not only do you potentially become infinite, but so do your chips. If you have a 3 BB/100 advantage, it's conceivable you could exist infinitely, and win infinitely, thus having infinite chips. It's also conceivable despite a 3 BB/100 advantage, over an infinite number of hands, despite how much you were up or down, that you could receive a streak bad enough to break you. I don't think any particular % probability can be associated with that chance on infinite trials.

PairTheBoard · #42 08-27-2005, 06:17 AM

[ QUOTE ]
Well, my take on this topic is I feel once you claim you are playing infinitely, not only do you potentially become infinite, but so do your chips. If you have a 3 BB/100 advantage, it's conceivable you could exist infinitely, and win infinitely, thus having infinite chips. It's also conceivable despite a 3 BB/100 advantage, over an infinite number of hands, despite how much you were up or down, that you could receive a streak bad enough to break you. I don't think any particular % probability can be associated with that chance on infinite trials.

[/ QUOTE ]

You do not understand the mathematics.

PairTheBoard

BillC · #43 08-27-2005, 11:36 AM

For those people in this thread sporting a conundrum withering in a cloud of mental haze (or are 6 years old), let me say that the way out is to do the math. The infinite and infinitesimal often lead to paradoxes. Figure out the risk of ruin in 1 bet, n bets, and then ask what happens as n gets big. That is the way to balance your expected increase in bank vs the risk of a downturn. That is assuming you have an advantage; for a pure coinflip, you will always go broke. (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...).

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.

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.

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.

Final note: if you bet more than 2 times Kelly, your win rate will be negative. You will never go broke with fractional betting. But you will asymptotically go to zero.

PairTheBoard · #44 08-27-2005, 01:06 PM

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BillC --
The infinite and infinitesimal often lead to paradoxes

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What paradoxes?

[ QUOTE ]
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...).

[/ QUOTE ]

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?

[ QUOTE ]
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.

[/ QUOTE ]

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.

[ QUOTE ]
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.

[/ QUOTE ]

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.

[/ QUOTE ]

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

David Sklansky · #45 08-27-2005, 07:02 PM

"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

Except that I believe he is right. (But don't confuse that with the statemnet that the expected value of your bankroll will go down.)

PairTheBoard · #46 08-28-2005, 05:32 AM

[ QUOTE ]
"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

Except that I believe he is right. (But don't confuse that with the statemnet that the expected value of your bankroll will go down.)

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What do You mean by "win rate"?

PairTheBoard

BillC · #47 08-28-2005, 08:47 PM

How about this for a paradox (response to PairtheBoard or his evil twin):

You are offered the following set up. A fair coin is flipped until it first comes up heads, say on the nth flip (n=1,2,...), at which point you are paid 2^n dollars and the game ends. The instantaneous flips are timed as follows: the nth flip occurs exactly 1/2^n minutes after the previous flip for n>1 and the first flip (n=1) takes place 1/2 minute after the start of the game. The game is over in less than 2 minutes. Do you see why?

How much is this game worth to you?

PairTheBoard · #48 08-29-2005, 06:31 AM

[ QUOTE ]
How about this for a paradox (response to PairtheBoard or his evil twin):

You are offered the following set up. A fair coin is flipped until it first comes up heads, say on the nth flip (n=1,2,...), at which point you are paid 2^n dollars and the game ends. The instantaneous flips are timed as follows: the nth flip occurs exactly 1/2^n minutes after the previous flip for n>1 and the first flip (n=1) takes place 1/2 minute after the start of the game. The game is over in less than 2 minutes. Do you see why?

How much is this game worth to you?

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The expected value of the game is infinite. So? If this is a series of questions please just go to the end and state your point.

As far as your previous post goes, what do You mean by "Rate of Return" in the scenario of playing with an edge and betting twice the Kelly criteria. You say the Rate of Return is negative. What do you mean by "Rate of Return"?

PairTheBoard

PairTheBoard · #49 08-29-2005, 07:35 AM

Correction to my last post. The last paragraph should read:

'As far as your previous post goes, what do You mean by " Win Rate " in the scenario of playing with an edge and betting twice the Kelly criteria. You say the Win Rate is negative. What do you mean by " Win Rate "?'

PairTheBoard

PairTheBoard · #50 08-29-2005, 09:23 AM

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BillC --
<font color="white"> .
</font>Final note: if you bet more than 2 times Kelly, your win rate will be negative. You will never go broke with fractional betting. But you will asymptotically go to zero.

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Is your meaning of the term "Win Rate" the same as BruceZ's when he said this?

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BruceZ --
<font color="white"> ,
</font> The ROR formula that I linked to is derived by assuming that the game with skewed payoffs can be modeled as a coin flip game with the same win rate and variance via the central limit theorem. There may be games for which this model breaks down, but it works well for blackjack and poker, and any game for which the risk of ruin depends primarily on the win rate and standard deviation, and very little on the higher moments.

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PairTheBoard