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General Gambling >> Probability

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Troll_Inc
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Reged: 03/18/06
Posts: 2566
Loc: FGHIJKLM STUVWXYZ
Re: farha vs PA, hsp episode 14 [Re: sixhigh]
#13193296 - 11/30/07 08:46 PM

Quote:

I don't get it Troll, you post a lot here and obviously have no idea what you're talking about. wtf?

Of course the variance approaches zero with many runs.

Say you have a \$100 pot, are all-in and have 50% equity. If you run it once you will have a variance of 2,500 (or SD of \$50). If you run it twice you will have a variance of 417 (SD=\$20). And if you run it 4 times you will have a variance of 125 (SD=\$11).
And that looks pretty quick to me.

Are you retarded or is English not your native language?

Variance of 125 does not equal 0.

And the original point I was responding to was the person used the word infinity and then talked about going to zero quickly. This is also a retarded statement.

I think you are the nitwit that backed down last time I challenged you on one of your statements.

I tell you what don't post here for a week and put together a cogent argument about how all-in variance goes to zero "quickly".

I'll do the same and show everyone why you are the probable retard, not me.

You up for the challenge? Or is your talk cheap?

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pzhon
Carpal \'Tunnel

Reged: 03/23/04
Posts: 4515
Re: farha vs PA, hsp episode 14 [Re: sixhigh]
#13194992 - 11/30/07 11:21 PM

Quote:

I don't get it Troll, you post a lot here and obviously have no idea what you're talking about. wtf?

He's a troll, someone who makes provocative, stupid posts. It's hard to tell when he is being intentionally stupid for the entertainment value. My guess is that this greatly decreases the level of feedback he gets, since no one wants to try to help him only to hear that he was just pretending to make that mistake, and is now laughing at them for believing him. I've ignored many incorrect statements of his because I didn't know whether he meant them, or just thought it was funny to try to contradict a mathematician whenever possible.

Quote:

Of course the variance approaches zero with many runs.

Yes.

Quote:

Say you have a \$100 pot, are all-in and have 50% equity. If you run it once you will have a variance of 2,500 (or SD of \$50). If you run it twice you will have a variance of 417 (SD=\$20). And if you run it 4 times you will have a variance of 125 (SD=\$11).

These calcluations are a bit off. The variance drops by a factor of n^2 in each pot when you run it n times. If the runs were independent, that would mean the total variance would be n/(n^2) or 1/n times the variance of running it once. Since the runs are anti-correlated, the actual variance of running it n times is slightly under 1/n times the variance of running it once. The standard deviation is reduced by about 1/sqrt(n). The exact extent of the anti-correlation depends on the hands.

Troll did make a tangentially relevant point, whether he meant to or not, that all-in variance is only part of the overall variance you experience when playing poker. (His analysis in the other thread was bad, however.) If you find someone who is happy to run each all-in situation 5 times, this will cut your all-in variance, but you will still experience large swings based on how frequently you get good hands, and how frequently your opponent gets good hands, and which hand is better when you both get good hands. However, when you are all-in, you can reduce the variance on that hnd quite a bit by running it multiple times.

As has been discussed in the Poker Theory forum recently, there are many other effects in practice when you run a hand multiple times, since it may affect the stack sizes in subsequent hands, and it may have metagame effects when you play against risk-averse players.

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Troll_Inc
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Reged: 03/18/06
Posts: 2566
Loc: FGHIJKLM STUVWXYZ
Re: farha vs PA, hsp episode 14 [Re: pzhon]
#13195611 - 12/01/07 12:22 AM

Phzon,

Do you play poker at all? If so, is it limit?

Because it seems that you lack empirical experience.

You are certainly smart enough with the math but once it comes to real situations the formulas that you learned seem to fail you.

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pzhon
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Reged: 03/23/04
Posts: 4515
Re: farha vs PA, hsp episode 14 [Re: Troll_Inc]
#13195932 - 12/01/07 12:56 AM

Quote:

Phzon,

Do you play poker at all? If so, is it limit?

Because it seems that you lack empirical experience.

That is ad hominem. You have lost the argument, so you are trying to disparage me. You are speculating that because I have an obvious strength, I must have some weakness which means my advice is suspect, or which at least gives you some reason to feel superior despite losing. How pathetic your world must be if every strength is paired with such a flaw, and if you must constantly insult people whenever you make a mistake.

Your wild speculation is wrong. I have plenty of experience playing both NLHE (and PLO) and limit, as my hundreds of posts on NL strategy, many involving hands I have played, should have indicated to you had you bothered to check instead of making a fool of yourself by speculating publicly.

By the way, do work on copying 5 letters in order even if you can't figure out what they mean.

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Troll_Inc
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Reged: 03/18/06
Posts: 2566
Loc: FGHIJKLM STUVWXYZ
Re: farha vs PA, hsp episode 14 [Re: pzhon]
#13196025 - 12/01/07 01:06 AM

Quote:

He's a troll, someone who makes provocative, stupid posts.

It's hard to tell when he is being intentionally stupid for the entertainment value.

phzon,

Are these attacks without support?

The problem for you if you choose to deviate from your math is that I will own you if it only attacks.

As far as the substantive part of this thread, the best part is that you agree with me.

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Troll_Inc
abcdefgh nopqrstu

Reged: 03/18/06
Posts: 2566
Loc: FGHIJKLM STUVWXYZ
Re: farha vs PA, hsp episode 14 [Re: pzhon]
#13196106 - 12/01/07 01:14 AM

Quote:

That is ad hominem. You have lost the argument

Just to be clear of my intellectual superiority over you....

What argument did I exactly lose in this thread?

Apparently another problem of yours is that your arrogance blinds you such that you are incapable of framing a logical argument.

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pzhon
Carpal \'Tunnel

Reged: 03/23/04
Posts: 4515
Re: farha vs PA, hsp episode 14 [Re: Troll_Inc]
#13196443 - 12/01/07 01:49 AM

Quote:

Quote:

That is ad hominem. You have lost the argument

Just to be clear of my intellectual superiority over you....

What argument did I exactly lose in this thread?

You are so confused that you have lost track of what you were saying before the ad hominem? How is that supposed to demonstrate your superiority?

You said, "I tell you what don't post here for a week and put together a cogent argument about how all-in variance goes to zero "quickly". " I explained that the variance is bounded above by c/n. Whether you believe it or not, it is quite reasonable to describe that as "going to 0 quickly."

Your statement, "it doesn't even lower the variance that much," is wrong in the context where it is most naturally interpreted, the variance of the hand under discussion. Running it 4 times (as they did on that hand) cuts the variance to less than 1/4 as much.

Quote:

Apparently another problem of yours is that your arrogance blinds you such that you are incapable of framing a logical argument.

More ad hominem. One meaning of arrogance is an irritating, unjustified belief in one's superiority. Which of us is exhibiting that here? The mathematician who is making correct mathematical statements, or the one who is insulting people left and right when they point out he is wrong about basic mathematical ideas like limits?

Is your game selection this bad in poker, too? When you meet people who know a hell of a lot more than you, that is a great opportunity for you to learn something. It's not a good time to raise the stakes, insist that you are right, and that you are (incorrectly) convinced you are smarter and that other people are retards, etc. What you are displaying is willful stupidity and unpleasantness. Are you this way every time you are wrong?

You're boring me. I can't tell which of your posts are intentionally stupid, and which are accidentally stupid. I can tell I don't want to waste any more time trying to help you. I'm going to ignore you henceforth.

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Troll_Inc
abcdefgh nopqrstu

Reged: 03/18/06
Posts: 2566
Loc: FGHIJKLM STUVWXYZ
Re: farha vs PA, hsp episode 14 [Re: pzhon]
#13196841 - 12/01/07 02:30 AM

Running it 4 times does lower the variance almost exactly 1/4 but that is still "not much" for the metric that matters, namely the net result of playing poker.

The reason is that it is still way above the average winrate.

This is what I mean about not thinking about the problem at hand. You get caught up in your formulas and don't think things through.

So in summary for those that care about the right answer, if you ran into this situation one hundred times and had the choice between running it once or running it four times, it doesn't matter which method you chose because you wouldn't be able to tell the difference.

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