Rick';s "Fundamental Theorem of Disagreement" (version 0.1)

[Rick Nebiolo]

My friend and budding superstar mike l. and his minions disagree with me regarding a post he made a day or two ago. The pivotal point in his post was his turn play (which we all loved), but while looking at the hand I questioned his flop call.

In reality I think his flop call would have been fine if he could have made it for about 60% of a small bet. He and most others who found the post think it was a clear call. For arguments sake let's say his supporters believe that his flop call has a positive expectation of about half of a small bet. The difference between our estimates is significant since knowing when to take one off on the flop after several callers is an important skill if you want to be a winning player.

Now in a day or two I hope to fairly restate the flop play in a lead post to solicit more opinions. Maybe that will resolve the question, maybe it won't. Which leads to my "Fundamental Theorem of Disagreement". Now the more astute among you may realize that this is neither fundamental nor a theorem (this line is stolen from an old Abdul Jalib post regarding Sklansky's "Fundamental Theorem of Poker") but that won't stop me. It is late, I'm wired, and I need to bore myself to sleep.

Anyway, an example might help explain my theorem.

Let's say Dynasty and Clarkmeister disagree on a poker problem for a given street where all the important parameters can be clearly stated. Dynasty thinks the correct play is to call and he believes it isn't even close. Clarkmeister believes the correct play is to fold but it is close between calling and folding (for this example let's pretend raising isn't a valid alternative). They post the problem and because they are both respected posters and Pooh Bahs (sp?) all the best minds (obviously not me) on 2+2 perform an analysis. The consensus is that the correct play is calling, but calling is only slightly better than folding. Now Dynasty thought that a call was the correct play, but he didn't recognize that folding was almost as good a play. Clarkmeister incorrectly thought folding was the best play, but he recognized the play was close.

Clearly, Clarkmeister was "more correct" in his analysis. My theorem of disagreement is "when two players disagree regarding the correct play, the player who comes closest to the correct answer is "more right"; even if he had the incorrect absolute answer" (I need to work on the wording for version 0.2).

I'm concerned regarding my opinion regarding mike l.'s flop play. Mike is beating the heck out of the bigger 40/80 to 100/200 games (while I beat the heck out of the 10/20 to 20/40). Because he plays bigger and is clearly smarter, his opinion should have more validity.

OTOH, he may be beating the bigger game despite his tendency to make weak flop overcalls (or because the chance to make flop overcalls doesn't come up often). Or I may be beating the games despite my reluctance to take one off (which comes up often at the lower middle limits, therefore the answer may be more important to me). We both seem to think our choice is clear, and we can't both be right. If it turns out that the expert consensus indicates that the correct play is to fold but it is very close, then mike l. and I are about equally right (or wrong). But it matters more to us lower mid limit players, because the situation comes up so often.

Which is why I plan to repost the problem in a day or so [img]/images/graemlins/grin.gif[/img]

~ Rick

[anatta]

I dig what you are saying especially the part about it being late, wired, and boring myself to sleep...

I agree with you that Clarkmeister would be more correct then Dynasty since he was closer to the right answer and although his fold cost him a small amount of EV on that hand, on the subsequent 1000000 hands, Clarkmeister's analysis that made him just miss the right answer will serve him better than Dynasty's flawed analysis that gave him the wrong answer.

An expert can be confronted with a very complicated situation, and factor in all sorts of conflicting concepts, but make a small mistake which leads to a decision which is actually slightly -EV. A monkey can be faced with the same decision and make the correct play.

On Mikel.'s call and whether folding is correct on his hand, I think a clear call for Mikel. can be a close play for someone else, and even a mathmatically correct fold. Like Tommy and his infamous tight SB play which Sklansky says sucks, I think, and some may disagree, that poker is more than just making the absolute correct play. Its the flow and feel of your Mojo as someone called it. Mikel. is a mojo machine right now, running good for the last 8 months, playing bigger and bigger, getting involved, gamblin it up, reading, raising, raising, reading...of course I am calling I got top pair, I will kick their asses with a great turn raise, check it out. Then I will wimp out on the river and think I play goot. [img]/images/graemlins/tongue.gif[/img]

[Tommy Angelo]

Rick,

What I'm seeing from your words looks like a number line with gradations of correctness and incorrectness of a specific betting decision. At zero is the betting decision itself. Let's say the options are check and bet. Left of zero is check. Right of zero is bet.

To the right and left of zero, the numbers 1, 2, 3 ... and -1, -2, -3 ... indicate degrees to which "call" and "bet" are deemed to be correct or incorrect.

When we get a final answer from an agreed upon authority, we ask them to not only tell us the correct play, but also, by how much it is correct, and then we plot the answer on the number line, and see which of us is closer.

(This a lot of specificity to ask from phrase like "not close, not even close, really serious now it's not even remotely close, etc." But that's another thing. Back to the number line.)

Let's say I say the answer to a question is -2, and you said it is +12. And the correct answer, as it turns out, is +1. I missed by 3. You missed by 9. But you had the right answer. Who wins the prize?

Am I close?


Tommy

[stoxtrader]

why not simply assign fractional bet amounts to the amount of correctness? that is, afterall the point at which we are all trying to get.

[chezlaw]

[ QUOTE ]
Clearly, Clarkmeister was "more correct" in his analysis. My theorem of disagreement is "when two players disagree regarding the correct play, the player who comes closest to the correct answer is "more right"; even if he had the incorrect absolute answer" (I need to work on the wording for version 0.2).

[/ QUOTE ]

I think this is mistaken. In your example you have two players who have made a mistake in their analysis. You then look at the results of their faulty analysis and decide which result you think is closer to the correct answer and then say the closest one had the best reasoning.

But it may be that the one who got closest made a conceptual error and got lucky while the other had the right concepts but made an arithmetic mistake. Which one had the best reasoning then?

chez

[andyfox]

"when two players disagree regarding the correct play, the player who comes closest to the correct answer is 'more right'; even if he had the incorrect absolute answer"

Dynasty says call and it isn't close: you'll be +$100 if you call; Clarkmeister says fold, but it's close: you'll be -$10 is you call. Turns out the answer if call, but it's close: you'll actually be +$10 is you call. Dynasty is $90 off, but he calls and makes $10. Clarkmeister was much closer to being correct, only $20 off, but he does not make the $10. He's "closer" to being correct, by your definition, but worse off because he made the wrong decision.

Tommy's continuum is key here, I think. While the closeness of their answers can indeed be measured along that continuous line, poker actions are not so structured. One can't call 60% of a small bet. In limit poker, you either fold, call, or raise a specified amount. If a call is only slightly correct, rather than "it isn't close," it's still correct and the player who calls, rather than folds, is better off despite being farther away from the absolutely correct answer.

[Rick Nebiolo]

[ QUOTE ]
Let's say I say the answer to a question is -2, and you said it is +12. And the correct answer, as it turns out, is +1. I missed by 3. You missed by 9. But you had the right answer. Who wins the prize?

[/ QUOTE ]

You win and you are helping me get to version 0.1.1 [img]/images/graemlins/wink.gif[/img].

Sometimes when I show Hero a problem from an important post the focus of the post is a decision on a betting street. Often enough the decision is one of two choices i.e., call versus raise, call versus fold, or perhaps bet versus check with the intention of checkraising.

In the case of call versus raise she might say "of course I'll raise" (Hero does not lack aggression) and I might respond "No, I think it is a call but the decision is very close."

Next I might ask "Did you consider a call?" When she says no I might respond "Let's see what the experts think." So we read the responses from mike l., Dynasty, Ikke, Clarkmeister, Tommy Angelo, skp, and all the other bright minds and try to find a consensus.

The consensus averages out to be raise but not by much. You know it is close because Sklansky chimes in that "Since it is a close decision, the decision is not important. Concentrate on the turn play!". (BTW, I would respond to David that it is important if it is in fact close but you don't think it is close (because this indicates you have major flaws in your thinking).

~ Rick

PS You were kidding in your first response to mike l., right?

[Rick Nebiolo]

[ QUOTE ]
why not simply assign fractional bet amounts to the amount of correctness? that is, afterall the point at which we are all trying to get.

[/ QUOTE ]

This is a good idea. In mike l.'s "60-120 hand Th3h" thread the turn was the key play but the flop decision was were I had a quibble (and it is an important quibble because it may identify a trend were either I'm much too unwilling to take one off on the flop in a big pot or mike l. is all too willing).

For those of you who said "call", I could ask "How much would you be willing to call before the price is too high?" They could ask, "How much of a discount would you need to be willing to call?"

For these simple situations you would arrive at a better answer than what you get when people (like me) say "I just don't make these kind of overcalls on the flop." or when mike l. says "folding top pair backdoor draws here is out of the question."

~ Rick

[Rick Nebiolo]

[ QUOTE ]
I dig what you are saying especially the part about it being late, wired, and boring myself to sleep...

[/ QUOTE ]

The melatonin recently recommended on the "Other Topics" forum has been helping too. Plus it generates cool dreams.


[ QUOTE ]
"I agree with you that Clarkmeister would be more correct then Dynasty since he was closer to the right answer and although his fold cost him a small amount of EV on that hand, on the subsequent 1000000 hands, Clarkmeister's analysis that made him just miss the right answer will serve him better than Dynasty's flawed analysis that gave him the wrong answer.

An expert can be confronted with a very complicated situation, and factor in all sorts of conflicting concepts, but make a small mistake which leads to a decision which is actually slightly -EV. A monkey can be faced with the same decision and make the correct play.

[/ QUOTE ]

And I'd add the obvious - the expert will do better in the long run than the monkey, although not for this hand. Then I'll tell Andy Fox below to look at your response [img]/images/graemlins/smirk.gif[/img]


[ QUOTE ]
On Mikel.'s call and whether folding is correct on his hand, I think a clear call for Mikel. can be a close play for someone else, and even a mathematically correct fold. Like Tommy and his infamous tight SB play which Sklansky says sucks, I think, and some may disagree, that poker is more than just making the absolute correct play. Its the flow and feel of your Mojo as someone called it. Mikel. is a mojo machine right now, running good for the last 8 months, playing bigger and bigger, getting involved, gamblin it up, reading, raising, raising, reading...of course I am calling I got top pair, I will kick their asses with a great turn raise, check it out. Then I will wimp out on the river and think I play goot. [img]/images/graemlins/tongue.gif[/img]

[/ QUOTE ]

No question that a mentally tough, knowledgeable, aggressive, smart bully, "in your face so every opponent is half tilted", super card reader mike l. can play more hands and take more cards off than let's say me. But in the hand in question, I don't even think mike l. had a flop call (unless he could have gotten about a 1/3 of a small bet discount). He seems to think the call was so correct that I imagine he would have paid more than a small bet (had he been forced to pay a surcharge). I wonder how much more [img]/images/graemlins/wink.gif[/img].

~ Rick

[Rick Nebiolo]

[ QUOTE ]
Rick wrote:"when two players disagree regarding the correct play, the player who comes closest to the correct answer is 'more right'; even if he had the incorrect absolute answer"

Dynasty says call and it isn't close: you'll be +$100 if you call; Clarkmeister says fold, but it's close: you'll be -$10 is you call. Turns out the answer if call, but it's close: you'll actually be +$10 is you call. Dynasty is $90 off, but he calls and makes $10. Clarkmeister was much closer to being correct, only $20 off, but he does not make the $10. He's "closer" to being correct, by your definition, but worse off because he made the wrong decision.

[/ QUOTE ]

Clarkmeister is worse off for this hand only. If the pattern continues where one player continuously evaluates situations more correctly, in the long run he will come out ahead (even if he didn't this time).

[ QUOTE ]
Tommy's continuum is key here, I think. While the closeness of their answers can indeed be measured along that continuous line, poker actions are not so structured. One can't call 60% of a small bet. In limit poker, you either fold, call, or raise a specified amount. If a call is only slightly correct, rather than "it isn't close," it's still correct and the player who calls, rather than folds, is better off despite being farther away from the absolutely correct answer.

[/ QUOTE ]

For the purpose of evaluating the correctness of a call versus fold decision, you can certainly ask the folder "How much of a discount would you need to call?" and ask the caller "How much extra would you be willing to pay before you would now fold?

Anyway, look at anatta's post and my reply elsewhere in this thread. I mentioned your name in vain [img]/images/graemlins/grin.gif[/img]

~ Rick