The \"Emperor\'s nose\" fallacy & poker
 

This is a classic logical fallacy that all poker players need to be aware of, because it appears so often in poker reasoning.

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According to legend, there was a Chinese peasant who wanted to know how long the Emperor's nose was. However, law forbid him from going to court and gazing on the royal beak directly. So instead he asked everyone he knew how long the emperor's nose was, and averaged the answers. He was very proud of the result - being the average of so many answers, it must be highly accurate. It even had nice properties of numerical stability - it wasn't heavily influenced by any one person's response. As such, the peasant was very surprised and felt more than a little silly when the emperor traveled through the village and his nose bore no resemblance to the averaged result.


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The point of this, of course, is that averaging numerous inaccurate values gives you an accurate value if and only if the inaccurate values are distributed such that their mean is in fact the accurate value. In the peasant's case, since everyone he asked was as ignorant of the Emperor's nose as he was, there was no such guarantee, and his result was worthless no matter how many people he asked.

This fallacy usually shows up in poker when reasoning using hand ranges. Here, you calculate the equity you and your opponent would have for each candidate hand, and then average. However, what you should know is that this average is inaccurate unless the candidate hand range more or less brackets (In terms of equity) the actual hand he has. You would hope this is the case, but often it is not. In particular, when someone tries to use a "sufficiently large" hand range, they are usually able to add only more weak hands, because all hands up to the nuts have already been included in the range. And as such, as the range is expanded, your "average" equity inevitably goes up. You might think that, by averaging more hands, the result becomes more accurate, but instead it just becomes more optimistic. By following this line of reasoning you can almost always find a call in any scenario where the FTP says you should fold. In other words, it's nothing more than a very mathematically complicated justification for calling station behavior.

Moral of the story: beware hand range math, and be doubly concerned about a wide range, and be triply concerned when someone widens the range to find a call. Like that Chinese peasant, you'll feel pretty silly when villain flips over the solid hand you should have known he had.

Re: The \"Emperor\'s nose\" fallacy & poker
 

In case anyone is curious, SplawnDart's post was inspired by the exchange in this thread . He disagrees with the result of a poll that was posted; whether asking random readers of the O8 forum to estimate a villain's chance of holding certain cards is actually an example of the fallacy I leave to you to decide...

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
In case anyone is curious, SplawnDart's post was inspired by the exchange in this thread . He disagrees with the result of a poll that was posted; whether asking random readers of the O8 forum to estimate a villain's chance of holding certain cards is actually an example of the fallacy I leave to you to decide...

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That actually wasn't the motivating example, although it did remind me of this particular fallacy and is an example. Obviously it's the more classic "averaging a bunch of people's answers" version rather than the poker-specific hand range math version.

That said, there's at least one OTHER example of this fallacy in that thread. So it is still of interest.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Nice post! I see it all the time too. People talk themselves into overcalling, or raising no matter what is happening during the round. Then when they are crushed at the river, they get this surprised 'how did that happen????' look on their face....

Re: The \"Emperor\'s nose\" fallacy & poker
 

I agree, and am surprised at the amount of flak I get in the uNL forum for taking this stance. I think the issue is that many new players have a terrible misconception about the idea of a "non-thinking" player. They seem to labor under the assumption that such a player uses absolutely no criteria or thought process whatsoever when making the decision to call, raise, or fold and therefore use range calculations as a merciful shortcut instead of going through the sometimes agonizing task of discerning the sometimes bizarre and baffling thought processes of bad poker players.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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I agree, and am surprised at the amount of flak I get in the uNL forum for taking this stance. I think the issue is that many new players have a terrible misconception about the idea of a "non-thinking" player. They seem to labor under the assumption that such a player uses absolutely no criteria or thought process whatsoever when making the decision to call, raise, or fold and therefore use range calculations as a merciful shortcut instead of going through the sometimes agonizing task of discerning the sometimes bizarre and baffling thought processes of bad poker players.

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I can see why you would get a lot of flack there. And I agree that you simply have to buckle down and understand the fish thinking, rather than widening the range which strangely enough often makes you play like the fish yourself.

Re: The \"Emperor\'s nose\" fallacy & poker
 

You still need some means to evaluate the strength of your hand against that of an opponent.

If you're consistently finding that your hand range estimates are too wide, you adjust and refine them - you don't just abandon the process! That's a flaw in your reading ability, not the process itself.

Another point is that you can adjust for estimated chance of each of the hands in the range - they don't have to be equal, particularly if you have a decent idea of how an opponent plays certain hands. A lot of players will have difficult doing this accurately with the time constraints online, but it's valuable if you can do it even roughly.

I'm not sure what Splawndarts is proposing as an alternative. I'm sure he'll wow us with some rediculous tale and starting arguing his points to death as usual...

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
You still need some means to evaluate the strength of your hand against that of an opponent.

If you're consistently finding that your hand range estimates are too wide, you adjust and refine them - you don't just abandon the process! That's a flaw in your reading ability, not the process itself.

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No, there's a flaw in the process itself.

Averaging is only useful if the mean of the things you are averaging equals the accurate value you're trying to get. In this case, the value we're trying to get is our expectation with respect to villain's hand.

There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

So in fact there's a subtle problem with the process above and beyond any problems of execution.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Great post.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Useless. No alternative suggested. This is no more profound than "garbage in, garbage out." I agree with the Goose; if you are consistently adding too many weak hands to the range you need to adjust your thinking. Whats the alternative? Tea leaves and tarot cards?

Re: The \"Emperor\'s nose\" fallacy & poker
 

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There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

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Of course not - but then, we are doing this whole process because we're not sure what the villian has. If we actually saw his cards as in FTP, there wouldn't be a need to put a villian on a range, would there?

The Chinese peasant is in a similar predicament. He makes a reasonable effort to reach an accurate answer, even though it turns out to be incorrect. The Census isn't completely accurate either, but that doesn't mean you stop counting and just guess.

I'm not sure what else you're suggesting a player do?

EDIT:

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if you are consistently adding too many weak hands to the range you need to adjust your thinking.

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Exactly - how could there be a problem with the method if you're able to come up with a fairly accurate range? You going to put the guy on an exact holding every hand? (No, you can't.)

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Whats the alternative? Tea leaves and tarot cards?

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Seriously

Re: The \"Emperor\'s nose\" fallacy & poker
 

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If you're consistently finding that your hand range estimates are too wide, you adjust and refine them - you don't just abandon the process!

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The process is : reading hands.

The process is not flawed if you do not abuse it the way you describe. Putting someone on a hand is done for a reason (duh). You can't just put someone on one hand (unless you're right most of the time, but you'll be very rich by now) so you have to put someone on a possible range. If you compare your expected results of your actions to that range you will be able to make a decision based on your opponents possible hands. If you don't, well that's up to you, but you're missing out. If there is something principally wrong with putting your opponent on a hand, than I'd like to know what it is [img]/images/graemlins/smile.gif[/img]. I agree many people fail to be realistic with the ranges they put their opponents on, but that is an entirely different mistake. They tried the right process, but implemented it wrong.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

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Of course not - but then, we are doing this whole process because we're not sure what the villian has. If we actually saw his cards as in FTP, there wouldn't be a need to put a villian on a range, would there?

The Chinese peasant is in a similar predicament. He makes a reasonable effort to reach an accurate answer, even though it turns out to be incorrect. The Census isn't completely accurate either, but that doesn't mean you stop counting.

I'm not sure what else you're suggesting a player do?

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The fact that you sympathize with the peasant's fallacious reasoning explains a lot. The peasant's answer from averaging was no more accurate than asking a single person or no one at all (ie. not at all accurate) because he wasn't averaging things with a mean value equal to the value he was trying to find.

What he did bears no resemblance to the census (which in turn has little to do with averaging). Do you see why?

Re: The \"Emperor\'s nose\" fallacy & poker
 

You still haven't answered the question - what is your alternative?

(For the peasant OR the poker player)...

Re: The \"Emperor\'s nose\" fallacy & poker
 

Oh, and before you start playing your little semantic games, and the "obviously you are not very smart" nonsense, I'll tell you right now you're just going to embarrass yourself again. You can try to weasal out of it, but you are just flat wrong, again.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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You still haven't answered the question - what is your alternative?

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My alternative is to avoid fallacious reasoning and replace it with correct reasoning. The particular type of correct reasoning I would employ would of course depend on the circumstances.

Even if you find yourself with no alternative whatsoever, that doesn't justify fallacious reasoning. You must simply admit you don't know rather than employing it. The peasant was incapable of getting an actuarte value, but that didn't make his averaged one any more useful. It would have been more accurate for him to simply admit that he had no idea how long the nose was, and move on.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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Oh, and before you start playing your little semantic games, and the "obviously you are not very smart" nonsense, I'll tell you right now you're just going to embarrass yourself again. You can try to weasal out of it, but you are just flat wrong, again.

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wtf?

Re: The \"Emperor\'s nose\" fallacy & poker
 

So... you don't have an answer?

The peasant should just quit and the poker player cannot make a decision?!?

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wtf

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Toward Splawndarts

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
[ QUOTE ]
Oh, and before you start playing your little semantic games, and the "obviously you are not very smart" nonsense, I'll tell you right now you're just going to embarrass yourself again. You can try to weasal out of it, but you are just flat wrong, again.

[/ QUOTE ]

wtf?

[/ QUOTE ]

He's got his panties in a twist. Nothing to worry about.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Agreed, but you have an idea of the hands your opponent might and might not be holding. So what's wrong with taking that into account? It'll be a reasoned estimate of the probabilities he's holding certain hands and a mathematical estimate/calculation of your expectation against these hands which leads to an expectation of your different actions that will make a good choice possible. If you do this intuitively, calculate everything or just go through the range in your head and pick an action, you DO make use of this range and you want it to be as accurate as possible.

I don't see how the example relates to poker (there are many hints that might tell you the length of the nose in poker, while there are none in your story). Also to replace 'fallacious reasoning' with 'correct reasoning' will not mean that you replace 'putting your opponent on a range and reacting appropriately' by something else. You just make sure you do a better job of putting him on a hand.

All you're realy saying is: Do not assume things to easily. And I agree on that.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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So... you don't have an answer?

The peasant should just quit and the poker player cannot make a decision?!?


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The peasant should just quit if he doesn't have access to anyone with any actual information about the nose. Nothing he does with respect to asking people or averaging will acomplish anything whatsoever.

Likewise, the poker player should adopt some other line of reasoning. What that would be, obviously, is highly dependent on the situation.

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
Agreed, but you have an idea of the hands your opponent might and might not be holding. So what's wrong with taking that into account? It'll be a reasoned estimate of the probabilities he's holding certain hands and a mathematical estimate/calculation of your expectation against these hands which leads to an expectation of your different actions that will make a good choice possible. If you do this intuitively, calculate everything or just go through the range in your head and pick an action, you DO make use of this range and you want it to be as accurate as possible.

I don't see how the example relates to poker (there are many hints that might tell you the length of the nose in poker, while there are none in your story). Also to replace 'fallacious reasoning' with 'correct reasoning' will not mean that you replace 'putting your opponent on a range and reacting appropriately' by something else. You just make sure you do a better job of putting him on a hand.

All you're realy saying is: Do not assume things to easily. And I agree on that.

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To be clear, I'm not at all opposed to reasoning based on the hands you believe your opponent holds. I'm simply pointing out that averaging is not the correct method by which to conduct that reasoning unless you know the mean of what you're averaging is the value you're trying to find.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Averaging the hands on the probabilities he was dealt that hand, i agree, no... Weighing your EV on the probabilities YOU give him holding that hand, yes.

That last is really dependant on the situation indeed. There is more to hand reading than probabilities. We all knew that [img]/images/graemlins/wink.gif[/img]... What's your point?

Re: The \"Emperor\'s nose\" fallacy & poker
 

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To be clear, I'm not at all opposed to reasoning based on the hands you believe your opponent holds. I'm simply pointing out that averaging is not the correct method by which to conduct that reasoning.

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I smell a little backpedaling here - and you just don't average between all of the hands in the range as I pointed out earlier

Re: The \"Emperor\'s nose\" fallacy & poker
 

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To be clear, I'm not at all opposed to reasoning based on the hands you believe your opponent holds. I'm simply pointing out that averaging is not the correct method by which to conduct that reasoning.

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I smell a little backpedaling here

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Nope. Where did I say I was opposed to using information about opponents holdings? Please quote, with context and link, and without editing, or admit I said nothing of the sort.

Thanks.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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Averaging the hands on the probabilities he was dealt that hand, i agree, no... Weighing your EV on the probabilities YOU give him holding that hand, yes.

That last is really dependant on the situation indeed. There is more to hand reading than probabilities. We all knew that [img]/images/graemlins/wink.gif[/img]... What's your point?

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This weighting thing is a bit of a misnomer. The only wieghting I can think of that gaurantees the weighted average equals your expectation is to weight the hand he has at 1 and everything else at 0. Which is a decidedly degenerate weighting.

Otherwise, various forms of weighted averages are not in any way immune to this fallacy.

Re: The \"Emperor\'s nose\" fallacy & poker
 

The way you can't admit that:

1) You are not, and were never, a winning poker pro
2) You never played with Dan Harrington
3) You are not a millionaire

Just a sample of claims you've made - I'm willing offer a full apology AND $100 Stars transfer to you or anyone else that can offer definitive proof I am wrong on any of the above.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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The way you can't admit that:

1) You are not, and were never, a winning poker pro
2) You never played with Dan Harrington
3) You are not a millionaire

Just a sample of claims you've made - I'm willing offer a full apology AND $100 Stars transfer to you or anyone else that can offer definitive proof I am wrong on any of the above.

[/ QUOTE ]

And now you're just randomly throwing [censored] at the wall to see what sticks, and thereby wasting everybody's time including your own.

Hope that works out for you [img]/images/graemlins/laugh.gif[/img]

Re: The \"Emperor\'s nose\" fallacy & poker
 

I'm pretty much calling you a flat-out liar, you know that right? You've made these claims yourself, and it's not as if I've never seen you before (Harmony Central)

Re: The \"Emperor\'s nose\" fallacy & poker
 

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I'm pretty much calling you a flat-out liar, you know that right? You've made these claims yourself, and it's not as if I've never seen you before (Harmony Central)

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OK, you can feel free to believe I'm a liar. Store it in the same bin with the other misconceptions you've displayed in this thread.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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OK, you can feel free to believe I'm a liar.

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Thanks, but you've more than earned it. Don't sweat it though, before too long 2+2 will get to know you the way we do over at Harmony.

I doubt you're even a winning player, certainly your 8bb claim from the recent thread (where you backed down off a challenge when confronted, remember that?) demonstrates that.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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OK, you can feel free to believe I'm a liar.

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Thanks, but you've more than earned it. Don't sweat it though, before too long 2+2 will get to know you the way we do over at Harmony.

I doubt you're even a winning player, certainly your 8bb claim from the recent thread (where you backed down off a challenge) demonstrates that.

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You may have missed it, but I negotiated a prop bet with DuBot and now he's been very scarce to avoid firming up the details. I suspect he'll bail out.

Re: The \"Emperor\'s nose\" fallacy & poker
 

Casual lurker, first-time poster here. Just wanted to say, I was enjoying this thread quite a bit. Then it turned into this petty fight about nothing. Lame. I'm looking to improve my thought process at the table and there was some good discsussion going on I thought.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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Casual lurker, first-time poster here. Just wanted to say, I was enjoying this thread quite a bit. Then it turned into this petty fight about nothing. Lame. I'm looking to improve my thought process at the table and there was some good discsussion going on I thought.

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There are a lot of good resources on 2+2, however there are some here who are not qualified to give advice. It's one thing to lie and boast all of the time... that is pretty harmless in itself. It's another thing to masquerade as something you're not and consistently be contrary to other posters with all kinds of nonsense, some of whom have vastly more experience and understanding of the game.

Sorry the thread was spoiled for you, that is if you're not actually Splawndarts himself... (I don't really think you are, but he has been known to post under different names at another site I frequent). Sorry you choose this for a first post.

Here and here will kind of give you the idea of what the guy is all about.

He's quickly becoming known for the same crap here. Talks big, can't back up his (often extraordinary) claims, gets super-defensive and arrogant when told that he's wrong, even when he knows he is.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

So in fact there's a subtle problem with the process above and beyond any problems of execution.

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I have to object here - this statement (as far as I can work out) is meaningless. What is "the expectation for a number of hands"? What is "expectation for the hand that the villain actually has"? I respectfully suggest that you should spend some time reviewing your understanding of expectations and distributions. The "process" is not flawed. If you find yourself making bad calls because of overestimating the villains hand range, then it is likely a flaw in your hand reading skills.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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Averaging is only useful if the mean of the things you are averaging equals the accurate value you're trying to get. In this case, the value we're trying to get is our expectation with respect to villain's hand.

There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

So in fact there's a subtle problem with the process above and beyond any problems of execution.

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This looks pretty dodgy to me. Would you care to give an answer to a simple thought experiment, just to see if we are on the same page?

Suppose you are given an opportunity to choose either

A) a guaranteed payoff of $100

or

B) a chance to choose from one of three boxes, with each box having a different amount of money inside it. Let's say the amounts are $50, $80, and $200.

In fact, if you take option B you don't actually choose the box, but it is chosen for you by someone else having randomly pre-selected one of the three boxes. Your choice is simply to take either A) the $100 payout, or B) one of the three boxes.

Presumably you see where I'm going with this. On the assumption that we are interested in maximizing our expected value, what is wrong with averaging across the payouts of the three boxes in order to figure out whether we prefer option A or option B?

You appear to have a strange take on probability if you want to insist that the only expected value that matters is the one for the opponent's actual holding. Certainly if we knew the opponent's actual holding then we'd make our calculations based on that, but your position equates to someone who insists, in my little experiment, that whether they should choose option A or B depends on which box has been pre-selected under option B. The whole point is that we do not have information that would allow us to distinguish between the $50, $80, and $200 cases for option B. Given this, the best thing we can do is to average over them.

You have built up a bit of a straw man, I think, by suggesting that many people when faced with poker decisions will do the equivalent of throwing in some more possibilities for the cash amounts in the boxes under option B. If I weirdly suppose that instead of the three equiprobable boxes as stated, there is a fourth box that has only $5, or that the box with $50 is much more likely than the others to be chosen, then certainly this will lead to me incorrectly assessing the expected value of option B. However, my error has nothing to do with the process of averaging across expected values, and everything to do with plugging in bad information at the beginning of that process.

In, summary, I can't understand when you've gone after averaging when all you really mean to criticize is poor information gathering and parameter estimation when putting people on hand ranges.

Re: The \"Emperor\'s nose\" fallacy & poker
 

After all, this became a very useful thread. This is despite (no, indeed because of) Splawn Darts' inability to provide any explanation whatsoever for the gibberish he posted when repeatedly asked for an alternative to typical hand range analysis.

Let me make sure I am clear: it is not that I fault him for being wrong, or not having another "insightful" legend to make some sort of a semblance of a useful statement. I have been wrong before, and will be again. It's instead that he is pretending that there is some deep, hidden meaning to all this when there's clearly not, and in the process of doing so, has made it crystal clear (to me at least)that the point of the original post (and one can only assume, perhaps some of his other posts) is simply to engage in semantic BS. Which is, of course, useless. But it is indeed entirely useful to know his modus operandi, lest I spent another minute of my life pondering these deep, dark psuedo-mysteries. Do You See Why?

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
Casual lurker, first-time poster here. Just wanted to say, I was enjoying this thread quite a bit. Then it turned into this petty fight about nothing. Lame. I'm looking to improve my thought process at the table and there was some good discsussion going on I thought.

[/ QUOTE ]

You can expect the people who've just been shown to be employing a logical fallacy to get defensive and useless like he did. It's par for the course.

Re: The \"Emperor\'s nose\" fallacy & poker
 

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Averaging is only useful if the mean of the things you are averaging equals the accurate value you're trying to get. In this case, the value we're trying to get is our expectation with respect to villain's hand.

There's absoloutly no rigorous reason to believe that the expectation for a number of hands averages to the expectation for the hand villain actually has.

So in fact there's a subtle problem with the process above and beyond any problems of execution.

[/ QUOTE ]

This looks pretty dodgy to me. Would you care to give an answer to a simple thought experiment, just to see if we are on the same page?

Suppose you are given an opportunity to choose either

A) a guaranteed payoff of $100

or

B) a chance to choose from one of three boxes, with each box having a different amount of money inside it. Let's say the amounts are $50, $80, and $200.

[/ QUOTE ]

The way you described it, B).

However, your situation B) is not analogous to anything that occurs in poker except for a blind all-in. Do you see why?

Re: The \"Emperor\'s nose\" fallacy & poker
 

[ QUOTE ]
After all, this became a very useful thread. This is despite (no, indeed because of) Splawn Darts' inability to provide any explanation whatsoever for the gibberish he posted when repeatedly asked for an alternative to typical hand range analysis.

Let me make sure I am clear: it is not that I fault him for being wrong, or not having another "insightful" legend to make some sort of a semblance of a useful statement. I have been wrong before, and will be again. It's instead that he is pretending that there is some deep, hidden meaning to all this when there's clearly not, and in the process of doing so, has made it crystal clear (to me at least)that the point of the original post (and one can only assume, perhaps some of his other posts) is simply to engage in semantic BS. Which is, of course, useless. But it is indeed entirely useful to know his modus operandi, lest I spent another minute of my life pondering these deep, dark psuedo-mysteries. Do You See Why?

[/ QUOTE ]

There's plenty of deep meaning here. If you don't want to "waste" your time on it, that's OK though.