The "Emperor's nose" fallacy & poker

[SplawnDarts]

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

[ QUOTE ]

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.


[/ QUOTE ]

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.

[bbartlog]

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...

[SplawnDarts]

[ 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...

[/ QUOTE ]

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.

[Mike]

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....

[Sean Fraley]

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.

[SplawnDarts]

[ QUOTE ]
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.

[/ QUOTE ]

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.

[PhantomGoose]

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...

[SplawnDarts]

[ 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.

[/ QUOTE ]

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.

[Bang584]

Great post.

[El_Hombre_Grande]

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?