BBO Discussion Forums: LoTT is a parabola - BBO Discussion Forums

Rik: that seems fair. I would just add the "round" function, meaning e.g.

"for trumps < 20, total tricks approximates trumps more than any other value"

For the total trumps 16 to 18, E(tricks) = trumps.
30% of the time tricks > trumps.
40% of the time tricks = trumps.
30% of the time tricks < trumps.
It isn't random. Today we know the main reason tricks < trumps is flat patterns.
The main reason tricks > trumps is skewed patterns.
Lawrence/Wirgren wanted SST to replace trumps as the estimator for tricks.
Their approach was wrong. They should have merged SST with trumps to
create a more complete and better estimator.
The actual independent random variable to measure our tricks is pattern. It is the
the joint suit pattern of my 13 cards with partner's 13 cards.
Trumps is the neck end. SST is the tail end. Radio before TV. Trumps is the
coarse adjustment knob. SST is the fine-tuning knob.
Our tricks is nearly independent of their tricks. We should bid our hands based
on our trumps and our SST. SST=5 is always flat. SST=4 is neutral with 8
trumps and flat with more trumps. SST=<3 is generally skewed.
.....................
HCP is part of the other independent random variable to measure tricks.

 mikeh, on 2014-November-04, 16:02, said:

Cohen's statement's sounded absolute.
From page 11.

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Cohen has since backed down and changed 'is' to 'approximately'.

From page 70.

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This is the basis of Bergen raises. 1M - 4M. 4M-1 against air has proven that statement incorrect.

 jogs, on 2014-November-09, 19:50, said:

To paraphrase: There are lies, damn lies and quotes taken out of context.

1. To bid or not to bid is a text book meant to teach something. It is not a scientific paper where all scientific insecurity might perhaps be included within every statement. The two quotes you give are clear statements that show the basic principle and adjunct of the LoTT. When you are teaching, you should first get the main message across in clear statements, exactly as Larry Cohen did. Only after that should you explain the nuances. Nobody who reads these two statements in To bid or not to bid is as stupid to think that a complex game like bridge can be summarized in such a simple Law that will be working 100% correctly 100% of the time.

2. You have come up with two sentences (no need to try, you may well be able to find some more) to argue that To bid or not to bid intended to portrait the LoTT as the absolute truth that is always correct. But you failed to mention that the book contains 2 entire chapters (of 6 and 26 pages, respectively) dealing with situations where the total number of tricks is not equal to the total number of trumps. Note that Larry Cohen has done this in the exact way that I described above, like a good teacher should: First postulate the Law in clear terms, then present the nuances and caveats.

I would think that these two chapters strongly support MikeH's statement:

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Rik

The LOTT, even in its "trumps = tricks" (wrong) formulation, is a useable tool because it's simple. One can even argue that it's a GOOD tool, provided one understands that the correct statement is "E(trumps) = tricks" and, cumulatively, one knows what standard deviation is, and how to estimate which way the deviation might be going at the table. (I.e. calculate what Larry calls "corrections".)

L/W is probably more precise but is terribly more complicated to use and because of it will never be as popular as the LOTT. I actually manage to apply L/W reasonably often, but I'm a bit of a geek

 Trinidad, on 2014-November-10, 00:51, said:

Nonsense, look at the book. Both of those statements were highlighted in bold print in a box.

Cohen was clearly aware of LoTT shortcomings. Look at the chart on page 216. The key to applying LoTT in proper context is making the proper adjustments. This chapter is forgotten by most readers.

 jogs, on 2014-November-10, 08:51, said:

You clearly don't understand what a quote out of context is. The first part of the context is that this is a textbook. That means that it starts simple and complexity is added later. In fact, your first quote ("The Total Number of Tricks available on any deal is equal to the Total Number of Trumps", page 11) is introduced nicely with the author providing a clear context:

Quote

(emphasis mine)

In principle, it is fine to leave that part of context out, except when you want to argue that Larry Cohen never warned his readers that the LAW was a little more complex. In that case, you are clearly quoting out of context.

The second part of context is that Larry Cohen wrote two entire chapters in that very same book on adjustments. Fortunately, you seem to be aware of that now yourself:

 jogs, on 2014-November-10, 08:51, said:

Exactly, which is why Larry Cohen devoted two chapters of To bid or not to bid to adjustments. The chart on page 216 is part of the second chapter on adjustments.

But you are overlooking a more convincing chapter. It is titled "IS THERE A DOWNSIDE?". One of the issues (he shows more) with the LoTT that Larry "the LAW" Cohen describes in that chapter is the fact that the LAW breaks down for large numbers of trumps. (So, the core of this thread was already published in 1992 in the standard work on the LAW.)

So, you really cannot claim that Larry Cohen simply presented the LAW without any criticism. Of course, he presented the criticism at the end of his book. After all, the reader will first have to understand what the LAW is before he is capable of understanding Larry's criticism of it.

 jogs, on 2014-November-10, 08:51, said:

I don't think so. These chapters are very hard to miss.

I do agree, though, that these chapters are lost on many bridge players. They have heard about the LoTT, but never read the book. So, at some point they ask someone in their club: "Hey... this Law thing... what is that all about?" Do you think that they will get an answer on adjustments, or the limitations of the LAW for large number of trumps or would they just get to hear "trumps = tricks" (probably because the other guy didn't read the book either)?

But we can't blame Larry Cohen for people not buying his book, can we?

Rik

Am I the only one who is bothered by the term parabola? It's probably closer to a sigma function. Not every nonlinear function can be fitte with a second-order polynomial (or a square root).

I think so.. after all, the quadratic term is the second of a Taylor expansion

(Provided the function is differentiable, which clearly isn't the case lol.)

 whereagles, on 2014-November-11, 03:27, said:

What do the terms "Taylor expansion" and "differenatiable" mean when we are taling about a domain with only 13 elements?

At least we know that there is a 12th degree polynomial that fits perfectly .....

They don't mean anything, of course. It's just a pun.

And yes, you can always find perfect fits. Trouble is, perfect fits reproduce unwanted random noise, not necessarily the main trend.. but of course, you know that

 gwnn, on 2014-November-11, 02:46, said:

Not really. parabola = not a straight line (as near as makes no difference to me for the purpose of the thread)

Ah. I get it. There are straight lines and parabolas.

And I keep complaining that the datahandling software that comes with our analytical instruments doesn't have enough fit functions. I am just spoiled.

Rik

 Trinidad, on 2014-November-11, 06:26, said:

Just like the definition of "Acol": any bidding system which is not Precision.

 Trinidad, on 2014-November-11, 06:26, said:

Hmm. I forgot about hyperbole.

I took these courses nearly 50 years ago.

http://en.wikipedia.org/wiki/Parabola

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If you want to nikpik, I should have written the parabola is a better fit for LoTT than a straight line.

Sigmoid functions would be odd functions so a parabola is quite an awful approximation to it actually. Of course it's not a real sigmoid function either, but it just looks more like one to me than a parabola.

Sigmoid functions are differentiable, so to 2nd order they are paraboli

They are odd functions so they are a straight line up to "second order."

What game are you guys playing here? Looks interesting.