LoTT is a parabola

[whereagles]

well.. z-tests on Ginsberg data yield disagreement with E(tricks) = trumps, even for trumps < 20. The high sample size makes that clear.

 

Clearly, even for E(tricks) the LOTT only holds approximately.

[jogs]

1) You don't give any decent arguments to support this statement. We just saw in this tread that a function describing the total number of tricks, only based on the number of trumps that both sides hold (no adjustments or anything), has a standard deviation of about 1 total trick. This scales to a standard deviation of 0.5 tricks for the number of tricks one side can take. I cannot think of a method that can predict the number of tricks with an accuracy of half a trick. Yet, you claim that estimating total tricks is much less reliable than estimating our own tricks. What magical method do you have that leads to a standard deviation of less than say 0.05 tricks? (I'll be nice to you and say that a factor of 10 is "much less".)

 

 

Rik

 

All those std dev calculations assume you actually know the total trumps. Which isn't true. Your trump estimates is often off by one and sometimes off by two or more.

Also std dev isn't linear. Variance is linear.

[jogs]

http://jogsbridge.weebly.com/uploads/1/8/0/2/1802582/554030.jpg?617

 

The green line is a 5-4 trump fit with observations taken from BBO minis. The HCP and tricks are shifted to HCP=20.

The blue line is a 4-4 trump fit with observations taken from a dataset of experts vs experts from the Richard Pavlicek site.

SST = short suit totals.

 

Our tricks

E(tricks) = trumps + (HCP-20)/3 + SST

We often know our combined trumps. We know our own contribution to SST. We only sometimes know the complete SST.

 

Well they also have their tricks.

E(tricks) = their trumps + (HCP-20)/3 + their SST

We have difficulty learning of their trumps. Nearly impossible to know their SST.

 

Anyone who thinks he knows total tricks of a board frequently is deluding himself.

[whereagles]

Analysing Ginsberg big data has convinced me that is highly unlikely that someone finds a formula that relates E(tricks) to basic factors such as HCP, trump length or short suit. Maybe the correct formulation should be something like

 

round[ E(tricks) ] = trumps

 

or

 

round[ E(tricks) ] = c + c1*trumps + c2*trumps^2

 

Edit: fixed formulae

[Trinidad]

My conclusion would simply be:

for total trumps <20: total tricks = total trumps

for total trumps >=20: total tricks = total trumps - (total trumps - 19)/2

 

In addition:

for total trumps <20: Use adjustments -as described in Cohen's books- but don't adjust by more than 1 total trick.

for total trumps >=20: Use your own judgement based on the location of controls/shortness and secondary fits to "adjust freely".

 

Rik

[whereagles]

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"

 

:)

[jogs]

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.

[jogs]

I have no idea what your point is.

 

Besides, nobody ever said, as far as I can recall, that the LOTT was anything other than an approximation. I have the original book by Cohen, and while I can't be bothered to check it I am fairly confident that his point was that it was a pretty good tool for estimation, not calculation, and that even in the first book he acknowledged that there were factors that would tend to make the estimation less reliable in some situations than in others.

 

Cohen's statement's sounded absolute.

From page 11.

The Total Number of Tricks available on any deal is equal to the Total Number of Trumps

 

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

 

From page 70.

You should always bid to the level equal to the combined trumps held by your side

 

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

[Trinidad]

Cohen's statement's sounded absolute.

From page 11.

 

The Total Number of Tricks available on any deal is equal to the Total Number of Trumps

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

 

From page 70.

The Total Number of Tricks available on any deal is equal to the Total Number of Trumps

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

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:

Besides, nobody ever said, as far as I can recall, that the LOTT was anything other than an approximation. I have the original book by Cohen, and while I can't be bothered to check it I am fairly confident that his point was that it was a pretty good tool for estimation, not calculation, and that even in the first book he acknowledged that there were factors that would tend to make the estimation less reliable in some situations than in others.

 

Rik

[whereagles]

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 :)

[jogs]

 

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

 

Rik

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.

[Trinidad]

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

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:

Using its simplest definition, the LAW of TOTAL TRICKS states:

(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:

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.

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.

This chapter [on adjustments] is forgotten by most readers.

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

[gwnn]

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).

[whereagles]

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.)

[helene_t]

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.)

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 .....

[whereagles]

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 :)

[NickRW]

Am I the only one who is bothered by the term parabola?

 

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

[Trinidad]

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

[helene_t]

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

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

[NickRW]

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

 

Hmm. I forgot about hyperbole.

[jogs]

I took these courses nearly 50 years ago.

 

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

 

y=ax²+bx+c

 

so the graph of any function which is a polynomial of degree 2 in x is a parabola with a vertical axis.

 

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

[gwnn]

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.

[whereagles]

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

[gwnn]

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

[kuhchung]

What game are you guys playing here? Looks interesting.