[helene_t]

Have Campboy and Ginsberg defined the problem in the exact same way? If a pair has two 8-card fits you could count the number of tricks they take in whichever suit gives the highest number of tricks, or you could take one suit at random. If you take the average of the two you will underestimate the variance and if you count both with full weight you will overestimate the mean. A similar issue relates to choice of declarer.

[campboy]

helene_t, on 2014-November-06, 04:26, said:

Have Campboy and Ginsberg defined the problem in the exact same way? If a pair has two 8-card fits you could count the number of tricks they take in whichever suit gives the highest number of tricks, or you could take one suit at random. If you take the average of the two you will underestimate the variance and if you count both with full weight you will overestimate the mean. A similar issue relates to choice of declarer.

Good question. Where there are two fits of the same length my script uses the higher-ranking suit, so essentially picks one at random. It does assume that contracts are right-sided, where relevant.

[edit]
Based on the mean, it seems Ginsberg is also right-siding the contract but either picking the suit at random or averaging the two suits where there is a double fit. For 14 total trumps (where there is always a double fit), on a sample of 1000 (different to the previous sample but the same one for each calculation) I got the following means:

average over both suit and declarer	13.763
average over suits of better declarer	13.848
better suit and better declarer		14.426
better suit; average of declarers	14.341
(Ginsberg's mean			13.85)

The mean alone can't tell me whether he is averaging for the two suits or picking a random one; the fact that his standard deviation is lower suggests the former, but making that change would only push the standard deviations in my previous post down, and the most striking difference is that the deviations for the higher numbers are already much lower than his. I also think picking a random suit is a better way to estimate the standard deviation, since that is more like what happens at the table (whereas I expect contracts are right-sided most of the time in practice).

[helene_t]

whereagles, on 2014-November-06, 04:22, said:

Actually, you can fit a non linear regression model to Ginsberg's data and run significance tests on c, c1, c2. I might set c = 0 from the start, though.

I'll try and do it this week-end... gotta read an MSc thesis right now, and see if I can dig up a few embarassing questions to the candidate lol.

I would call this a linear regression model. That one of the covariates happens to be a transform of something doesn't make it nonlinear.

A nonlinear model would be something that could not be rewritten as a linear model, for example

E(Tricks) = a*x +b*x^c

where a, b and c are parameters to be estimated.

[jdeegan]

Big problem. When you abstract a situation to a level where you can easily model it, you can easily create a situation that is so different from the reality you were originally concerned with as to be uninteresting.

For example. With two 8 card fits, if one is 4-4 and trumps = 5+ possible tricks. What about the other one - a side suit? If it is also 4-4, not so hot. If it is 6-2 and solid = six tricks.

Over the years I have modeled many things using statistical methods - credit card default rates, various financial markets, parts of the US economy, optimal fast food joint locations, drilling rig utilization, you name it. I have taught more courses in statistics and econometrics than I can remember.

Modeling Bridge is really, really tough, and I have little confidence anyone can get very far with it. Again, there is the underlying problem is that Bridge is not played double dummy.

[whereagles]

helene_t, on 2014-November-06, 05:55, said:

I would call this a linear regression model. That one of the covariates happens to be a transform of something doesn't make it nonlinear.

A nonlinear model would be something that could not be rewritten as a linear model, for example

E(Tricks) = a*x +b*x^c

where a, b and c are parameters to be estimated.

hmmm you might be right. I'd have to check my definitions. As posed, it's certainly linearized (at least).

[jdeegan]

whereagles, on 2014-November-06, 06:07, said:

hmmm you might be right. I'd have to check my definitions. As posed, it's certainly linearized (at least).

News flash! If your equation can be transformed into something linear, you can use least squares. You might want to consider what a transformation does to your error term, though few actually worry about it.

[helene_t]

The transformation applies to a covariate so it doesn't do anything to your error term.

[jogs]

helene_t, on 2014-November-06, 04:26, said:

Have Campboy and Ginsberg defined the problem in the exact same way? If a pair has two 8-card fits you could count the number of tricks they take in whichever suit gives the highest number of tricks, or you could take one suit at random. If you take the average of the two you will underestimate the variance and if you count both with full weight you will overestimate the mean. A similar issue relates to choice of declarer.

From the Ginsberg TBW article NOV1966 page 9.

Quote

The program selected randomly among trump suits of equal length but always assumed that the contract was played from declarer's best side.

[jogs]

whereagles, on 2014-November-06, 04:22, said:

Actually, you can fit a non linear regression model to Ginsberg's data and run significance tests on c, c1, c2. I might set c = 0 from the start, though.

I'll try and do it this week-end... gotta read an MSc thesis right now, and see if I can dig up a few embarassing questions to the candidate lol.

Do you have a copy of the Ginsberg article? There's a chart of the data in its raw form on page 10. The tricks are occasionally +/- 4 from trumps.

[campboy]

jogs, on 2014-November-06, 09:00, said:

From the Ginsberg TBW article NOV1966 page 9.

Quote

The program selected randomly among trump suits of equal length but always assumed that the contract was played from declarer's best side.

Thanks. The answer to Helene's question is "yes", then.

[jogs]

jdeegan, on 2014-November-06, 05:58, said:

For example. With two 8 card fits, if one is 4-4 and trumps = 5+ possible tricks. What about the other one - a side suit? If it is also 4-4, not so hot. If it is 6-2 and solid = six tricks.

I certainly think it's true.
8-0 fit > 7-1 fit > 6-2 fit > 5-3 fit > 4-4 fit
The skewed fits generate more tricks than the flatter fits.

Quote

Modeling Bridge is really, really tough, and I have little confidence anyone can get very far with it. Again, there is the underlying problem is that Bridge is not played double dummy.

I like to use observed results from BBO minis. Only it is really hard to find boards which fit the desired conditions.

[jogs]

navahak, on 2014-November-05, 13:10, said:

Our trump length correlates with opponents trump length. Basically if e have 9 card fit opponents have it too or they have two times 8 card fits.

The correlation is weak.

We have 8 trumps. Think in terms of trumps for the partnership. They have 5 in that suit.
5=7=7=7
They can have 7 as their longest suit.
We have 8=8=8=2. They can have 11 as their longest suit.
Therefore when we have 8, they have from 7 to 11 trumps.

We have 9 trumps. They have 4 in that suit.
4=8=7=7
They can have 8 as their longest suit.
We have 9=9=8=0. They can have 13 as their longest suit.
Therefore when we have 9, they have from 8 to 13 trumps.

[navahak]

jogs, on 2014-November-06, 19:07, said:

The correlation is weak.

I knew about multiple fits increasing the opponents fit. But if you take into account probabilities of different distributions the correlation is a lot stronger than if you just look extreme examples. This correlation is very similar to LoTT and how accurate it is on average.

Same as Mike explained in long detailed post: I follow law only loosely and base my decision in many other factors too.

[jdeegan]

jogs, on 2014-November-06, 14:57, said:

I like to use observed results from BBO minis. Only it is really hard to find boards which fit the desired conditions.

I am with you all the way, but consider:

The original Verne analysis modeled world championship Bridge circa the late 20th century. Your approach is, no doubt, better and more sophisticated than this original work, but you are left with the undeniable fact that you are 'just' modeling BBO minis. This should help you beat BBO minis, but what else?

I am afraid that the best you can really do with modeling is to define the kind of game you are trying to beat - both in a time and a place - and figure out the best way to beat it. Social science modeling is not like modeling in physics. The bastards you are trying to model react and keep moving.

Put another way, my credit card default model worked like a champ in its time. It even made me some pretty good money for a while. I would not advise using it today even reestimated using current data.

As far as selecting just the right kind of hands as a sample for any kind of valid statistical analysis. Welcome to the real grunt work involved in modeling Bridge. Computer screens have to be loose enough not to truncate your sample too much, if at all, and how much is too much, anyway? I think you need multiple screens customized for your specific application. In other words, screen the sample, then screen the rejects using a looser screen, etc., etc. I don't know of any canned programs you might use, but by now, they may exist.

Good luck. I am afraid a certain amount of hand selection may end up being called for.

P.S. There may a way to use BBO data from 'better' players. Several 'salons' featuring high level players have emerged on BBO. They feature sponsors like JEC and hosts like Susina. Those hand records are available to anyone using BBO software back for 2 or 3 months. You might be able to get more history if you asked BBO and reassured them you would keep it confidential. I can't see why they would object, assuming they trusted you.

[campboy]

jogs, on 2014-November-06, 19:07, said:

The correlation is weak.

FWIW the correlation coefficient is 0.58645 by my calculations.

[whereagles]

jogs, on 2014-November-06, 09:16, said:

Do you have a copy of the Ginsberg article? There's a chart of the data in its raw form on page 10. The tricks are occasionally +/- 4 from trumps.

No, I don't. Where can I find that chart? I could use it for the analysis.

[Trinidad]

campboy, on 2014-November-07, 04:41, said:

FWIW the correlation coefficient is 0.58645 by my calculations.

Just out of curiosity: Did you solve this analytically or did you just run a sim?

Rik

[campboy]

Trinidad, on 2014-November-07, 06:22, said:

Just out of curiosity: Did you solve this analytically or did you just run a sim?

Analytically.

[RMB1]

whereagles, on 2014-November-06, 04:22, said:

Actually, you can fit a non linear regression model to Ginsberg's data and run significance tests on c, c1, c2. I might set c = 0 from the start, though.

I don't think c=0 is safe.

A naive fit to the data looks something like: trumps - (trumps - 16.5)^2/24, where c <> 0.

[whereagles]

Fitting with c <> 0 is better/easier than c = 0. But if you can do with c = 0, that seems more logical.