[helene_t]

whereagles, on 2014-November-04, 17:38, said:

It's better said "relationship between average tricks and trumps". But anyway, while the parabola-like relationship actually seems plausible, making a case for it it needs more evidence than what you present. Some data and statistics is needed to prove it at, say, 95% confidence level.

Prove what? Significance levels are used when you are interested in rejecting a null hypothesis. Here the null hypothesis might be that the LOTT is accurate but we know that that isn't true. If you want to prove that the parabola is "correct" then you could postulate an noninferiority hypothesis, i.e. the hypothesis that the optimal parabola is not so much worse than the optimal generic model that it matters for practical purposes.

Alternatively, you could test the hypothesis that the lott is not so much worse than the optimal parabola that it matters for practical purposes.

Either way, we need to agree on what accuracy level is relevant for "practical purposes".

But I agree with Campboy that for simulation studies, 95% confidence is not enough. Just keep sampling until the 99.9% confidence interval is small enough to be insignificant for practical purposes.

[navahak]

whereagles, on 2014-November-05, 04:21, said:

2. They did present an alternative: the SST/WP stuff. Just that it's a bit too complicated to use at the table. But yeah, I tend to agree that LOTT + corrections, while not ideal, should be good enough for most practical cases.

I think SST+WP is replacement for HCP+SSP instead of LOTT. It is surprising accurate at predicting own side trick taking potential if bidding manages to transfer SST information. Too bad in many sequences SST is unknown value making predictions poor. Of course one could try to predict opponents SST+WP based on trump suit fit and HCP for on side but that has a lot variables to guess and needs a lot work.

In table one needs to adapt evaluate method depending on own hand and information available from partner and opponents.

[campboy]

yunling, on 2014-November-05, 01:42, said:

Simulation by Matt Ginsberg(published in Bridge World, Nov 1996)
Length Samples Total tricks
14 46944 13.85±0.63
15 47281 14.86±0.64
16 120525 16.10±0.70
17 102184 17.02±0.75
18 69792 17.99±0.83
19 37561 18.78±0.87
20 15845 19.50±0.99
21 5041 20.11±1.20
22 1286 20.69±1.48
23 237 21.22±1.83
24 45 21.78±2.27

LoTT works fairly well when total trumps is 18 or shorter, but with longer trumps, LoTT overestimates the total tricks and has a high variance. At this level I think SST is more important.

It's not clear to me how he's calculated these numbers. Assuming the ± bit gives a confidence interval for the expected number of tricks, the greater uncertainty for the 21+ range would just be a consequence of the low sample size; it doesn't mean there is a higher variance in the number of tricks made. However, the actual numbers given make this interpretation a bit implausible.

[helene_t]

The +/- numbers are much too large to indicate confidence intervals unless the sample size is ridiculously small. Ginbergs public database contains about 800,000 hands.

it would be interesting to see how much variance can be explained by specific adjustment factors such as purity, shortness duplication and double fit.

[Trinidad]

campboy, on 2014-November-05, 05:45, said:

It's not clear to me how he's calculated these numbers. Assuming the ± bit gives a confidence interval for the expected number of tricks, the greater uncertainty for the 21+ range would just be a consequence of the low sample size; it doesn't mean there is a higher variance in the number of tricks made. However, the actual numbers given make this interpretation a bit implausible.

The larger range is not due to the sample size.

What Ginsberg seems to have done is simply create a lot of deals and let a computer play them. Since it was Ginsberg, he probably used GIB. Then he kept track of the number of tricks and the number of trumps. So, in a way, we can say that he determined the number of tricks experimentally.

In my garden, I have an apple tree with about 30 apples. I could weight each apple and calculate the average weight and the standard deviation. Let's say that I find that the average is 110 g with a standard deviation of 15 g. What does that mean?

Does it mean that all apples are 110 g, but that my scale is so poor that for one apple it gives 110, whereas for an other it gives 125 g? Or does it mean that some apples weight 110 g and others 125 g? Unless my scale is really poor, and I have a magic apple tree, I would think the latter. That means that the standard deviation represents the standard deviation of the apple weight distribution function. It does not represent the error in my scale.

If instead of one tree, I would have an orchard full of similar trees, I could weight all these apples. Would this standard deviation decrease? NO! Because the standard deviation is a property of the apple weight distribution. I will be able to determine the average weight more accurately, and I will be able to determine this standard deviaton more accurately, but there is no reason to assume that their values will increase or decrease.

The same holds for Ginsbergs experiment. There are deals with a larger amount of tricks than trumps and there are deals with less tricks than trumps, just like there are heavy apples and light apples. The deviation in the number of total tricks is a property of the total trick distribution of bridge deals. If he would have used more deals, he would have been able to determine the average number of tricks, as well as the standard deviation, more accurately, but there is no reason why the value for the standard deviation would decrease or increase. From the start, the reported standard deviation has been the best estimate for the standard deviation of the total trick distribution. More measurements will lead to a better estimate for this standard deviation, but we cannot say whether it will be higher or lower.

Rik

[whereagles]

helene_t, on 2014-November-05, 04:40, said:

Prove what? Significance levels are used when you are interested in rejecting a null hypothesis. Here the null hypothesis might be that the LOTT is accurate but we know that that isn't true. If you want to prove that the parabola is "correct" then you could postulate an noninferiority hypothesis, i.e. the hypothesis that the optimal parabola is not so much worse than the optimal generic model that it matters for practical purposes.

It's not proving that LOTT is accurate (i.e. tricks = trumps). It's rejecting H0: E(tricks) = trumps. I think you can do it with a chi-square test.

[barmar]

campboy, on 2014-November-05, 05:45, said:

It's not clear to me how he's calculated these numbers. Assuming the ± bit gives a confidence interval for the expected number of tricks, the greater uncertainty for the 21+ range would just be a consequence of the low sample size; it doesn't mean there is a higher variance in the number of tricks made. However, the actual numbers given make this interpretation a bit implausible.

Since he probably calculated them using either GIB or a DD solver, he could presumably generate enough hands to avoid sampling error.

But high total trump hands don't come up so often in the real world, so the accuracy of LOTT is not so critical for them in practical terms.

[jogs]

GreenMan, on 2014-November-05, 01:25, said:

Eh? New prescription drugs get 0.1% or less, don't they?

Don't know. Only know that it sometimes costs nearly $1B to get a drug pass the FDA.

[helene_t]

GreenMan, on 2014-November-05, 01:25, said:

Eh? New prescription drugs get 0.1% or less, don't they?

The 95% significance level is quite widely accepted AFAIK but FDA often requires two trials, so if both pass 95% you have 99.875% combined.

Anyway, for a superitority trial it is not enough to reject the hypothesis of zero superiority.

[campboy]

Trinidad, on 2014-November-05, 08:12, said:

The same holds for Ginsbergs experiment. There are deals with a larger amount of tricks than trumps and there are deals with less tricks than trumps, just like there are heavy apples and light apples. The deviation in the number of total tricks is a property of the total trick distribution of bridge deals. If he would have used more deals, he would have been able to determine the average number of tricks, as well as the standard deviation, more accurately, but there is no reason why the value for the standard deviation would decrease or increase. From the start, the reported standard deviation has been the best estimate for the standard deviation of the total trick distribution. More measurements will lead to a better estimate for this standard deviation, but we cannot say whether it will be higher or lower.

Ah ok. It just didn't occur to me that the second number was supposed to be the standard deviation, because the way it is written with +/- makes it sound like a confidence interval. But of course the actual numbers are much more consistent with it the former interpretation.

[jogs]

I had forgotten about the Ginsberg article posted by Yunling. The info was wedged into the back of my mind.

LoTT has its limitations. We know our own trumps. Often we can deduced partner's trumps. How often can we decipher opponent's trumps? Using total trumps 3/4ths of our estimator is unknown.

whereagles, on 2014-November-05, 04:21, said:

Your chart looks better than mine.

Look at the Ginsberg chart. As trumps increase the std dev increases. That means with as trumps increase, trumps play a smaller role in the estimates.

At the table it is really easier to think in terms of our tricks. Total tricks is too much beyond our control. There are 26 cards in our partnership hands, 13 in each hand. All 26 cards play a role in determining the number of tricks our partnership can make. It is my suit pattern's fit with my partner's suit pattern. The independent random variable is our joint pattern pair. Trumps is the primary component of pattern. With many trumps flat patterns become less likely. Lawrence/Wirgren's short suit totals play a larger role as trumps increase. SST is another component of pattern.

Quote

1. Well, HCP count works fine until a fit is found. That's why people teach it After fit is found, HCP needs corrections (points for singletons, voids, etc). In fact, it is much like the LOTT + corrections.

2. They did present an alternative: the SST/WP stuff. Just that it's a bit too complicated to use at the table. But yeah, I tend to agree that LOTT + corrections, while not ideal, should be good enough for most practical cases.

Use our tricks

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

Notice with 9 trumps, one can bid game with 22 points. An additional trump is worth an additional trick.

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

You can use SST to adjust the estimates both up and down. You know your hand's contribution to SST. Sometimes you can deduce partner's.

[navahak]

jogs, on 2014-November-05, 12:50, said:

LoTT has its limitations. We know our own trumps. Often we can deduced partner's trumps. How often can we decipher opponent's trumps? Using total trumps 3/4ths of our estimator is unknown.

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.

[mikeh]

jogs, on 2014-November-05, 12:50, said:

Use our tricks

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

Notice with 9 trumps, one can bid game with 22 points. An additional trump is worth an additional trick.

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

You can use SST to adjust the estimates both up and down. You know your hand's contribution to SST. Sometimes you can deduce partner's.

This is just silly. Yes, there are hands on which we can, should, and do bid games on 22 hcp (or less, haven't we all bid and made slams on 15 counts or less..admittedly usually as a save that happens to make!) but that doesn't mean that we should always be bidding major suit games on 9 card fits every time we hold a combined 22 count.

Bridge valuation is a fuzzy process. I accept that in theory it ought to be possible to come up with a mathematical approach that does better than the best judgment of the best players in the world. After all, in chess it is now accepted that the best software running on the best computer will trounce the best human players.

The problem is that we humans are not capable of being able to apply such a 'perfect' or 'near-perfect' mathematical model. We can't hold the parameters or equations in our heads (if one ever figured out what they would be) and we can't crunch the numbers unaided, or in a realistic playing time.

Meanwhile, focusing on some bits of what an ultimate theory would encompass, while ignoring other just as important bits, is an exercise in futility.

When we ascertain, or assume, that we have 22 combined hcp and a 9 card fit, we look at where the cards are, and what they are. We upgrade for the presence of 9's and 10's in our long suits. We upgrade for honours in our long suits, but downgrade the J in the 9+ suit, since it may be redundant. We downgrade Queens and Jacks in short suits. We look kindly on Aces, somewhat also on Kings.

We pay attention to the bidding by the opps, including passes on occasion.

We weigh the merits of exploratory bidding, which informs the opps as well as partner, against the merits of blasting (or passing low).

We weigh our partnership style. We weigh the state of the match, and the relative strengths of our teams, if playing a head-to-head team game. We look at the vulnerability.

Even if we could build an effective set of equations that would include all of these factors, and correctly assign weights to them, which probably vary between every hand and every match, we couldn't possibly come up with a method that a human could play at the table.

Which means that what we need to develop is a series of methods that are relatively easy to use, and offer reasonable approximations, and then synthesize, through experience, discussion with better players, and so on, what will largely be an unconscious analytical approach.

By spending so much attention on narrow aspects of this process you run the risk of being able to count the leaves on an individual tree while having very little idea of what the forest looks like....when it is the forest that concerns you, not the tree you are staring at so intently.

I can tell you, for example, that when I am playing well, what I note mostly about my successful aggressive auctions and decisions is that I 'like' or 'dislike' my hand. Of course, I will think carefully about the various factors I listed above, but the single most important criterion is how I feel about the hand...do I like it or dislike it? In my opinion, that feeling, when I am 'on', is the result of an unconscious synthesis of a lot of little bits of information. It's called judgment, and we all have it to some degree.

[jogs]

mikeh, on 2014-November-05, 13:23, said:

This is just silly. Yes, there are hands on which we can, should, and do bid games on 22 hcp (or less, haven't we all bid and made slams on 15 counts or less..admittedly usually as a save that happens to make!) but that doesn't mean that we should always be bidding major suit games on 9 card fits every time we hold a combined 22 count.

18 trumps, 20-20 HCP for each partnership.

Both sides are willing to bid to the 3 level now. 3 HCP is a king worth a trick.

Bergen is telling ppl to bid 4M after partner opens 1M. Doesn't work when neither pard has a singleton(or void).

5-4 fit. If there is a singleton with the 4-card suit, yes you should always bid 4. Also it doesn't always make. IMPs, you are suppose to bid every 45% game. Some bid lower % games.

[jogs]

campboy, on 2014-November-05, 04:28, said:

On the contrary, I think we should expect more convincing proof in this case than for a medical study. It should be trivial to get huge amounts of data on the LoTT, just running random hands through a double-dummy analyser. Even with the resources of a massive multinational company, you just can't do medical trials on enough people to compete.

Bridge is a probabilistic game with high variance. Regardless of the size of your study you cannot lower the true population variance. Large sample sizes can only improve the estimate of the means.

[jogs]

whereagles, on 2014-November-05, 08:22, said:

It's not proving that LOTT is accurate (i.e. tricks = trumps). It's rejecting H0: E(tricks) = trumps. I think you can do it with a chi-square test.

H0: E(tricks) = trumps


H1: E(tricks) = c + c1 trumps + c2 (trumps)²

H1 represents LoTT better than H0.

[yunling]

campboy, on 2014-November-05, 05:45, said:

It's not clear to me how he's calculated these numbers. Assuming the ± bit gives a confidence interval for the expected number of tricks, the greater uncertainty for the 21+ range would just be a consequence of the low sample size; it doesn't mean there is a higher variance in the number of tricks made. However, the actual numbers given make this interpretation a bit implausible.

No it is not a some % interval, it is just sample variance.
By running DD analyses, he gets a distribution of number of total tricks given the total number of trumps.
x±y means that the mean of the distribution is x and the standard error is y.
I agree with jogs that it shows trump number plays a smaller role as they increase.

[jdeegan]

When LC published his first book called, as I recall To Bid or Not to Bid, Bob Hamman's comment was reported to be "Bid!". The fundamental problem is that with a blind opening lead and with two of the hands concealed, figuring out the number of total tricks in a given hand is not even achievable. Bridge is not played double dummy.

Still, LOTT is a considerable aid. Later LOTT 2.0 with adjustment factors was an improvement. Imho, IFTL is a better tool than even LOTT 2.0, but it has its limits. The main thing I got out of it was that honors in the opponents' suits are deadly in a competitive auction. Of course, this is exactly what my mentors were telling me 50 years ago when I was first learning to play.

Many trumps are good. More trumps even better.

"Purity" of the hand good.

1098762
A109
A32
32

vastly better weak 2 opener than,

Q87542
872
K76
K4

Bottom line is that Bridge is a game based on incomplete information.

[campboy]

yunling, on 2014-November-05, 20:21, said:

No it is not a some % interval, it is just sample variance.
By running DD analyses, he gets a distribution of number of total tricks given the total number of trumps.
x±y means that the mean of the distribution is x and the standard error is y.
I agree with jogs that it shows trump number plays a smaller role as they increase.

It would, if that is what he means by "x±y" and the figures are accurate. But I tried doing the same thing (with Thomas Andrews' Deal program), and got completely different values for the sample standard deviation. I used 1000 samples for each number of total trumps; I'll try again with bigger samples if I have time.

trumps		sample mean	sample s.d.
14		13.82		0.866
15		14.873		0.909
16		16.113		1.010
17		17.032		0.999
18		17.947		1.095
19		18.783		1.131
20		19.55		1.186
21		20.138		1.208
22		20.679		1.192
23		21.192		1.195
24		21.675		1.111

[whereagles]

jogs, on 2014-November-05, 17:26, said:

H0: E(tricks) = trumps
H1: E(tricks) = c + c1 trumps + c2 (trumps)²

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.