[Cascade]

Just some random thoughts ...

If you forget for the moment any thoughts that bidding systems and non-transitive as Richard often asserts - that is given System A is better than System B and System B is better than System C it does not necessarily follow that System A is better than System C - then the problem of choosing a bidding system can be view as a constrained optimization problem where the constraints are the system regulations.

My recollection of optimization theory suggests that an optimum will occur either at a local optimum or at the boundary.

This explains why we have so many problems with some system regulations. It is natural that they best approach will occur near these boundaries or at least the boundaries should be investigated to see if the optimum exists there.

If those boundaries are not well set then this will exasberate any problems that occur.

Examples of problems at the boundary will occur for example when the boundary condition is set in terms of a method of judgement that is not universally used by players. This occurs in practice when regulations use "high card points" or "Rule of 18" etc which were only ever intended as guides to judgement not fixed standards by which to create a rule. This results in anomolies where it is legal to bid with some hand or other but it is illegal to bid with a different hand that it is reasonable to argue is stronger.

There are also anomolies where the regulations are badly written and/or ambiguous e.g. The definition of convention, defintion of HUM etc, so that it is not always clear which bids with which hands will in fact violate the regulations.

To my mind this is a good arguement for fewer system regulations or at least to make sure that any we have are clear and are not based on flawed methods of judgement. In fact I would go further and argue that it is wrong for a regulation to be based on any method of judgement. I want my opponents to exercise their bad judgement as often as possible. I don't want the regulators telling them they are not allowed to use their bad judgement.

[helene_t]

Not sure if I can follow you. What is the relevance of "System A is better than System B"? Nobody would say that good systems should be banned or that bad systems should be banned. What (if anything) should be banned are systems against which standard defense is grossly inferior or even undefined. It sounds as if you're confusing the "optimal system" problem with an "optimal regulation" problem.

If I understand you correctly, you say that a HUM-definition based on HCP is bad because HCP is not necessarily an accurate gauge of playing strength. There was an editorial in Bridge World a couple of years ago saying basically the same. The editor said (I don't recall the exact example but the idea was the same) that if HUM regulations require 8 HCP for an opening then you could agree to open
with
xxxxxxx-xx-KQ-QJ
but not with
AQJxxxx-xx-xx-xx
but maybe you could get away by calling the opening with the second hand a "judgment call".

I think this is silly. Rules must be simple. Requiring 8 HCP does not mean that you must open with Jxx-Jxx-KQJ-xxxx. Players can use whatever evaluation criteria they fancy as long as their opening threshold is far enough above the 8 HCP to assure that effects of non-HCP evaluation will not cause them to open with less than 8 HCP. For example, if the relation between Cascade Points (CP) and HCP is |CP-HCP| < 4 you can agree to open with 11 CPs and you're safe.

Anyway, I think (and here we seem to agree, but maybe for different reasons) that any discusion about how high this threshold should be and what strength scale should be used, is premature. It's not clear to me why anybody would want to constrain 1-level opening based on strength. Under a HUM/BSC ban, I can open a natural 2♥ (or a multi or transfer 2♦) with xxx-xxxx-xxx-xxx so I don't see why I can't open at the 1-level with the same hand.

Here's a more relevant on, IMHO: Lorenzo's overcall style is mainly lead-directing. He would overcall on a 3-card like AQx. He does that frequently enough for his p to catter for it. This is a BSC. Is it reasonable that the regulations ban such an overcall, while an overcall on xxxxx (or even xxxx) is allowed? I think it's highly problematic if the regulations in effect force players to emphasize "p will raise me on the basis of the LOTT" rather than "p will lead my suit".

[Gerben42]

Quote

you could agree to open
with
xxxxxxx-xx-KQ-QJ
but not with
AQJxxxx-xx-xx-xx
but maybe you could get away by calling the opening with the second hand a "judgment call".

No, I think the rules are meant as absolute borders, meaning you can agree to open the 1st hand but probably shouldn't, but they want you to make your minimum a bit higher than this and get to the limit with judgement calls, not over it.

[MarceldB]

Cascade wrote:
>There are also anomolies where the regulations are badly written and/or ambiguous >e.g. The definition of convention, definition of HUM etc, so that it is not always clear >which bids with which hands will in fact violate the regulations.

I would like to make a compliment to the writer of the HUM-regulations.
(I'm really serious, inspite of my avatar)

Keep in mind that the HUM regulation was made only, and I repeat only, to ban WOS with a pass=13+ and a fert with 0-7 HCP.
There is really no "gap" , even not for mixed systems, in rules 1-3 to practice such WOS. So the aim was reached herewith.
If in the mid-sixties the zones were designed with a Fert = 0-8, I'm pretty sure that 9HCP in the regulations should be the minimum HCP for a 1-level call.
Rule no 4 (no short OR long cq. suit a or suit b as a guess principle) looks like an additional rule. Why?
There was a system called "no Name" (later Suspensor) with short or long, cq. Lambda with the guess principle, so banned too with one simple rule.

As a matter of form in some events HUM's were allowed (read: Catch 22).

So the final result is in practice a complete ban, exactly as the intention was.

The rules are very clear. If you open a certain 8-pointer or not it's up to you. (please don't forget full disclosure in your CC).

If you pass some flat or bad 12-pointers you are not suddenly a "Strong Passer"; judgement is not banned.
That's exactly the reason why the regulator has stipulated the min/max HCP only.

If you can live with those HUM-regulations and specially when and where allowed, that's a complete other matter.

But the HUM regulation is in my opinion not ambiguous, far from that.
If you say rigid, I agree (compare f.e. in a WOS Ace+any King = a 8-12 pointer zone, but alas 7 points only!).
On the other hand if rules are based on f.e. judgement only it can be hard to handle it in practice (your judgement opposite an other one) as you mentioned too.
So the "rigid" way of limiting the HCP in regulations, taking account of the intention/origin of the HUM-regulation, is the simple and probably the most workable way.
Reason why I can understand the merit.


Regards,
Marcel

[david_c]

Cascade, on Jul 10 2007, 02:25 AM, said:

To my mind this is a good arguement for fewer system regulations or at least to make sure that any we have are clear and are not based on flawed methods of judgement.  In fact I would go further and argue that it is wrong for a regulation to be based on any method of judgement.  I want my opponents to exercise their bad judgement as often as possible.  I don't want the regulators telling them they are not allowed to use their bad judgement.

But we do need to regulate conventions based on the strength of the hand somehow. To give an extreme example, we want a 1♦ bid which shows "17+ HCP any shape" to be allowed, but we don't want a 1♦ bid which shows "0-8 HCP any shape" to be allowed. So there has to be some mention of strength - not necessarily in terms of HCP, but enough to differentiate between things like those two examples. More generally, players should be given more flexibility for bids which show strong hands than for bids which might be weak.

Agree with Helene and Gerben that a rigid boundary based on HCP does not mean players are not allowed to use judgement: it just means that players must set their agreements sufficiently high that all the hands they judge to be worth that bid meet the HCP requirement.

[Cascade]

helene_t, on Jul 10 2007, 06:58 PM, said:

Not sure if I can follow you. What is the relevance of "System A is better than System B"? Nobody would say that good systems should be banned or that bad systems should be banned. What (if anything) should be banned are systems against which standard defense is grossly inferior or even undefined. It sounds as if you're confusing the "optimal system" problem with an "optimal regulation" problem.

I am just thinking of system regulations as the constraints of an optimization problem and the consequence of that is that players will want to push the boundaries.

A better than B better than C not necessarily meaning A is better than C was simply a disclaimer since I know nothing about optimization problems where transitivity does not hold.

[helene_t]

Cascade, on Jul 10 2007, 01:30 PM, said:

helene_t, on Jul 10 2007, 06:58 PM, said:

[....] It sounds as if you're confusing the "optimal system" problem with an "optimal regulation" problem.

I am just thinking of system regulations as the constraints of an optimization problem and the consequence of that is that players will want to push the boundaries.

Oh sorry, I missed that.

So if the boundary of the opening space is defined by HCP>7 then one might fear that the optimum is at the boundary, which would "force" the users to use HCP as a measure of strength? There is some truth in that but I don't think it is that severe. Since if Cascade Points satisfy |CP-HCP|<4 abnd you are devoted to the CP scale, the boundary becomes defined by CP>10. This is less permisive than HCP>7 so you will not enjoy as many openings as the HCP-counters, but since it is more important to open with the "right" hands than to open as often as possible, I think the impact of the regulations in this particular case is limited.

I could easily be wrong. Or there could be other examples of regulations that have more severe impact.

[barmar]

Cascade, on Jul 9 2007, 08:25 PM, said:

In fact I would go further and argue that it is wrong for a regulation to be based on any method of judgement. I want my opponents to exercise their bad judgement as often as possible. I don't want the regulators telling them they are not allowed to use their bad judgement.

A problem with this is that system regulation is closely related to system disclosure. In order to accomplish full disclosure, there needs to be a common language to describe hands; e.g. how can you disclose your 1NT range if you don't have an agreed-upon way to describe the strength of balanced hands?

Given that we need such language for disclosure purposes, it seems natural to reuse it for regulation as well. As david_c points out, regulations need *some* criteria to distinguish hand types -- what else is there?

[DrTodd13]

I think the problem statement is somewhat misformed. If one side in the auction were always silent then it is easy to show that since the systems don't interact with each other that if A beats B and B beats C that A will beat C. Once you start talking about competitive auctions then the notion of systems sort of breaks down. You could divide someone's system into their opening system and their overcall system. Then the question becomes how effective is A's overcall system versus B's opening system and vice versa. Moreover, A's overcall system can and should depend on B's opening system. You may have some systems where the system is very accurate barring interference but terribly inaccurate if there is interference. In this case, the opps would surely intervene and render your system inaccurate. So, when picking a system, you have to balance accuracy in a non-competitive auction with accuracy in competitive auctions assuming that the opponents employ the best overcall structure possible. If A is playing their opening system then both B and C will want to play the best overcall structure possible to combat A's opening system. B and C could still employ radically different opening systems themselves. However, if everyone is obstinate, lazy, or ignorant and tries to play the same overcall system against every system then I don't think that transitivity necessarily holds. A could have a good defense against B but B not have a good defense against A so A wins. B could counter C's opening system good but not vice versa so B wins. Finally, C could use the optimal defense against A and thus C wins. So, in summary, transitivity should hold if people employed optimal defenses but may not hold if they don't.

If there was one bridge law I could write, it would be that SOs cannot mandate one method of hand evaluation nor can they state system regulations in terms of that method. As such, all mention of HCP should be stricken from all the rules and regulations. Some regulations are written as "king below average strength" and I think this is a fine way to express things in an evaluation independent way. In this case though, you have to look at the people's evaluation methods on a case-by-case basis to determine what is "K below average" for them.

[jtfanclub]

DrTodd13, on Jul 10 2007, 11:24 AM, said:

I think the problem statement is somewhat misformed. If one side in the auction were always silent then it is easy to show that since the systems don't interact with each other that if A beats B and B beats C that A will beat C.

That's not true.

If my partner and I are the best players by far at a tournament, and all the other tables are playing SAYC, then we should play SAYC too. We'll all end up at the same contracts (or we'll end up at better ones), and we'll play them better, and we'll win.

On the other hand, if I'm below average at playing, then if everybody else is playing Best System A, I should play Next Best System B, so I end up at different contracts, which gives me a chance of winning. Playing where everybody else is playing is a fool's game for us.

So the interaction isn't always with your opponents at the same table. There is also interaction with what the people are doing at other tables.

And then, there is interaction with partner! If I play much worse than my partner, perhaps we want to design a two-way system where my openings are transfers and partner's openings are standard with transfer responses.

Or maybe I didn't understand your statement.

[DrTodd13]

I'm not sure this has anything to do with the question that Wayne asked. He was asking if system "betterness" is transitive. He didn't say anything about what system should I play if the event is matchpoints. Given an infinitely long event, you should always want to play the better system. The problem comes that events are relatively short and the variance even within a better system may cause you to win some events by a landslide but lose others. If you play the same system and get to the same contracts then the good pair would win by say a small amount each time. So, given short events it is practical to play the same system at matchpoints but again that wasn't the question.

[jtfanclub]

DrTodd13, on Jul 10 2007, 12:20 PM, said:

I'm not sure this has anything to do with the question that Wayne asked. He was asking if system "betterness" is transitive. He didn't say anything about what system should I play if the event is matchpoints. Given an infinitely long event, you should always want to play the better system.

No, I never mentioned match points.

Let's suppose the following is true, for a small team match, like 24 boards:

1. If I and a partner of equal strength were to play against experts, using our Precision variant, I'd have a small but significant chance of beating them, let's say 5%.

2. If I and a partner of equal strength were to bid against experts, using our Precision variant, and then GIB played the boards at both tables, we'd have an excellent shot of winning. Not 50%, of course, but maybe a little under 25%. It'd just be luck- we'd happen to bid a successful 40% game, they'd bid an unsuccessful 45% game, etc. Often Precision will expose holes that SAYC doesn't and vice versa, the problem hands are different, etc.

3. If I and a partner of equal strength were to play against experts in which GIB bid the boards for both tables (and presuming it did so identically), and then we and the experts played the hands, the odds of us winning would be right around 0. Missing a strip and endplay or a squeeze opportunity is not usually the way to win tourneys, even short ones.

Now, if we were playing an 'infinite' length tournament, then it doesn't matter- the better players always win if playing a good system, so the whole argument is moot. But for any finite length team match, the experts best chance of beating us is to play our system. Always get to the same contracts we do, and let their superior card play crush us. While it is possible that they could play a system that was so much better than ours that they'd end up with a higher chance of winning, unless our system is a whole lot worse than theirs it isn't worth the extra variance in the bidding. Variance is bad for the experts- slow and steady will win the race for sure, more random factors means more chances for us non-experts.

So, if you follow so far, you should already have concluded that if the experts are playing the best system, then we non-experts increase our odds of winning by playing an inferior system. Ideally, the inferior system should simply switch when there are two equally good choices: if 3NT and 5 clubs are each 50%, if they choose 3NT we should choose 5 clubs and vice versa. If 3NT is 50% no matter who plays it, if they have North as declarer we should use South and vice versa. Since that's generally impossible, then even losing a little is worth it: if 3NT is 52% and 5 clubs is 50%, then when they take 3NT we're probably better off taking 5 clubs, since that gives us a chance of a swing without that much of a risk. If 6NT isn't quite worth it, maybe we should bid it and take a chance. Gotta generate some swings while minimizing loss.

So if your opponents (individually or collectively) are using a system, that should affect your choice of systems, in terms of better vs. variance. So if the field is using system B, it's entirely possible that the system that will mathematically give you the best chance of winning will be system A, and the system that will give a different pair the best chance of winning will be system C.

[DrTodd13]

Why are you bringing up issues like variance and "what system should I play to maximize my chance of winning"? The question was "is system goodness transitive." To answer that question, we have to answer what makes one system better than another. I propose that we define "better" in the following manner. Take two teams (or pairs) of equal ability. Let one by play system A and the other B. Let them play an infinite number of hands. The team with the best result was playing the best system. Even for your comments, you have to define system goodness because you say a weaker team should play an inferior system to generate variance. This is a well known and valid way of increasing your chance of winning but as far I as I gather, has nothing to do with this thread.

[awm]

Cascade is probably remembering some optimization theory that doesn't apply here. What's known is that if a constrained, convex optimization problem has an optimum solution, the solution will appear at a vertex of the constraint set. In other words, for convex functions your best solution always lies along the boundaries.

But for bidding systems, there's absolutely no reason to think that finding the best bidding system would be convex. That would mean if system A is somehow "better" than system B, then a system which is somehow the "average" of systems A and B would be better than system B and worse than system A. I don't see any reason why this would follow. In particular, one might be able to argue that "standard with weak twos" is superior to "standard with strong twos" and the average would be something like "standard with intermediate twos" which could easily be better (or worse) than either of the two extremes. Obviously this depends on how you define your optimization and what "averaging two systems" means, but assuming it to be convex is a huge stretch. Without convexity, there's no particular reason that the best solution should lie near the boundary.

Of course, the real problem is that selecting the "best system" is game theoretic. To give a simple example, it's easy to imagine that which notrump range is "best" for me depends on which defense to notrump my opponents are using. One could argue that if the opponents aren't using a penalty or value-showing double, I should play weak notrump, whereas if they are using such a double I should play strong notrump. My best approach may be to "play the weakest notrump where they will not use a penalty double" or to "play the strongest notrump where they will use a penalty double."

[Echognome]

I don't think Wayne was thinking of convex functions at all. He simply said that boundaries may be an issue. We can get boundary solutions for concave functions in constrained optimization.

For example, maximize f(x) = 1 - x^2 for x >= 0.5

[jtfanclub]

DrTodd13, on Jul 10 2007, 01:46 PM, said:

Why are you bringing up issues like variance and "what system should I play to maximize my chance of winning"? The question was "is system goodness transitive."

No, that wasn't his question. In fact, what he starts with is asking you to forget whether it's transitive or not.

He was asking whether the optimum would hit at a regulation boundary, no matter where you put the regulation boundary.

I claim that is not the case. I claim the optimum will be based on the predominant system, primarily based on improvement vs. variance. So if all rules in the U.S. were eliminated tomorrow, the most successful system wouldn't be the most extreme ones, as at some point the extreme variance would beat out the slight improvement for all but the worst players. Because the predominant system is not going to be the best system (it's based primarily on ease of use), that isn't a factor either.

[awm]

For this to work, you need to make a series of highly unlikely assumptions:

(1) There exists a "best system."

(2) The best system is not, in fact, allowed.

(3) Given that the best system is not allowed, the legal system which is "most similar" to the best system will be the best constrained solution.

All three of these assumptions seem dubious to me.

A more likely explanation is that the effectiveness of a method is highly dependent on the defense which your opponents are using. Good opponents tend to have a good defense to methods which they see frequently. Therefore, it is to a pair's advantage to play methods (subject to some degree of non-ridiculousness) which are unfamiliar to the opponents. The regulatory structures are designed such that "mainstream" methods are close to the "middle" of the constraint set -- this allows people to deviate in small ways (for example playing opening bids a queen lighter than normal, or weak twos with a card less) without running afoul of the regulations. Therefore methods which are close to the boundaries of legality are likely to be "further from mainstream" and therefore less familiar and more advantageous.

[DrTodd13]

awm, on Jul 10 2007, 11:56 AM, said:

For this to work, you need to make a series of highly unlikely assumptions:

(1) There exists a "best system."

(2) The best system is not, in fact, allowed.

(3) Given that the best system is not allowed, the legal system which is "most similar" to the best system will be the best constrained solution.

All three of these assumptions seem dubious to me.

A more likely explanation is that the effectiveness of a method is highly dependent on the defense which your opponents are using. Good opponents tend to have a good defense to methods which they see frequently. Therefore, it is to a pair's advantage to play methods (subject to some degree of non-ridiculousness) which are unfamiliar to the opponents. The regulatory structures are designed such that "mainstream" methods are close to the "middle" of the constraint set -- this allows people to deviate in small ways (for example playing opening bids a queen lighter than normal, or weak twos with a card less) without running afoul of the regulations. Therefore methods which are close to the boundaries of legality are likely to be "further from mainstream" and therefore less familiar and more advantageous.

1) This assumption seems provably true to me. Here's a proof sketch. The number of possible bidding sequences is finite. The number of possible meanings for any bid in those sequences is finite. (There's only so many things you can say about combinations of 52 cards!) Each of these meanings is encodable in a finite string. The number of hands is finite as well. Therefore, it is a finite task (and therefore theoretically possible) to apply all possible hands to every possible combination of bidding sequences and meanings. You compute the goodness of these applications using a double-dummy solver. Then you define the best system in the following way. The best system is a slice through the bid meaning space such that at each opportunity for NS (w.o. loss of generality) they choose the bid meaning that maximizes their result assuming that EW are going to choose the best possible defense. If they don't choose the best possible defense then you again select the best offensive to their inferior defense and this will result in a higher score for you on average. This is akin to simple alpha-beta pruning from computer science. In simple language, you try to do the best that you can assuming that your opponents are going to do the same.

If you mean what is the best system available in the world today then you'd have to go through the laborious effort of codifying every extant system and applying to all hands but likewise you could get an answer. Neither one of these are currently practical since the number of possibilities is enormous. Without a doubt, _the perfect system_ is not in use today and would probably be exceedingly complex.

2) Without any idea what the metaphysically superior system is there's no way to know if it would be allowed or not. You need to be clear whether you refer to the metaphysically best possible system or just the best possible system that might happen to be available in the world today.

3) I agree there is no reason to believe this assumption to be true.

[joshs]

I was about to comment on convexity and lagranian multipliers but Adam beat me to it.... I strongly doubt that this is a convex problem. Now if this is a continuous function real valued function on a compact set....

This also is an interesting game theoretic problem where transitivity almost certainly does not hold. You can easily imagine a rock paper scicors situation with regard to systems (where we include defensive methods and competative methods in a system).

Like many of the people here I will mention that boundary type system regulations do have a serious negative effect on the effectiveness of methods.
when you play a 15-17 NT you can upgrade KTx Ax AQJxx T9x and you can downgrade KJx KQ Qxxx KJxx. My claim is being able to upgrade and downgrade improves the results you get with the method.

When you play 10-12 NT you can't upgrade ATx xx KQT9x T9x which is better than 80% the hands you do open a 10-12 NT. This hurts the effectiveness of the 10-12 NT in constructive auctions. Because of this, ranges like 11-13 or 10+ to 13- are probably more effective than 10-12.

[Echognome]

joshs, on Jul 10 2007, 01:21 PM, said:

I was about to comment on convexity and lagranian multipliers but Adam beat me to it.... I strongly doubt that this is a convex problem. Now if this is a continuous function real valued function on a compact set....

Lagrangian is fine and dandy if you have a simple function with an equality constraint. Once you have inequality constraints (such as hcp >7) or mixed constraints, you are talking about Kuhn-Tucker conditions.

Again, I don't see what convexity has to do with the problem. You can still hit boundaries with concave functions.

You of course can use Bolzano-Weierstrauss to show a maximum exists if it's continuous. We don't have continuity of course, but I don't think it's too big a step to approximate with continuity. We have a pretty good range once we start adding texture into the hands, such as comparing a suit of AK432 with AK984 or with AKT98.