What's the rule of 17 for supporting partner's preempts?

[pilowsky]

In a post concerning 'Oddities of GIB' 'barmar' asks "What's the rule of 17 for supporting partners preempts?"

 

This is an interesting question so here, after some thought, is the start of an answer. If there is a real Integer mathematician out there I would really enjoy reading their ideas on this matter.

 

Bridge, as Matt Ginsberg (GIB) realised, is a problem in integer mathematics.

 

The preempting rule of 17 (like all other Bridge rules) is a rule that is based on integer mathematics. For those of us that like to open with a weak 2 (Generally 2♥️, ♠️, ��but also 2♣️ in some systems) then the rule is as follows Opener has 5-9 HCP not vulnerable; 7-10 vulnerable and 6+ cards in the suit ('Preempts' Warren Watson 2019; Masterpoint Press). If responder applies the following formula ∑HCP+TRUMPS and the result is ≥ 17 then bid 4 of that suit. In a major contract, the advantages are clear.

 

Although not discussed by Watson in his excellent book, but I do think possible, is a generalised extension to the 'rule/principle' as for example shown here: for slam bidding: if ∑HCP+TRUMPS ≥ 20 bid 6.

 

The same formula can be applied to bidding at the 1 level and to bidding in NT over a minor opening, I now have a growing collection.

 

The rule is clearly affected by interference, partnership agreement and vulnerability. All of which should be considered.

 

Many other authors suggest that other methods should be used and that rules of this type are no substitute for thinking. No doubt this is true. On the other hand, if you do not have a roof over your head you're going to get very wet during the rain while you have all those thoughts. My suggestion is that while you think, remember that common things occur commonly. 5 cards out against you will usually break 3:2 and the rule of 17 will apply almost all the time. Being able to find an exception does not prove the rule wrong. It simply proves that improbable events occur occasionally. No surprise to anyone familiar with stochastic thinking: of course, one should be aware that there are situations where it will fail. We're bridge players, not airline pilots. That does not mean that it is not a useful starting point.

 

As an aside, I find (at the moment) that GIB seems to employ 'The Law' (as in the Law of Total Tricks) slightly differently to the way that I would apply the rule of 17 and so I have adjusted my preempt values to cope. Although to be fair this may equally be due to inadequate quality of Bridge playing on my part - still working on that.

[mikeh]

Simplistic numerical rules can provide some help to the aspiring player, but it is essential to recognize that hand valuation is far more subtle, and complex, than can ever be reflected in a two-factor equation. So long as the user understands that these rules should be discarded as his or her understanding of the game improves, it can maybe help.

 

However, and to provide a simple example, say partner opens 2S and I hold Kxxx x AJxxx xxx

 

That’s nowhere near the rule of 17, but I’m bidding game right now.

 

Give me QJxx KQJ Axx Jxx. And my hand exceeds 17, but not only may we have no lay, but my hand is such that they probably can’t bid game and may well not make it if they do.

 

Like I say, provided one understands that simplistic rules should only be used while en route to gain now no a better understanding, then I think they have their place.

[pilowsky]

Simplistic answers that my students bring to me that are poorly thought out and are unsupported by data, references or evidence, score low grades and are of little value: although they seem to enjoy a happy audience of one. Appeal to authority in the form of previous success in competition - well done by the way Mike - is not a substitute for a well-reasoned discussion.

 

As I was very careful to explain: Did you get to the last paragraph? Yes, it is easy to find examples where one should break the rule; ho-hum, how clever are we. Sometimes the hoof-beats outside the window are a zebra, but they are never a unicorn. Good job that's statistics for you. Now back to bridge folks.

 

 

Here is the hand that you claim will not make:

[hv=pc=n&s=sqjt9hkqjdat9cjt9&w=s32ha543dk83c8743&n=sak8765hd765cq652&e=s4ht98762dqj42cak&d=n&v=0&b=1&a=2sp4sppp]399|300[/hv]

As you can see, GIB double-dummy has it at 4♠+1.

 

Here is a hand that I played recently. GIB plays a 2/1 system where 2♣ is 3+ ♣ and 11+ HCP applying the rule ∑HCP+TRUMPS gave a value of 22 so I called 6♣ and made 6♣+1. (94.2%, 1390, ACBL daylong B 2020-01-14). Others in the same spot did not get the same result possibly because GIB makes a different lead if the same contract is reached without a preempt.

Of course I am not advocating that people stop thinking. Exactly the opposite. What I am suggesting is that we try to understand the architecture that underpins the thinking. Throwing up random hands and saying I believe this or that without evidence is not unhelpful.

 

[hv=pc=n&s=s32hatdaqjcaj9742&w=saj54hq652dt85ct8&n=sq76hkj84dk72ckq3&e=skt98h973d9643c65&d=n&v=n&b=5&a=1cp6cppp&p=h3hthq]399|300[/hv]

[sfi]

Here is the hand that you claim will not make:

[hv=pc=n&s=sqjt9hkqjdat9cjt9&w=s32ha543dk83c8743&n=sak8765hd765cq652&e=s4ht98762dqj42cak&d=n&v=0&b=1&a=2sp4sppp]399|300[/hv]

As you can see, GIB double-dummy has it at 4♠+1.

 

[...]

 

Throwing up random hands and saying I believe this or that without evidence is not unhelpful.

 

You try to disprove someone else's point by claiming they are "throwing up random hands" and you come up with this example? Just lol.

 

Two points:

- Almost any change to the hand you provide supports Mike's point rather than disproves it.

- North has a 1S opener, not a 2S opener.

 

And your second example is so ridiculous it's not even worth discussing.

 

The rule you quote is a bad rule. Even basic judgment can do better than it.

[mikeh]

Simplistic answers that my students bring to me that are poorly thought out and are unsupported by data, references or evidence, score low grades and are of little value: although they seem to enjoy a happy audience of one. Appeal to authority in the form of previous success in competition - well done by the way Mike - is not a substitute for a well-reasoned discussion.

 

As I was very careful to explain: Did you get to the last paragraph? Yes, it is easy to find examples where one should break the rule; ho-hum, how clever are we. Sometimes the hoof-beats outside the window are a zebra, but they are never a unicorn. Good job that's statistics for you. Now back to bridge folks.

 

 

Here is the hand that you claim will not make:

[hv=pc=n&s=sqjt9hkqjdat9cjt9&w=s32ha543dk83c8743&n=sak8765hd765cq652&e=s4ht98762dqj42cak&d=n&v=0&b=1&a=2sp4sppp]399|300[/hv]

As you can see, GIB double-dummy has it at 4♠+1.

 

Here is a hand that I played recently. GIB plays a 2/1 system where 2♣ is 3+ ♣ and 11+ HCP applying the rule ∑HCP+TRUMPS gave a value of 22 so I called 6♣ and made 6♣+1. (94.2%, 1390, ACBL daylong B 2020-01-14). Others in the same spot did not get the same result possibly because GIB makes a different lead if the same contract is reached without a preempt.

Of course I am not advocating that people stop thinking. Exactly the opposite. What I am suggesting is that we try to understand the architecture that underpins the thinking. Throwing up random hands and saying I believe this or that without evidence is not unhelpful.

 

[hv=pc=n&s=s32hatdaqjcaj9742&w=saj54hq652dt85ct8&n=sq76hkj84dk72ckq3&e=skt98h973d9643c65&d=n&v=n&b=5&a=1cp6cppp&p=h3hthq]399|300[/hv]

Are you by any chance related to the possum character who spent so much time here in the past year? You play against robots and think you’re playing bridge, and you’re proud of bidding a silly slam that made on the wrong lead. I’m just surprised that you aren’t devising a rule that let you bid the grand, lol.

 

Plus, as soon as anyone posts even a hint of constructive criticism you respond in a truly bizarre manner. Ok, enough. If you are the possum, I expect we’ll see a lot of your inanity in th3 next few weeks, but you won’t be seeing any comments by me. It took a while but I finally learned the wisdom of not feeding the trolls.

[pilowsky]

Well, 'sfi' (Stephen) good luck abusing other people. You might open hands with less than 11 HCP, most people playing on BBO don't. The hand is exactly the cards provided by Mike. The other hand is not an example, it's a real hand from a real ACBL Tournament - try one yourself.

Actually knowing what you are talking about, based on real research, education and a solid understanding of mathematics, and probability is more useful than any opinion even yours, which as your card says, can be 'fake'. Making assertions about 'basic judgement' is entirely unhelpful. I hope that you do not attempt to assist others to learn using an educational technique that starts with "...your second example is so ridiculous it's not even worth discussing. The rule you quote is a bad rule. Even basic judgment can do better than it....". In the education business we call this type of phraseology, anodyne. It numbs the senses and provides no useful information.

[sfi]

Well, 'sfi' (Stephen) good luck abusing other people. You might open hands with less than 11 HCP, most people playing on BBO don't. The hand is exactly the cards provided by Mike. The other hand is not an example, it's a real hand from a real ACBL Tournament - try one yourself.

Actually knowing what you are talking about, based on real research, education and a solid understanding of mathematics, and probability is more useful than any opinion even yours, which as your card says, can be 'fake'. Making assertions about 'basic judgement' is entirely unhelpful. I hope that you do not attempt to assist others to learn using an educational technique that starts with "...your second example is so ridiculous it's not even worth discussing. The rule you quote is a bad rule. Even basic judgment can do better than it....". In the education business we call this type of phraseology, anodyne. It numbs the senses and provides no useful information.

Once again, lol.

 

By the way, there was a pretty good real-life two-week tournament a couple hours down the road from you that just finished today. Shame you missed it. See you at the next one?

[sfi]

That would be a no then.

[FelicityR]

[hv=pc=n&s=s32hatdaqjcaj9742&w=saj54hq652dt85ct8&n=sq76hkj84dk72ckq3&e=skt98h973d9643c65&d=n&v=n&b=5&a=1cp6cppp&p=h3hthq]399|300[/hv]

 

I'm always leading a ♠ (attacking) against a contract bid this way, GIB or no GIB.

 

Even though you say that Mr Ginsberg says bridge [bidding] is a problem in (integer) mathematics, it is a lot more besides. That's when personal judgement comes to the fore. I have Kx in a suit: bid on the right of me by an opponent it is probably an asset; on the left probably a liability.

 

I have absolutely no idea how bridge computers are programmed, but given that chess computers can beat the top players in the world now but bridge computers cannot just proves that 'number-crunching' is no match for understanding the subtleties of this beautiful game.

[nige1]

[hv=pc=n&w=saq8742H32d84C952&e=SJ53HAQ94DAQ93CA7&d=w&v=0&b=8&a=2s(Weak%206%20!Ss%205-9%20HCP)p4sppp]266|200|IMO we should accept rules-of-thumb for what they are -- unnecessary for the likes of MikeH -- but rough aids to judgement for ordinary players. I use the WTC (Winning Trick Count), a variation of the LTC ...

A=1.5, K=1, Q=0.5.

Void=3, Singleton=2, Doubleton=1.

Add a winner for trump control.

Adjust for duplication and intermediates.

Applying this yardstick for the hands on the left ...

West=4 (2 for ♠AQ, 1 each for red doubletons] (about average for a weak two)

East=6.5 (♥AQ=2, ♦AQ=2, ♣A=1,5 winner, ♣doubleton=1 winner)

Trump control=1. (enough to draw trumps and ruff losers).

Total winners = 11.5 Enough for 4♠.

Amusingly this also satisfies Pilowski's rule of 17 :)[/hv]

[Tramticket]

A few things:

 

The rule of 17:

 

Larry Cohen mentions it here. If you read the article, Larry Cohen is less than enthusiastic and states:

Do I like this rule? Not really. It is a crude guideline which might have appeal to new players.

 

and also:

Summary: The Rule of 17 is a guideline--no more. I don't recommend that experienced players use it.

 

I find the rule to be rather bizarre. Raising a weak two to game can be based on multiple hand types:

- Hands expecting game to make based on strength.

- Hands with no expectation of making game, but wishing to raise the level of preempt.

- Hands combining elements of these two - i.e. shapely hands where game "might" be making either way.

 

The rule does not really meet these multiple objectives.

 

 

A weak 2

 

OP states:

 

For those of us that like to open with a weak 2 (Generally 2♥️, ♠️, 🔶but also 2♣️ in some systems) then the rule is as follows Opener has 5-9 HCP not vulnerable; 7-10 vulnerable and 6+ cards in the suit ('Preempts' Warren Watson 2019; Masterpoint Press).

 

7-10 vulnerable seems like a rather high hurdle and most will choose to have a lower range.

 

 

Integer Mathematics

 

OP states:

 

If there is a real Integer mathematician out there I would really enjoy reading their ideas on this matter.

 

I understand of course what an integer is and what a mathematician is. I was not aware that there are mathematicians who specialise in the study of integers, but I am quite prepared to believe that there are. But I don't understand why a specialist knowledge of integers should be helpful to bridge, rather than some other branches of the subject, such as (say) probability theory?

[barmar]

I have absolutely no idea how bridge computers are programmed, but given that chess computers can beat the top players in the world now but bridge computers cannot just proves that 'number-crunching' is no match for understanding the subtleties of this beautiful game.

I don't know about other programs, but GIB essentially uses two processes in its bidding:

 

1. A large database of bidding rules. Rules are associated with a particular state in the auction (e.g. a rule may only apply after 1 minor - 1 Major, or with a particular vulnerability), various features of the bidder's hand (HCP, controls, shape, etc.), the information that other players have shown in the auction (e.g. partner's point range), and they specify what to bid. Sometimes multiple rules may fit a situation, so we'll get a number of candidate bids, and they're prioritized. It also applies some rules that apply to similar hands to the one it has (e.g. a few points stronger or weaker, or one more or less card in a suit), but these bids are given low priority.

2. Simulations. It deals out a number of hands consistent with the auction so far (and a few that aren't, to allow for psychic bidding), simulates how the auction will proceed after each candidate bid. Then it performs a double dummy analysis to see what the final result will be in each case. Some rules prohibit simulation (e.g. responding to Stayman or Blackwood), some low priority rules require it, and most simply allow it. For each candidate bid, it gets the average final result across all the hands, and the one with the best result is chosen.

 

Including rules that don't exactly match the hand is how it emulates "judgement". And it's why GIB will sometimes not have a hand that fits the bid explanation.

 

These similations are also one of the differences between BBO's Basic and Advanced robots. Basic robots just bid according to the rules, they don't use simulations to improve judgement.

 

It certainly would be possible to write bidding rules that implement this Rule of 17, and there may be rules that have similar results. There are already rules that correspond to the Law of Total Tricks, and some of them even mention it in their explanations. But the simulations mean they don't follow the law robotically (pun intended).

[pilowsky]

Dear Brian - tramticket, A few things:

• Telling me that Larry Cohen said something does not mean that you are as clever as Larry Cohen, FYI, as I explain to students this is known as the fallacy of 'appeal to authority' I see it in bridge clubs quite a lot. It seems to be a common alternative to actual research and thinking. Quite funny when you recall that it was Larry Cohen who remarked that the rule of 17 was no substitute for the rule of thinking.
• Finding a rule to be bizarre is a challenge that you will have to overcome all by yourself.
• When you make statements such as 'most will choose a lower range' please try to back it up with evidence. Otherwise, it sounds a little bit like Donald Trump telling me that most people believe that what he says is true.
• I am surprised that someone who claims to know what an integer is can simultaneously not understand how integer mathematics might be useful to bridge. Notwithstanding this point, please be aware that this does not mean that other branches of knowledge or philosophy might not also be useful. The list of fallacies grows.
• Good for you knowing that Kent is near London.

[barmar]

Dear Brian - tramticket, A few things:

Telling me that Larry Cohen said something does not mean that you are as clever as Larry Cohen, FYI, as I explain to students this is known as the fallacy of 'appeal to authority' I see it in bridge clubs quite a lot. It seems to be a common alternative to actual research and thinking.

Appealing to authority is not really a fallacy when talking about something where judgement is involved. Since Cohen is a very successful player, what he's written is very credible.

 

We see this from time to time here: Someone new shows up with no known bona fides and proposes some new bidding system or revision of a popular convention, claiming that it's far superior to what experts play or recommend. When people criticise it, they get all defensive.

 

While it's true that many popular conventions are not optimal, and maintain popularity just because of momentum, you still need to provide good, clear justification for something new and untried. There's usually a good reason why experts haven't come up with something themselves.

[pilowsky]

While I have your attention though can you please tell me how to use the 'insert image' button on the editor (between link and mail)? This would be even more fun if illustrated.

[barmar]

While I have your attention though can you please tell me how to use the 'insert image' button on the editor (between link and mail)? This would be even more fun if illustrated. Poodles

https://drive.google.com/open?id=1JvRgVV09o2WwidXpQmPBCfaOyWQOZ48y

You need a link directly to the image file. See https://elfsight.com/blog/2018/02/how-to-upload-images-for-direct-url-in-google-drive/ or

for how to do that.

[JonnyQuest]

In a major contract, the advantages are clear.

 

Many other authors suggest that other methods should be used and that rules of this type are no substitute for thinking.

 

What was made clear? I'm missing something.

 

I agree with what "other authors" suggest. I think it's a good "starting point" for beginners, at least until "bridge judgment" has been accumulated over time.

[Zelandakh]

Just for the record I am a mathematician, albeit not a specialist in usage of the integer set, and this rule makes little bridge sense for reasons already outlined by Mike and Tramticket. My own silly example would be a 5=0=4=4 hand at green opposite a weak 2♠ opening. How many BBFers will wait for 13+hcp here before raising? Or 12+hcp for a 6=0=(4-3)? The simple truth is that the number of trumps is just a more important attribute than the hcp so assigning them a 1:1 ratio of importance is unsound. It may be that there is some guideline rule for intermediates that can be created that is an improvement over the existing guideline (LoTT) but even if such a rules exists, this is categorically not going to be it.

[mikeh]

Just for the record I am a mathematician, albeit not a specialist in usage of the integer set, and this rule makes little bridge sense for reasons already outlined by Mike and Tramticket. My own silly example would be a 5=0=4=4 hand at green opposite a weak 2♠ opening. How many BBFers will wait for 13+hcp here before raising? Or 12+hcp for a 6=0=(4-3)? The simple truth is that the number of trumps is just a more important attribute than the hcp so assigning them a 1:1 ratio of importance is unsound. It may be that there is some guideline rule for intermediates that can be created that is an improvement over the existing guideline (LoTT) but even if such a rules exists, this is categorically not going to be it.

Indeed. I don’t ‘add points’ for distribution when evaluating a hand, and only use hcp as an important aspect of bidding judgement on balanced hands, but I do think that shape (not merely the number of trump) is an important aspect of knowing when and how to raise a preempt. This is not at all the same as saying I don’t consider shape: I very much do, but I don’t generally ‘count’ or use hcp when deciding what to do, beyond being a very basic starting point.

 

Thus I will raise 2S or 3S to game with a trump fit and a side stiff or void on far fewer hcp than would be needed were my hand flat.

 

Perhaps more importantly, and seemingly ignored by this purported rule, one is often raising to game with no strong expectation, and sometimes no expectation, of making the contract. One is furthering the preempt, and being able to make the contract may sometimes be, if even possible, a secondary consideration.

 

Give me, say, AJxx x xxxxxx xx at equal and partner opens 2S, obviously we all bid 4S. Give me AJxx xxx xxx xxx, and I would be far more reluctant to do so, since we rate to be losing at least 6 tricks, and failing by more than the value of their game. Now, in real life I’d probably consider it anyway because neither opp is likely to be looking at a trump trick, and it may prove impossible for them to double and convert to penalties.

 

The ‘rule of 17’ values these two hands as being the same, which is pretty obviously an error.

 

There may be a role for a rule such as this when deciding whether to raise to gamevwith balanced hands and an expectation of making the contract, if taught along with some guidance as to when to raise as a two-way shot (we may make but if not it may be a save) or when to raise preemptively. However, points don’t take tricks: cards take tricks. All methods of generating numerical values for a hand are approximations and simplifications. The key to advancing as a bridge player is to develop the ability to assess the likely playing value of one’s hand in terms of trick-taking ability, rather than ‘points’. Trick-taking includes having cards win by power but also having side shortness, and adequate trump length, to ‘cover’ partner’s hoped-for weak length in that suit.

 

While I suspect that a fairly simple numerical rule could be developed for these purposes, my advice to all players wishing to become good at the game is to recognize that all of these ‘rules’, using numerical values, are very crude and unreliable guides.

 

I would offer a golfing analogy. The makers of golf clubs succeed, in large part, because most recreational golfers have some belief that buying new equipment will improve their game, with no effort on their part other than giving their credit card a workout. In reality, most would be far better off spending that money on lessons and practice. Rules that turn bidding decisions into simple arithmetic are like shiny new clubs. They afford the illusion of improvement, not the reality. Becoming better takes work. It probably takes mentoring, or at least serious levels of reading and playing, preferably with or against players better than oneself.

[JonnyQuest]

Here is what you missed: The clear advantage in a 'major' contract is that 4 is game. But in the minors, one needs to be at the 5 level.

 

Hope that clears things up.

 

No, it didn't.

 

I still fail to see where you've explained why and how the Rule-of-17 works, why it is better than not using such a rule, or examples of the type of hand where it works, or does not work.

 

Simply stating that "The clear advantage in a 'major' contract is that 4 is game," is misdirection. It's an advantage if game makes, or if game has a high enough probability of making that it should be bid. If it should not be bid, and the "Rule-of-17" directs us to bid it, then there is no "advantage."

[Zelandakh]

1. Tramticket did not advance any reasons. Perhaps if you locate them, you can point them out.

The main reasons that TT raised are included in Mike's post directly below yours so perhaps you can find something there. I think it is fairly clear that debating the merits of this rule is fairly pointless though, so instead I will provide you with an opportunity to prove your case to us. Let us designate the number of trumps in the hand as T and the hcp as H. Then your rule can be stated as:-

 

A. If T+H>=18, bid 4M.

 

So now I would like you to compare this with some alternative simple rules:-

 

B. If T>=4, bid 4M

C. If T>=4, bid 4M unless specifically 4333

D. If 2T+H>=22, bid 4M

E. If 3T+H>=26, bid 4M

F. If 4T+H>=30, bid 4M

 

I would like you to analyse these, ideally for both majors but let's start with spades as that is simplest. Assume Dealer holds 5-9hcp and a good 6 card spade suit and that second seat holds either 0-14hcp and 3+ spades or 0-10hcp and 0-2 spades (we can refine this if the results seem close). Then compare results for each of the 6 rules above against the par score for the deal. I am confident that even within this limited analysis it will be clear that Ro17 is sub-optimal. But perhaps you will find otherwise. So please go away and run some analysis and then come back with your results. If you do it properly, maybe you will even surprise yourself...

[pilowsky]

Dear Mark, Thank you for your ideas, but that is not how research works in real life. I knew a theoretical physicist who once approached a senior Professor of Biology and told him that he had a Theory about how the brain worked and asked him to conduct a specific experiment to test the idea: that did not end well. I suggest that you do your work, and I'll do mine. Yes, I am still working on this problem. It is a large and interesting one. If it piques your interest, then it is you that should also do some research. This habit that some people have of providing instruction to others along the lines of you must do this, or that is not conducive to progress. Quite the opposite; I am sure that you, as a mathematician, are more qualified than me to test this hypothesis for the benefit of all. The answers may be of interest beyond Bridge: who knows, that's why it's called research.

[Zelandakh]

Dear Mark, Thank you for your ideas, but that is not how research works in real life. I knew a theoretical physicist who once approached a senior Professor of Biology and told him that he had a Theory about how the brain worked and asked him to conduct a specific experiment to test the idea: that did not end well. I suggest that you do your work, and I'll do mine. Yes, I am still working on this problem. It is a large and interesting one. If it piques your interest, then it is you that should also do some research. This habit that some people have of providing instruction to others along the lines of you must do this, or that is not conducive to progress. Quite the opposite; I am sure that you, as a mathematician, are more qualified than me to test this hypothesis for the benefit of all. The answers may be of interest beyond Bridge: who knows, that's why it's called research.

To be honest I was working under the assumption that your previous post was accurate.

 

Actually knowing what you are talking about, based on real research, education and a solid understanding of mathematics, and probability is more useful than any opinion

If you are serious about promoting this rule and its "obvious advantages" then you need to be able to present your real research together with your understanding of maths and probability. My suggestion is a way that you might achieve that end comparing against some alternative simple rules for which the advantages are not clear. My assumption was that you will already have a substantial amount of research behind you to make the claim but that it is perhaps not in a form that lends itself to such mathematical presentation. The above test would provide you with the statistics to back up your argument or, alternatively, to improve your rule.

 

The problem that you have here is that one of those simple alternatives, the LoTT, already has a body of statistics broadly supporting it. At the moment there is no such similar body of evidence for the Rule of 17, So from a personal point of view I will for the time being stick with the formula that the maths backs up as a broad basis for decisions and adjust according to experience and judgement. Anyone that can gather evidence for an improved baseline rule would be more than welcome. This has already happened to me a couple of times, not only the LoTT but also in terms of adjusting the values of aces and queens in the Milton Work count when strong mathematical evidence came to light that earlier analyses were not completely accurate.

 

It might also interest you to understand why I chose the specific formulae. I am giving you the benefit of the doubt here that your existing research and analysis has found an optimal solution (14hcp) for 4 card trump support, which I noted was the case for all of your examples. Then I constructed formulae that use the identical values for 4 card support but offer a gradually increasing weight to distribution over hcp. It seems to me completely obvious that this process is essential for any construction of an optimal formula balancing trumps and hcp, so if you have not already done work in this area then it seriously calls into question any assertion that the rule has been properly formulated.

 

 

In any case, you asked at the start of this thread for the input of a mathematician. You have my input now; it is up to you what you choose do with it.

[masse24]

In a post concerning 'Oddities of GIB' 'barmar' asks "What's the rule of 17 for supporting partners preempts?"

 

The preempting rule of 17 (like all other Bridge rules) is a rule that is based on integer mathematics.

 

* * *

 

[T]he rule is as follows . . . If responder applies the following formula ∑HCP+TRUMPS and the result is > 17 then bid 4 of that suit. In a major contract, the advantages are clear.

 

 

I am not a mathematician. However, I can read. My reading of "the rule" differs.

 

The above rule is not the "Rule of 17." The error you've made is that the formula should read: ∑HCP+TRUMPS and the result is >= 17 then bid 4 of that suit.

 

I hesitate to cite my sources, since that might be construed as an Appeal to Authority. You are free to do your own research.

[pilowsky]

Yes, the correction is right, it should be ≧.