[cherdano]

mikeh, on Aug 8 2007, 09:24 AM, said:

If this had happened 20 years ago, I'd vote for the big club method. I think that big club contains more capacity for weird science than does 2/1. See the Meckwell approach... I know of no 2/1 method with anything like the level of detail that Meckwell uses in their agreements, and while that is (I assume) partly Rodwell's capacity for invention and Meckstroth's capacity to learn, it is also, in my view, a reflection of the underlying differences between the two methods: and I write that as someone who has played a very, very complex 2/1 method.

I am no Meckwell expert, but do they really have more complex agreements in their 1♣ auctions than in their 2/1 auctions after a 1M opening? Do their methods contain more weird science than the various Italian 2/1 methods?

[pbleighton]

Quote

I am no Meckwell expert, but do they really have more complex agreements in their 1♣ auctions than in their 2/1 auctions after a 1M opening? Do their methods contain more weird science than the various Italian 2/1 methods?

I am no Meckwell expert either, but I believe that a lot of their however many pages of agreements pertain to competitive auctions, especially the strong club auctions. I read somewhere that they are the only strong club pair to actually win IMPs on their strong club hands.

Peter

[helene_t]

pbleighton, on Aug 9 2007, 03:30 AM, said:

I am no Meckwell expert either, but I believe that a lot of their however many pages of agreements pertain to competitive auctions, especially the strong club auctions. I read somewhere that they are the only strong club pair to actually win IMPs on their strong club hands.

Makes sense. I'm sure they have specific defense against the 20 or so most common interference systems used against 1♣, plus generic defense against the rest, and psyche unmasking.

[Gerben42]

Usually the stronger player adapts to the weaker player in a partnership, systemwise. So I guess it will be Polish Club or 2/1 for me.

[kenrexford]

officeglen, on Aug 8 2007, 07:58 PM, said:

I never heard of a more complex version of 2/1 than Mike's - it had everything and a kitchen sink too

If you want a teaser, read the following analysis of an aspect of my 2/1 bidding style that may shed light on the comparison of complexity between approaches:

Let’s talk surrealism. I’ll warn you that perhaps no one will ever have agreements laid out to the degree as you will now read, if you do keep reading. However, I found the process of thinking through what follows to be fascinating intellectually and hilarious from the standpoint of creating the most esoteric and complicated theory I have ever imagined, for a very rare occurrence. However, it might be interesting to some as a thought experience. Plus, who knows? Someone might actually use this. Plus, I believe that you will agree that, esoteric though it might be, it is actually sound, even if admittedly frightening.

I have thought about the existence of the Empathetic Splinter in great detail recently and have realized a frightening reality. It is possible to expand Empathetic Splinter theory into one of the most complicated, and yet inherently logical, set of rules I have ever seen.

The Empathetic Splinter usually arises in the context of a specific double-fit matrix. The partnership, to make slam on HCP’s in 22-26 range, needs to have the following matrix:

1. One 4-4 fit, although a 5-4 fit would be better yet. (“The 4-4 Fit”)
2. One 5-3 fit, although a 5-4 fit might likewise be a suitable substitute. (“The 5-3 fit”)
3. One suit controlled by an Ace, although a King in that suit might offer the 12th trick. (“The Ace-only Suit”)
4. One suit controlled by shortness, preferably a void of course. (“The Shortness Suit”)

With this matrix, the partnership playing in the 4-4 fit can expect to take five tricks in the side suit, four obvious tricks in the trump fit, one additional trick in the trump fit by way of a ruff, and the side Ace, losing only one trick for the stiff. This is the case if all critical cards are held, meaning the A-K-Q of the two fits and the side Ace. That amounts to 22 HCP’s. Add in a jack or two for safety, and you get to 23-24 HCP’s, depending upon your risk preference and/or whether the fit is 4-4 or 5-4.

That gets the partnership to 11 tricks. The 12th trick comes from a void (two ruffs), the side King (now 25-27 HCP’s needed), and Ace in the stiff suit (26-28 HCP’s needed), a 5-4 fit for the 4-4 option and trumps 2-2, or a sixth card in the side suit.

Note that all of these slams make when traditional HCP analysis, even adding in distributional values, does not suggest that the slam will make. However, the play is usually simple.

Now, the Empathetic Splinter is an unusual call made by a 1NT opener, one that is clearly a slam try but made when slam cannot be possible (or is very highly unlikely) contextually (such as opposite a Responder who has limited himself to invitational values, for example) unless this matrix is present. (There is another matrix, the 5-3 fit coupled with a side 3-5 fit, but that is not yet discussed and often cannot be present. Further, this 44/53/A/stiff matrix pops up in other contexts, like the 1M-P-2M-P-new-P-3NT auction.)

The Empathetic Splinter can be made by Opener when any two suits of the matrix are known (for example, the 4-4 fit is known and the stiff is known), with the call made by Opener identifying the location of one of the two remaining unknowns. Thus, for example, if the 4-4 are known and the stiff is known, then Opener might identify the location of the 5-3 fit and perforce locate the location where only the Ace is relevant.

Now, when Opener “identifies” the 5-3 fit, he is not saying that a 5-3 fit exists. Rather, he is precisely stating that his hand caters to the 5-3 fit if Responder has five cards in this suit.

An example might clarify this. Somehow, after a 1NT opening, Responder uses a strange technique wherein his bid of the other major after Stayman is a short-suit game try, agreeing the major that Opener bid. Just accept that, for the purposes of a simple example. So, maybe 1NT-P-2♣-P-2♠-P-3♥ agrees spades, with 3♥ being a short-suit game try. Assume, also, that 3♥ for some reason cannot be a strong bid, limited to invitational only. Again, this is necessary to explain, even if this auction is bizarre. Real auctions occur, but rarely so obvious.

Anyway, hearing this, Opener might bid 4♣ to show a hand that would “fit” the Empathetic Splinter matrix where spades is the 4-4 fit, hearts is the known shortness, clubs is now identified as the suitable 5-3 “fit” if Responder happens to have five clubs, and, by force of elimination, diamonds becomes the Ace-only suit.

Identification of the matrix is necessary because the Empathetic Splinter, by definition logically derived, is a call that shows five of the seven cover cards that would be relevant for that possible matrix. The seven cover cards potentially described are the Ace, King, and Queen of the 4-4 fit and the 5-3 fit, plus the Ace in the Ace-only suit.

Thus, if Opener held, for instance, ♠ K Q x x ♥ x x x ♦ A x x ♣ A Q x, he would have five of seven cover cards in the proper matrix if Responder has 4135 pattern, but not if Responder holds 4135 pattern. Although the club Queen is a cover-card in the traditional sense, it is not a “matrix” cover card. The simple reality is that the Queen is a duplicated value opposite 4153 pattern, because Opener’s two losing diamonds could have been covered by the fourth and fifth club. Thus, the diamond Queen does not help the matrix.

So, again, Opener identifies to what matrix he can cater by his call. If two suits of the matrix are known, a requirement for the Empathetic Splinter, then the bid by Opener identifies the third and infers the fourth, completing the picture.

So far, bridge logic dictates this result. If Opener’s call must be a slam move to make sense, and if the slam move can only make sense if this matrix exists, then the call must clarify the matrix to which Opener can cater. Two of the four must be known for the call to be readable.

At this point in the discussion, partnership agreement must now kick in. There is no “bridge logic” that dictates which of the remaining two “unknowns” Opener should identify. Why? In the example of a known 4-4 fit and a known shortness, an effective partnership could identify the catered 5-3, thereby inferring the ace-only. Or, equally effectively, the partnership could instead elect to identify the Ace-only and infer thereby the catered 5-3. So, defaults must be agreed.

There are six possible scenarios needing agreement. My personal suggestions follow:

1. If the 4-4 fit is known and the 5-3 fit is known, then the Empathetic Splinter identifies the shortness suit (Opener shows no wasted values in a specific suit and infers five of the seven matrix covers, the other unknown being the Ace-only suit).
2. If the 4-4 fit is known and the shortness is known, then the Empathetic Splinter identifies the 5-3 suit, inferring by elimination the Ace-only suit.
3. If the 4-4 fit is known and the Ace-only suit is known, then the Empathetic Splinter identifies the shortness suit and infers the location of the 5-3 suit.
4. If the 5-3 fit is known and the Ace-only suit is known, then the Empathetic Splinter identifies the 4-4 fit and infers the location of the shortness suit.
5. If the 5-3 fit is known and the shortness suit is known, then the Empathetic Splinter identifies the location of the 4-4 fit and infers the location of the shortness suit.
6. If the shortness suit is known and the Ace-only suit is known, then the Empathetic Splinter identifies the location of the 4-4 fit and infers the location of the 5-3 suit.

These rules could be memorized. However, note the order of preferences. If the 4-4 fit is one of the unknowns, we always show the 4-4 fit. This is great, as it sounds like normal, natural bidding.

If the 4-4 fit is known, that issue is not present. However, because the term we use is “Empathetic Splinter,” it seems consistent for Opener to identify what empathized shortness would be most interesting. Thus, the default is to identify the shortness suit if the 4-4 fit is known.

When the 4-4 fit (first priority) is known and the shortness suit (second priority) is known, this sole circumstance is handled by identifying the 5-3 fit. Again, natural-sounding is best as the default when possible.

Now that we have an understanding of the reason for the Empathetic Splinter, the matrix necessary, the mechanisms for using this call, and the suggested defaults, let us assess the key practicality issue. What if only one of the “knowns” is clearly known. Can a second suit of the matrix become “known” by default rules? Actually, yes.

A second suit of the matrix is “known” if it may be necessarily inferred. What do I mean? As one simple default rule, the shortness suit is defined as “known” if it is the opponents’ known suit and therefore the most likely shortness. In other words, barring some exception, the opponents’ suit is the default “known” suit of the matrix, as it is “necessary” in the sense of practical realities. The exception to this is that if Responder (or Opener) has shown a no trump stopper in their suit, then their suit becomes the Ace-only suit.

Another default is that the shortness suit is “known” in a potentially ambiguous auction if Responder has heard Opener show a suit and has rejected that suit. This default makes sense because that suit is the most likely location for Responder to falsely perceive a duplication of values (shortness opposite values) and therefore downgrade a hand with potential. The most common example is an auction where Stayman is used, Opener shows hearts, Responder declines hearts and thereby shows or infers spades, and Opener can support spades.

You can also infer the 4-4 fit or the 5-3 fit, and establish it as known, if Opener makes the Empathetic Splinter under circumstances where the call clearly is fit-showing for the last shown suit.

So, the Empathetic Splinter can be used if two suits of the matrix are known, according to the defaults identified above. Further, the Empathetic Splinter may also be used if only one suit of the matrix is “known,” but if a second suit would inferentially or circumstantially be the default “known” according to pre-agreed rules or defaults. I have suggested a few, but more may be possible or might be agreed somewhat by fiat of choice.

Empathetic Splinter theory seems complicated so far? Let us take it to the next step. What if Opener has holding in the two unknown suits that cater to either of the remaining matrix options? How could this happen? Well, consider if the two unknowns are the Ace-only suit or the 5-3 fit. Axx in both suits means that Opener might cater in each of the two suits to each of the two possible matrix options, assuming three other covers in the known suits. Similarly, xxxx in two suits might cater to the 4-4 matrix, the shortness matrix, the Ace-only matrix, or the 5-3 matrix, assuming five matrix covers in the two knowns. These possibilities will occur when Opener has the right length in the two unknowns and Aces and/or spaces, or one-Ace-one-space, in the two unknowns.

When this occurs, all is not lost. Opener simply bids the lower of the two Empathetic Splinters. If Responder wants to know if Opener has the either-or holding, Responder bids the other suit, asking that question.

So, assume that Opener holds Axx in both minors after Responder’s calls establish that spades are 4-4 and hearts is the shortness suit. Opener would bid 4♣ (by our defaults showing the 5-3 suit and inferring diamonds as the Ace-only suit). If Responder could make slam if Opener has Axx in both suits, he can bid 4♦ to ask if Opener has equal holdings and simply elected the lower option. Opener would accept.

This same technique works for all times when an either-or situation arises.

What about space consumption issues? If interference gets in the way, or if our constructive auction gets in the way, such that Opener cannot fit both Empathetic Splinters in below game in the agreed suit, we also need agreements. My suggestions follow:

1. A bid of a known suit below game in the agreed suit operates as a substitute for an unavailable Empathetic Splinter, if one is unavailable and if a cuebid of the opponents suit, when a known suit, is not available.
2. A cuebid of the opponents’ suit, when that suit is a known suit, operates as a substitute for an unavailable Empathetic Splinter, if one of the Empathetic Splinters is not available and if a bid of one of our known suits below game is also not available.
3. If both a cuebid of the opponents’ suit (a known matrix suit) and a bid of a known suit below game in the agreed suit are available, the cheapest of the two is a substitute for the one unbiddable of the unknowns.
4. If neither of the unknowns is biddable, but both the cuebid of their suit (known matrix type) and a cuebid of our side known are available, then the cheaper option shows the cheaper unknown, higher for higher.
5. If all of this only allows for one Empathetic Splinter type to be shown, then the Empathetic Splinter identifies that which it would be expected to identify (clubs shows clubs), or, if artificially shown (cuebid or bid of non-focus known suit), it identifies the lower suit Empathetic Splinter.
6. If Opener has a two-way position, and can show each, then he uses the cheapest option (normal or artificial), with Responder bidding Opener’s higher option (normal or artificial) to ask for the double-possible layout.

One final concept. If any call is available but has no agreed definition, we use this as a Last Train to Clarksville. A frequent reason for this call is to discover whether the honor held in a suit expressed to be the 5-3 fit is the King. The Queen will almost never be useful. The Ace will often be described already, or through an either-or bid. But, a King will usually be described as a part of the 5-3 only and yet might be useful in, say, the Ace-only suit.

The election of a strong, forcing opening does not determine the level of complexity possible in a system. It is merely a reality that most scientific thinkiers spend their energy in the context of a strong club system. Having played Precision or Precision-like systems for years, and then canape systems (strong club or strong diamond) for more years, I am back to 2/1 GF myself. That does not mean that science is forfeited.

[awm]

For perhaps a simpler example, take a look at the Ambra notes on Dan Neill's website. This is a pretty complex "2/1" based system, with notes that are extremely dense and to which a lot could be added for a serious partnership adopting the methods. You can play a complicated 2/1 system, it's just that a lot of people don't.

[glen]

Understand that when I say "I never heard of a more complex version of 2/1 than Mike's", that I wrote the small-font 259 page ETM Gold (has mini-multi structures etc.), and the shorter ETM Victory that has the "Dan-complexity level" warning label. Btw I have a new plug n play system up, CANDY, that combines two-way club, canape majors and Fantunes 2M openings - so a system that Soloway will never play.

[mikeh]

At the risk of boring those with no interest in the topic, the 2/1 to which I and glen refer included:

1) variable notrump, with different relay structure responses to the different ranges, and specified defences to virtually all defence methods in use

2) Artificial 1♦ response to 1♣, with relay sequences thereafter

3) transfer jump shifts over 1♣

4) 2♣ artificial gf relay responses to 1♦/♥/♠ openings (2/1 2♦ or 2♥ bids were invitational plus, so it was still a form of 2/1)

5) gf relay initiated by 4SF in otherwise non-relay sequences. All relays (other than over weak notrump) allowed for:

- approximate shape
- precise shape
- number of controls
- sometimes number of queens
- location of controls
- location of secondary honours, including, in extreme cases, Jacks
- breaking of the relay at any time
- in some cases, general size ask early

Those who subscribe to the BW will have seen some of our ideas used by L'Ecuyer - Marcinski in the Challenge the Champs.. altho I am not really saying they used 'our ideas'.. since the concepts have been widely available for many years, and the L'Ecuyer-Marcinski method is quite different from ours. But they use some of the compression approaches we used, in particular the denial cue-bid structure. This is an example of convergent evolution, not plagarism

6) denial cue-bidding for controls in relays after shape/size asks

7) spiral keycard

8) simple relays after 2♦ opening

9) transfer advances after their takeout double, including transfer flower bids

10) transfer advances after our overcalls

11) complex major suit raise agreements, based on the lack of need for a forcing raise (2♣ included all forcing raises).

12) complex system of responding to our 2N opening (initially a relay method, later changed to a more natural, but still very complex approach)

13) a large number of specific agreements re competitive and constructive bidding beyond those above... a significant number of agreements actually never came up in 5 years of serious competition.... but we had the agreements!

Including compressed flow-charts, in which all relay developements could be charted in a one-half page chart, the notes exceeded 175 pages, and were in most cases condensed, altho a number of pages were devoted to examples.

It was, and is, a wonderful system provided that you have a taste for extreme detail and both the time and the memory required to internalize the relay 'engines', which were designed utilizing a Fibonacci analysis (to ensure the most common responses were shown cheaply) tweaked to maximize the chance that relayer became declarer. We had many auctions in which we'd arrive at slam and all dummy could/should say in response to any question about the auction was: "Given what he knows about my hand, he wants to play this contract".

Moreover, while the CNTCs are not the Vanderbilt or the US Team Trials or the European Open, etc, the method did very well at the Canadian level... and got us to a couple of WCs.

Having said all that, my then-partner, who did 99.9% of the system design, always pondered the idea of developing a more complex approach based on a big club method

[kenrexford]

See! Proof is provided. 2/1 GF can be VERY complex, if you so desire.

[han]

I doubt I would hire Soloway once I won the money. And you know what, I would probably ask the pro for advice about system.

[helene_t]

Hannie, on Aug 9 2007, 10:17 PM, said:

I doubt I would hire Soloway once I won the money. And you know what, I would probably ask the pro for advice about system.

Sounds like a good idea. But you won't have to win the lottery since you and Arend will get rich defeating my 3-card major system.

[Echognome]

mikeh, on Aug 9 2007, 10:19 AM, said:

It was, and is, a wonderful system provided that you have a taste for extreme detail and both the time and the memory required to internalize the relay 'engines', which were designed utilizing a Fibonacci analysis (to ensure the most common responses were shown cheaply) tweaked to maximize the chance that relayer became declarer. We had many auctions in which we'd arrive at slam and all dummy could/should say in response to any question about the auction was: "Given what he knows about my hand, he wants to play this contract".

A few points here.

1. I don't think your disclosure there is complete as stated. Given that you say above that relayer can break at any time, perhaps you might mention that relayer is also denying certain hands types by failing to break the relay. I'm not saying that you should describe all the possible hands that are denied, but maybe if you could categorize them as "and he has denied certain minimum hands that would have broken the relay," it might be better. I know it's not your intention in the slightest to hide anything, but against a slam, it's probably good to discuss both the bids that were chosen (relays) and those that were not chosen (breaks).

2. "Fibonacci analysis" seems like a strange term to me. Maybe it is appropriate. But, to me, the Fibonacci aspect of relays is just that the number of hand types that can be shown by a given level up to another given level is determined by the Fibonacci sequence. Usually as a target, the goal is to be able to describe as many hands as possible at or below 3NT. The hands that are described above 3NT typically have extreme shape. Furthermore a system designer will have several goals when designing relays. One such goal is to make Relay Asker the declarer. (Note how TOSR focuses on this aspect.) The reason for that is to make it harder for the defense to know declarer's assets. Another important goal in many designs is to reduce the memory load. That goal will often conflict with the efficiency of the relay (more common hands bidding at a lower level). Also, I found an important goal is to keep the more similar hand types together in case relay asker just wants to jump to game (in particular if the strain has already been taken by relay responder).

[mikeh]

Echognome, on Aug 9 2007, 05:36 PM, said:

mikeh, on Aug 9 2007, 10:19 AM, said:

It was, and is, a wonderful system provided that you have a taste for extreme detail and both the time and the memory required to internalize the relay 'engines', which were designed utilizing a Fibonacci analysis (to ensure the most common responses were shown cheaply) tweaked to maximize the chance that relayer became declarer. We had many auctions in which we'd arrive at slam and all dummy could/should say in response to any question about the auction was: "Given what he knows about my hand, he wants to play this contract".

A few points here.

1. I don't think your disclosure there is complete as stated. Given that you say above that relayer can break at any time, perhaps you might mention that relayer is also denying certain hands types by failing to break the relay. I'm not saying that you should describe all the possible hands that are denied, but maybe if you could categorize them as "and he has denied certain minimum hands that would have broken the relay," it might be better. I know it's not your intention in the slightest to hide anything, but against a slam, it's probably good to discuss both the bids that were chosen (relays) and those that were not chosen (breaks).

2. "Fibonacci analysis" seems like a strange term to me. Maybe it is appropriate. But, to me, the Fibonacci aspect of relays is just that the number of hand types that can be shown by a given level up to another given level is determined by the Fibonacci sequence. Usually as a target, the goal is to be able to describe as many hands as possible at or below 3NT. The hands that are described above 3NT typically have extreme shape. Furthermore a system designer will have several goals when designing relays. One such goal is to make Relay Asker the declarer. (Note how TOSR focuses on this aspect.) The reason for that is to make it harder for the defense to know declarer's assets. Another important goal in many designs is to reduce the memory load. That goal will often conflict with the efficiency of the relay (more common hands bidding at a lower level). Also, I found an important goal is to keep the more similar hand types together in case relay asker just wants to jump to game (in particular if the strain has already been taken by relay responder).

1. The answer I gave assumed that relayer had relayed until he placed the contract. Obviously, if relayer broke the relay, and the auction continued, as it often did, we would explain the inferences from the relay break. A common break was after a cheap response to 2♣, a bid of 3♣ announced a gf hand with clubs and no slam interest. Furthermore, our agreements were that the more one relayed, the stronger one's hand, so that if we relayed several times, and then broke the relay, opener had rights. And, my explanation in this forum was not intended to be a complete description of what we'd announce at the table: thus responder would give a detailed description of opener's hand...once in a while we could claim before the opening lead and we did, at least once, expose declarer's hand to the opps before the opening lead. That was before we realized that sometimes we'd screw up the relay

2. I agree with your description of the goals, and excuse me for a possibly poor use of the term fibonacci analysis: my partner was the math major/computer whiz who designed the system. We focussed on maximizing concealment of declarer's hand and nesting hand-shapes to maximize bidding space below 3N: we had the only responses to 1M/2♣ beyond 3N as 5=4=2=2, with the major and clubs as the long suits and significant extra values including at least 5 controls... responder always held either a gf in clubs, a gf raise of the major or big notrump hand or some other hand with strong slam ambitions opposite a minimum hand, so that in all cases we had 4 level safety. We were not so interested in minimizing memory work, since we had agreed that we had a specific goal in mind: to play in the BB.. which was a lofty goal given that neither of us had previously won a CNTC when we got together, and we were prepared to WORK on the method.

I certainly would not recommend our method for anyone other than a work-alcoholic. I don't regret the work at all: it was a lot of fun, and when we were 'on' we were a pretty formidable partnership. But I doubt that I would ever do it again... I was only 42 when we started, and I'm not sure that I could or would do it again, hence my choice of 2/1 in response to the OP: I didn't mean a relay 2/1 either

[Echognome]

mikeh, on Aug 9 2007, 03:03 PM, said:

<snip>
2. I agree with your description of the goals, and excuse me for a possibly poor use of the term fibonacci analysis: my partner was the math major/computer whiz who designed the system. <snip>

I certainly would not recommend our method for anyone other than a work-alcoholic. I don't regret the work at all: it was a lot of fun, and when we were 'on' we were a pretty formidable partnership. <snip>

Mike,

I probably did post this with the correct language. My point was not to find fault with your terminology, but rather to say that the concept isn't as complicated as it is often made out to sound. I know *you* understand the concept, but I'm going to post the logic behind it for those that do not.

Imagine that we have a set of possible hand types. Typically these types are in the form of hand shapes. For example, one hand shape might be 4=1=5=3 and another 4=3=1=5. In order to show each of these hand types, we need at least two bids (one for each shape) if we want to show this exactly. We often call this a "full" relay. If we only want to show that the pattern is, say 4=x=5=y, where x and y could be any length, then we have a "partial" relay. Either way, the number of types of hands we can show depends on how much bidding room we have left below a given level (which I'll set at 3NT as it's the most common one).

So imagine that we have described our hand up until now and the next asking bid (relay) from partner is going to be 3NT. Obviously, since partner asks with 3NT we have no room to describe any hand types, so we assume only the 1 hand type is shown. If partner asks with 3♠, we have a similar problem. We can only bid 3NT (and stay at or below 3NT). But suppose now that partner asks with 3♥, then we can bid either 3♠ or 3NT. That is to say, we can now show 2 hand types. If partner asks with 3♦, then we can show 3 hand types: one each for 3♥, 3♠, and 3NT. However, the complexity goes up when partner asks with 3♣. Why? Well we can group together more than one hand in our 3♦ response, since partner can make a further ask with 3♥. Thus we can put 2 hand types in the 3♦ response and 1 each in the 3♥, 3♠, and 3NT response, for a total of 5 hand types. If we carry this on, we get:

Ask #Hand Types
3NT---1
3♠---1
3♥---2
3♦---3
3♣---5
2NT---8
2♠---13
2♥---21
2♦---34
2♣---55
1NT---89

This sequence you will not is one where the next value in the sequence is the sum of the two previous values. (3 = 2 + 1, 13 = 8 + 5, etc) That sequence is known as the Fibonacci sequence. It is useful for planning how much information you can extra at a given level. Thus for Mike and his partner, if they use 2♣ as their relay after 1M, they can show 55 types of hands at or below 3NT. If they used a 1NT relay instead, they could show 89 hand types. It actually gets more useful than that. Suppose they do use 2♣ as their relay. They can go further with the classification. As those 55 hand types can be broken down as follows:

2♦ - Can hold 21 hand types
2♥ - Can hold 13 hand types
2♠ - Can hold 8 hand types
2NT - Can hold 5 hand types
3♣ - Can hold 3 hand types
3♦ - Can hold 2 hand types
3♥/♠/NT - Can hold 1 hand type each

For a total of 55 hand types. So the subsequent sequences are also Fibonacci. I measure how efficient my relay systems are by seeing how much of a load each of the "buckets" holds. Maybe I'll put 20 hand types in my 2♦ bid, 11 in my 2♥ bid, 8 in my 2♠ bid, etc. That tells us how much use we are getting out of each bid.

I guess my point is that designing the relay can be fun and makes you think of how much information you can share. Maybe your goal is not to divide everything by full shape, but rather partial shape and also some measure of strength or controls. At least you can figure out how much you can describe.

[Badmonster]

Big club sure looks interesting. But 2/1 is accessible.