Friday, February 23, 2007

Abandon All Hope Ye Who Enter Here

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.

No comments: