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.

Monday, February 19, 2007

Yet Another Empathetic Splinter?

I must admit that I missed this one on the post as a possible continuation. I must change the hand slightly for a 15-17 NT.

You hold AQx-Ax-Jxxx-KQJx. You open a meaty 1NT. Partner transfer to spades (2H), and RHO doubles this. You complete the transfer (2S), and partner surprises you by bidding 3NT.

It seems that partner has five spades but wasted values in hearts (from his perspective). RHO must hold cruddy hearts (long) and justification. Most likely, this cause was ordained because he holds a red two-suiter, longer hearts, and he was planning a two-bid auction if needed. (Diamonds his likely second suit because my clubs are too good.)

Could we have a slam in this auction? What if partner holds something like K10xxx-KQx-x-Axxx? Twelve is easy that way. Make his hearts KJ10, same result -- slam makes. 6C makes if he actually has Kxx in hearts.

So, how do you move, if you elect to not pass 3NT? It seems that "empathetic splinter" theory works here. However, the parameters are strange.

You assume, from partner's 3NT call, that you must have the heart Ace to invite slam. Thus, the "top control" suit is known. What is not known, then, is which suit will provide the weakness and which will provide the secondary fit. 4C would seem to indicate the secondary fit potential (5 of seven critical cards in spades, clubs, and the top heart).

So, this is a strange new Empathetic Splinter matrix, the third beast.

Type One: The necessary shortness is established, so we jump into the secondary fit suggestion, making the fourth suit the top-control suit. E.g., 1NT-P-2C-P-2H-P-2S-P-4C. Here, hearts must be xxxx because the heart stiff is the known downgradable value. 4C then isolates clubs as the source for slow control values and diamonds as the Ace-only suit.

Type Two: The necessary second suit is known, so we jump in the suit for the empathetic splinter. E.g., partner shows invitational with spades and clubs. 4D, then, might agree spades, clubs as the secondary fit, diamonds isolated as the xxxx suit, and hearts as the Ace-only suit.

Type Three: The necessary Ace-only suit is known, so we jump into the secondary fit potential. The example above.

Notice that Type One and Type Three always involve a jump into the secondary fit, whereas Type Two involves a jump into the hole (where the stiff is needed). You could easily have different defaults as to what you jump into, as long as these are agreed in advance. For example, you could have a scheme where you always jump into the "strongest" of positions between the two unknowns when one is known. This would change your agreement as to Type Two that you jump into the "Ace only" suit, because the "Ace Only" suit is in a sense a "stronger" holding than the "xxxx" suit.

I believe that these are the only three possibilities. My defaults are as above.

Monday, February 12, 2007

A Bit of General Theory

A very complicated question I recently received, not reproduced because of the complexity, brought up an aspect of theory that may be of interest to some.

There are occasions when you just plain do not seem to have space to tell your tale. In such auctions, a little bit of general theory can be useful.

Internal/External Values

The Serious 3NT call and Last Train to Clarksville are often used to fill the gap between what can be directly shown and what must be shown in “general terms.” Obviously, if you can tell you tale with one final cuebid, or with two prepared cues that you will be able to make when it matters, that is your solution. Equally, if you do not tell your tale with that one final cuebid, or two prepared cuebids, you must have a hand that cannot be completely described in that manner. This may seem obvious, but the subtlety is often missed.

When you need a “general terms” auction, it is a good idea to have default understandings as to what specific “general cuebids” (Serious 3NT and Last Train) mean. One default that I often use is that a Serious 3NT call, a call that shows “extras” in general terms, tends to be based upon good trumps when neither I nor partner could show good trumps any other way. For instance, if a major is agreed at the three-level, there is no ability to cuebid trumps. Thus, a Serious 3NT often is justified because of good trumps.

Conversely, the “companion” default is that Last Train, a bid that asks for “extras,” tends to be the call used to ask about external controls that may still be needed. Thus, you would tend to bid 3NT when you need to express the strength of your internal values (trump quality), but you would tend to use Last Train (or rely upon partner to use Last Train) to ask about the strength of the unknown external values (controls).

By default “tendencies,” this does not mean that a Serious 3NT or a Last Train call always is defined according to these defaults. Rather, you “think trumps” when interpreting a Serious 3NT and “think outside controls” when responding to a Last Train invite, always governing your interpretation on the preceding auction. The “defaults” really are designed to guide a partnership when ambiguities develop or when deciding between two courses that seem equally plausible.

Touching Controls

A similar problem might occur in the context of an auction where, perhaps, trump quality is completely known. For example, one person bypasses 2NT (two trump honors) and then someone cues trumps to show the third top trump honor.

However, the four-level may provide insufficient space to tell some vital part of your story. This often happens when you have a holding that would justify cuebidding a suit twice if you had space; for example, showing two top honors in partner’s suit when you have not yet had a chance to show any top honor in his suit. These two cuebids might be collapsed into justifying a Serious 3NT call because, in a sense, the two cards of value are “touching” and not otherwise biddable.

Similarly, you may have a desire to cuebid two suits that are touching. Consider having the need to cuebid clubs (4♣) then hearts (4♥). This will be easy if you expect, or will need, a 4D cue from partner, right? Well, what if you would like to cue clubs and diamonds? If you cue 4♣, partner’s next call per force will preempt you out of ability to cuebid your value in diamonds. This is bad. Again, however, 3NT may solve the problem, insofar as 3NT again is handling two “touching” values.

So, when deciding whether to use a Serious 3NT call or not, consider that another default tendency is for 3NT to handle “touching” values. Conversely, keep that in mind when interpreting a Serious 3NT call from partner.

Note that both of these defaults have a common sense logic to them. We often tend to overstate our strength if we hold unexpected strength in trumps or in partner’s side suit because we expect partner to be conversely cautious because of his obvious weakness in trumps or in his side suit. Using Serious 3NT makes sense as a practical solution to this recurring problem. Articulating this theory and recognizing it in practice should help to define ambiguous auctions in a meaningful way.

Tuesday, February 6, 2007

Another Forum Discussion

Another recent forum discussion convinced me of the utility of an approach to handling one-of-a-minor raised directly to 3NT. What I propose as a sound agreement follows.

After 1D-P-3NT-P-?

Opener bids his shortness with slam aspirations. 4D is long diamonds without shortness. Cuebidding follows, but 4NT is to play.

This leaves some questioning what to do if you opened 1D with six diamonds and five of a major. As I would only do that with "extras," I'll now bid five of the major as a pick-the-slam bid.

This also caused some to wonder what to do with 4-4 or 5-4 in the minors and no shortness. With that, I'll bid 4NT, after which minor-suit scrambling is allowed.

Finally, what to do with a minor two-suiter? That is "simple" but subtle. Opener shows his short major. If this is fitting, Responder (or Opener later, as the auction develops) can introduce clubs at the 5-level or 6-level, pass-or-correct. Thus, for instance, if Opener has 1354 pattern he can bid 4S after 3NT. If Responder can accept the slam try, he can, for instance, cue 5C. Opener might raise this to 6C, which Responder can convert to 6D.

What if 1D-P-3NT may feature a 4-card major? For those who do this, 1D-P-3NT-P-4C-P-4M can be natural, or 1D-P-3NT-P-4H-P-4S. With hearts, there is a problem if the auction goes 1D-P-3NT-P-4S. So, perhaps you should not bid 3NT with hearts if shortness in spades from partner might make 6H look good -- bid 1H with that hand.

After 1C-P-3NT-P-?

The same structure of pass-or-correct does not work well, because the new strain (diamonds) outranks clubs. Now, some technique is needed.

The solution.

Four-of-a-minor is a shortness bid, but each also promises four diamonds. Typical pattern is, for example, 1345 (4S). Now, Responder can select the game.

With short diamonds, bid 4D. Now, the minor two-suiter is not an issue. Hwever, if you insist that 3NT could hide a four-card major, then Responder should be allowed to introduce that major after 4D.

Without neither short diamonds nor long (4-card) diamonds, but long clubs, bid 4C. Responder can ask for shortness (4D), in which case you bid the shortness, or the appropriate level of NT for the strength with no shortness. For those who want to check back on a possible 4-4 major fit (those who might have a four-card major and bid 3NT), then you just bid the major directly over 4C, or wait with spades and hope for a 4H call.

You can, as always, also use a quantitative 4NT, or the 5-level major jump.

Monday, February 5, 2007

Cost-Benefit Analysis with Tools

A recent forum discussion on BBO brought up an issue that is worthy of analysis. One noted expert questioned whether an "Empathetic Splinter," for instance, might give up too much information to the opponents in a specifc auction.

The analysis of the cost-benefit to any slam move is a constant issue. Some times, resigning to a game when slam is remote may be the practical solution for a given hand, given event, given state-of-the-match. Of course.

However, knowledge of the tools necessary will help in the decision as to when to pounce, as events may suggest pouncing.

A simple example. After 1NT-P-2C-P-2H-P-3H, Opener holds AKx-KQxxx-Ax-xxx. Slam might make opposite Qxxxx-Axxx-xxx-x, right? The method to find the slam might be to use a cuebid of 3S, allowing 3NT from partner and 4D by you. (Empathetic splinters would be difficult here, because you cannot focus a suit and a hole, so cuebidding is used.) However, this might direct the defense to a club lead. So, you might forego the slam move for practical reasons.

However, studying this situation is useful. What if Opener's RHO had doubled 2C initially? Now, the cuebid may make sense for several reasons. First, a club lead is coming anyway, such that disclosure helps the opponents very little. Second, the chances of partner being stiff in clubs are higher, such that the possibility of the well-fitting slam increase. Third, a well-placed cue of 3S might occasionally help if the opponents happened to have been lurking and planning a sacrifice at 5C if you reach game, in which case your cuebid helps in the five-level (or slam) decision.

Of course, once 2C is doubled, empathetic splinters are more useful now, as the implied necessary shortness is known (clubs). Thus, 3S would imply five of seven keys, with spades and hearts being the focus suits and diamonds being the control suit. 4D, in contrast, would imply a similar hand, with diamonds-hearts focused and spades control-only.

A recap on empathetic splinter analysis. If the necessary shortness is established and known (their suit, or a previously-shown suit that might have caused improper discounting of reciprocal shortness value), the cue identifies the two-suit focus. If the necessary two-suit focus is established, the cue identifies the hole (where shortness would be of value). If neither is known, then normal cuebidding is used.

Thursday, February 1, 2007

Strange Demand RKCB

For a while, I had occasion to use a conventional RKCB that may be of interest to some, depending up their system.

I used to play with some people who opened 2D to show an intermediate hand (14-16 or so HCP) with 4-5/5-4 or longer in the minors, no 4-card major. A 2H response was an asking bid, seeking shape and strength. The rebids happened to be 2S with weak and three spades, 2NT weak without a major fragment, 3C weak with three hearts, 3M with a maximum and three of the bid major, and 3D with a maximum without a major fragment.

In any event, many conventions (Roman 2M, for example) operate similarly. Opener shows an unbalanced hand, and Responder asks for more clarification. However, the clarification often fails to identify whether the short suit is stiff (5431) or void.

As in many auctions, especially in this type of auction, there are times when one wants to ask more questions and times when one simply wants to answer RKCB himself. This was one.

We decided that, after the answer to the 2H asking bid, 4C set clubs as trumps and 4D set diamonds as trumps. Each "forced" Opener to use Kickback (the next suit up) as RKCB. However, Opener could opt to use Exclusion RKCB if he had a void, using the next-next up.

In other words, after 4C (clubs set as trumps), 4D would be RKCB and 4H would be Exclusion RKCB (void in the known short suit). After 4D (diamonds set), 4H would be RKCB and 4S would be exclusion for the known shortness. If either major could be short, then Kickback was on, you would bid the void as Exclusion, and 4NT was Exclusion for hearts if diamonds were agreed.

It even made sense, in this auction, for 4H or 4S, instead of 4C or 4D, to be Flag RKCB, setting trumps in the lower/higher minor and asking. Thus, you could either ask or tell. This only works, though, if a forcing call below four of the major was available.

In any event, this type of demand-that-you-ask call may be of interest to some who use similar conventions.