DIP: Ace and King Parity Revisited

Welcome to 2009! It’s been a month since my last blog, so I thought it was time I got back on the horse.

Over the festive season, whilst travelling and hanging about in airports, I’ve been revisiting my earlier thoughts on Control Showing. You may recall, I raised three questions about the JVCB method which I was proposing to somewhat emulate

1. When to STOP or GO when showing A and/or K parity (and why)
2. Why, in pure JVCB, A/Q’s are first considered in 5+ suits, whereas K’s are considered in 4+ suits
3. Why scan K’s before A/Q’s

I am still no closer to answering (2), but have some of an idea about (1) and (3) now, I believe.

With respect to (1), “Expected Parity”, as described in the previous blog, seems to work pretty well. It averages (from memory) 0.83 steps (where GO then GO is 0 steps and STOP then STOP is 2 steps) through the A and K parity phase. This is good when you consider that “Optimum Parity” (i.e. remembering the best combination by wrote) only gets you the marginal improvement average of 0.76 steps through the phase.

There are, however, at least two other considerations.

The first, raised by SD, is why commit to a pre-determined “opinion” on K parity before knowing A parity? It’s a fair question and one I hadn’t previously considered. I haven’t got around to modelling a post-facto choice on K parity based on expected A parity, but there is a reason for this – see below.

The second consideration is whether it is right to consider A parity first, or whether K parity might be the better option. Indeed, there are some in Australia who have considered adding a K parity step to more standard DCB methods because of its apparent value in determining “control structure” (by which, I mean the number but not explicit location of A’s, K’s and Q’s respectively in RR’s hand).

I think there may be some merit in K parity before A parity (but still keeping both asks). The reason I believe this is that I expect the answer to the K-parity question is more likely to be immediately beneficial (in guaranteeing or ruling out the safety of another ask). Why? Because I expect that knowing/deducing the number of K’s is more likely to give an immediate picture of the complete control structure than the number of A’s (because of needing a specific number of A’s to make up the known QP count, or because there are insufficient free Q’s, remember, singleton Q’s are treated as J’s, to permit some combinations). I would guess this rationale is largely behind the adoption of the idea by those who have done so in Australia.

To merge these two lines of thought into a solution, then, I need to

1. Determine the best way to model “Expected King Parity for given QP’s” (which will likely be a compromise between memory and efficiency)
2. Determine the best way to model “Expected Ace Parity based on known King Parity for given QP’s”

Some previous K parity work by others has suggested that GO=ODD for K parity on 2 and multiples of 3 QP’s (otherwise GO=EVEN) is a good mnemonic and quite efficient. It doesn’t work for 15 QP’s, but that isn’t too much of a problem! I have a suspicion that this (2 and multiples of 3) is where we might end up.

Working out what to do with A parity after that start will require some serious number crunching I expect.

I think a related rationale to that above is behind the showing K’s before A/Q’s when showing specific honours.  I’m still thinking about that, however.

Regards, DipBridge

DIP: Control Showing

I’m using WIndows Live Writer for the first time with this blog – let’s see how it goes.  One advantage is that the editing window is far bigger than that provided by default on the WordPress site, which should help for the kind of content of this blog.

Whilst continuing to procrastinate on aspects of DIP, I delve back into others.  This blog assumes some knowledge of relay methods and the need to have a structure for showing controls (whether A=2 or A=3 based).  If you are newer to relay methods, don’t worry about this blog too much for the minute – come back to it when the time is right.

SD and I have discussed the merits of many different possible methods for DIP’s use.  Currently, I favour basing DIP’s method on a Scandanavian method known as JVCB.  This is more difficult than it sounds, because I have an imperfect knowledge of the rationale behind some aspects of JVCB.  For those familiar with the method, this leads me to question and/or change three things

1. Whether to STOP on EVEN when showing Ace parity (and similar considerations for when showing King parity)?
2. Why are A’s & Q’s considered first only in 5+ suits, rather than the outwardly more intuitive 4+ suit option?
3. Why are K’s scanned before AQ’s?

My current ideas with respect to the above three considerations are

1. To try and optimise when to STOP & GO with the parity methods.
2. To switch to showing A’s & Q’s with 4+ suits first (but quite willing to change back to the JVCB default if and when I understand 5+ to be meaningfully superior – any help here appreciated).
3. No change.  Though I don’t understand the rationale (yet at least) maybe there is less information needing to be exchanged this way around, so maybe the reason is that the key to the hand may unlock more quickly showing K’s first.

OK, so how to optimise when to STOP and when to GO when showing A and K parity?  Whenever I have seen parity like methods, they for some reason seem to default to STOP = EVEN and GO = ODD.  SD has done some work with others on optimising K-parity, resulting in something that is difficult to remember, and consequently when used is watered down to an easier to remember form (doing something different with 2QP’s, or multiples of 3 QP’s).  Let’s try and figure out something different that is hopefully easily remembered OR derivable from first principles.

Intuitively, for a given number of QP’s (i.e. an A=3 based control count) which I intend DIP to use by default, the following seem likely to be the most frequent top honour structures, with their proposed GO showing parity steps following

• …
• 4: AQ (most likely, as opposed to KK or KQQ or QQQQ) … so GO = ODD (expecting 1) ace and GO = EVEN (expecting 0) kings
• 5:  AK … so GO = ODD aces and GO = ODD kings
• 6:  AKQ … so GO = ODD aces and GO = ODD kings
• 7:  AKQQ … so GO = ODD aces and GO = ODD kings
• 8:  AKKQ … so GO = ODD aces and GO = EVEN kings
• 9:  AAKQ … so GO = EVEN aces and GO = ODD kings
• 10: AAKQQ … so GO = EVEN aces and GO = ODD kings
• 11:  AAKKQ … so GO = EVEN aces and GO = EVEN kings
• 12:  AAKKQQ … so GO = EVEN aces and GO = EVEN kings
• …

As a guideline to building the above, it is intuitively assumed that

• AKQ (dispersed somewhere within the hand) is a more likely honour structure than KKK, and similarly
• AK is more likely than KKQ
• AQ is more likely than KK
• A is more likely than KQ

That is, to take an overly simplistic example, where H means one of A or K or Q, for a six QP hand, Hxxx Hxx Hxx xxx is (maybe six times) more likely than specifically Kxxx Kxx Kxx xxx.  I hope to be able to confirm this intuition either empirically or theoretically at some point.

I applied this theory to some statistics on parity that SD has previously generated for the 4 to 12 control range.  It appears to work well.  There was an insignificant blip on 8 QP’s for Ace parity (49% versus 51%) and minor blips on 7 QP’s and 12 QP’s for King parity (42% versus 58% and 45% versus 55% respectively).

I’m therefore comfortable with pursuing the above as a working hypothesis as when it is right it is often really right (into the 60%’s or 70%’s).  Let’s call the parity determined from the intuitively most likely case as “Expected Parity” or “EP”.  One key good thing about it is that you don’t have to remember it if you don’t want to – you can derive it from first principles easily when needed.

Knowing that one has a good theory/hypothesis is only part of the work, it remains to decide how to apply it.  There are, to my mind, two options

1. Use it to maximise the number of hands where no stops are required during the Ace-parity and King-parity phases (i.e. you GO then GO), or
2. Use it to minimise the number of hands where two stops are required during the Ace-parity and King-parity phases (i.e. you don’t STOP then STOP again).

To satisfy design criteria (1), one would have the Ace and King parity phases targeted at their “Expected Parity”.  That is, for a 6 QP hand you would STOP on EVEN ace parity (expecting to GO) and STOP on EVEN king parity (once again, expecting to GO) as described in the earlier tabulation.

Part of the reason at present not to aim instead at design criteria (2) is that it is not clear how to achieve it with a simple rule.  My best guess, which I will try when I do further statistical analysis, is to go for EP with Aces and the opposite of EP with Kings.  The reason for this is more readily apparent with lower QP count hands.  If a 3QP hand doesn’t have the Ace predicted by EP, it is far more likely to be KQ than QQQ, so if forced to STOP with no Ace you would then want to GO with one King if aiming to satisfy design criteria (2).  Intuitively, however, I would expect this reverse correlation to lessen slightly for higher QP counts where an Ace might indeed be replaced by three queens.  Hence, only some form of statistical analysis will suffice to confirm or refute this.

Subject to all the above, the rest of DIP control showing is currently planned to work according to my (possibly imperfect) understanding of the JVCB method, as outlined in phases (or “passes’) below

• Determine your QP count (known as ZZ controls in JVCB), A=3, K=2, Q=1, singleton K = 1 (subsequently treated as a Q) and singleton Q = 0 (subsequently treated as a J)
• Show Ace-parity derived from your QP count (GO = EP, STOP = not EP)
• Show King-parity derived from your QP count (GO=EP, STOP = not EP)

Having done the above, it is assumed (occasionally without merit) that partner can derive your exact honour structure (but not necessarily which suits they are in).  Even if he can’t, he may be able to reduce it to a limited number of possibilities and be able to gamble on the percentages if space becomes short.

After that, we intend to scan through the following phases in order, subject to the rules mentioned after

1. K’s in 4+ card suits (STOP = no K, GO = K)
2. A’s and/or Q’s in 4+ card suits (STOP = neither or both AQ, GO = A or Q only)
3. K’s in 2 to 3 card suits (STOP = no K, GO = K)
4. A’s and/or Q’s in 1 to 3 card suits (STOP = neither or both AQ, GO = A or Q only)
5. J’s (STOP = no J, GO = J)
6. Singleton J’s (STOP = no J, GO = J)

The clarifying or modifying rules are

• Scan longest suits first
• Scan lowest suits first when equal length
• Assume partner knows exactly what you’ve shown*, skipping subsequent bids accordingly, see examples inbuilt in some of the points below
  • If you have NO or ALL Kings that you might have (where ALL is 4 for balanced hands, or 3 for hands with a shortage – remember singleton K is treated thereafter as a Q) completely skip phases (1) and (3) above. As per the bullet point above, partner is assumed to know OR will figure it out as soon as a subsequent scanning anomaly reveals it.
  • Similarly, if you have NO or ALL the AQ’s you might have, completely skip phases (2) and (4) above.  For clarity, ALL means 4 aces and 3 queens when holding a singleton.
  • Similarly, if you have ALL Aces and NO Queens (or vice-versa) skip phases (2) and (4).
  • If you have NO or ALL Aces and some Queens (or vice-versa) ignore the NO or ALL one and scan the other one in the King scanning style.
  • Ignore thereafter a suit at all with no free slots (i.e. a void, or a singleton where an honour has been shown or implied)
  • Never scan the last suit with unknown cards during a phase, R is assumed already to know the answer*.

A couple of examples to illustrate the asterisked points above.  Assume you have shown 4441 with 5 QP’s and ODD king parity.  If your King is in diamonds, you show it and then move immediately to AQ scanning – you can’t have another K.  Similarly, if your King is in spades, you deny it in diamonds then deny it in hearts, then move immediately to AQ scanning – partner knows where it must be.

There’s bound to be a mistake, a typo or a mild misunderstanding somewhere above as it’s a fairly complex area (but elegantly simple once you get your head around it).  I’ll correct such things in-situ when I find them.

UPDATE:  I’ve done the number crunching on a million hands a time (thanks to Andrews’ Deal program again) and it seems my intuition was fairly much right.  That is, if you go for design criteria (1) and aiming your parity to match both A’s and K’s with their EP, you get

• Zero stops :  47%
• One stop:  24%
• Two stops:  29%

However, if you go for my guessed solution to design criteria (2) where you match A’s and mismatch K’s with their EP (hoping to get a K match when the A’s value is wrong), you get

• Zero stops:  14%
• One stop:  76%
• Two stops: 10%

So, for a 33% percent loss of zero stops you gain 19% of the two stops back.  It doesn’t seem good value to me, so I am going to stick with my original idea and aim for design criteria (1).

To set a reference point for both the above sets of figures, I have done the stats on the “standard” STOP EVEN, GO ODD approach to parity.  It is self-evidently fairly poor, as you will see from the results below

• Zero stops:  24%
• One stop:  47%
• Two stops: 29%

With reference to all the above statistics, I have ignored the fact that singleton K’s will be treated as Q’s and included them for purposes of this particular analysis. I’ll try and refine this and other aspects of the analysis further in due course, but I wouldn’t expect it to meaningfully alter the apparent lessons.

Regards, DipBridge

DIP: Some thoughts on relaying in DIP

Over the next few days, I hope to blog about the responses to the Intermediate range openings.  Before doing so, however, it seems prudent to discuss the DIP philosophy on relaying.

I’m sure most if not all long time proponents of strong club and strong pass systems will tell you that it’s all about the Intermediate range openings, not the Strong range (and the typically associated constructive auctions, including Symmetric Relay based ones).  The only time I suspect this may not have been true was the 60’s and 70’s (Neapolitan, Roman, Blue and Precision Clubs) when people were fairly respectful of the Strong 1C openings.  Certainly, if the above is the consensus view, I share it.

When I first came across FPR (Forcing Pass Relay) people used to relay up to S+2 or S+3 over interference, that is, they still continue relaying even when they had lost 2, or even 3, steps.  I imagine many still do so.  I come from the almost the opposite school of thought.  When the opposition interfere, and show a suit, or even strongly imply a suit, I don’t want to relay at all.  Further, even if they don’t show a suit, if they cost us any steps at all, I don’t want to relay (remember, the D structure opposite 1C is already up one step from S).  What do I mean by not showing a suit?  Well, there’s CRASH (Colour/Rank/Shape) but there’s also the kind of stuff I used to play against a forcing pass in my youth:  like a 1S fert over a strong pass, for example!

The significant other developer of DIP doesn’t completely share my views on relays in competition, but, for the present at least, is deferring to my preferences in this regard.

The reason I started the above from the end (i.e. relays in competition) rather than the beginning is that my thinking on relay use and optimisation pervades purely constructive auctions as well.  You have already seen an example of this with the decision to include direct semi-POS and transfer captaincy POS bids opposite 1C:  not optimal from a relay perspective.  The former are good, however, in competitive and fast-arrival auctions, and the latter more effective at determining the correct strain for game (if occasionally less effective at getting to a good slam).

Moving on to what is coming up in this blog, the same sort of thinking is applicable to the relay responses to the Intermediate strength openings (1D, 1H, 1S, 1NT & 2C).  DIP has largley adopted the ideas I first saw in MOSCITO2007, namely

• Allowing responders step R response to contain the kind of stuff you would expect (some INV hands without clear direction and almost all FG hands) but also what would have been a normal 1NT response
• As a consequence, the first round rebids by the intermediate strength opener are largely NAT, to cater for the “1NT” type hand and facilitate a pass by responder

This doesn’t hurt the subsequent relay structure too much, but it would be disingenuous to say it had no cost at all.

No longer needing to bid 1NT with the 1NT type hand obviously frees up an extra low-level bid.  To take 1D(=H) as an example, with 1H now R and including the 1NT type hands, you now have 1S, 1NT, 2C, 2D, 2H, that is, 5 bids at or below 2 of the shown suit.  It would be entirely normal to pre-allocate four of these:  one to a raise, and three to show the other suits (whether naturally, or via some sort of transfer).  The questions are, how to best use the valuable extra bid that has been freed up and whether to play transfers or natural to show the other suits?  Some obvious candidate answers for the former question

• As an extra raise, that is a stronger raise to 2 of the suit.  This is what MOSCITO2007 does IIRC (with 2D being a stronger way to get to 2H over 1D)
• As an explicit game force relay
• Some sort of puppet/Lebensohl’ish type structure

In a previous life, I’ve played the latter method in a slightly different system, and found it useful.  I plan also to use it in DIP in the first instance.  It also fits in quite well with NNF type responses in the other three suits, which I have a slight preference for over transfer responses (the latter obviously being more effective when a highly constructive auction would be useful, but less frequent and hence effective in this scenario IMO).

So, to give you a partial flavour of what is coming up, over 1D(=H)

• 1H:  R, either (i) ART, FG, or (ii) INV no primary support, or (iii) 1NT type hand
• 1S:  4+S, NNF
• 1NT:  “Puppet” to 2C, typically some form of discrete INV hand-type
• 2C:  5+C, NNF
• 2D:  5+C, NNF
• 2H: 3H, NNF

You’ll see the above principles in broader action shortly.

I suppose the final thing to say is that including the 1NT hand types in th R response is also not without cost.  It would not have been unreasonable, in their absence, to have the R response set up some sort of Forcing Pass type auction over interference, at some levels at least (e.g 2 and 4).  The inclusion of the 1NT hand type makes this impractical, so, it’s take-out doubles in competition as high as you want to play them (up to and including 4H is my preference) and transferable value doubles thereafter.

Regards, DipBridge