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
- Whether to STOP on EVEN when showing Ace parity (and similar considerations for when showing King parity)?
- Why are A’s & Q’s considered first only in 5+ suits, rather than the outwardly more intuitive 4+ suit option?
- Why are K’s scanned before AQ’s?
My current ideas with respect to the above three considerations are
- To try and optimise when to STOP & GO with the parity methods.
- 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).
- 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
- 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
- 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
- K’s in 4+ card suits (STOP = no K, GO = K)
- A’s and/or Q’s in 4+ card suits (STOP = neither or both AQ, GO = A or Q only)
- K’s in 2 to 3 card suits (STOP = no K, GO = K)
- A’s and/or Q’s in 1 to 3 card suits (STOP = neither or both AQ, GO = A or Q only)
- J’s (STOP = no J, GO = J)
- 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
