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
- When to STOP or GO when showing A and/or K parity (and why)
- Why, in pure JVCB, A/Q’s are first considered in 5+ suits, whereas K’s are considered in 4+ suits
- 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
- Determine the best way to model “Expected King Parity for given QP’s” (which will likely be a compromise between memory and efficiency)
- 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
