Tuesday, June 30, 2009

A straightforward (?) 6nt

I was kibitzing on bbo vugraph when declarer had to play this hand in 6nt:

Dummy: xx KQT9 AKxx AKJ

Declarer: KTx AJx Qxx Q9xx

A heart was led.

Apologies for the length of this analysis; as in my favorite Twain quote, “I didn’t have time to write a shorter one."

The obvious question is, do you (a) play a spade to K without testing diamonds, or (b) test diamonds first? As a straight percentage problem, the easiest thing to calculate, I think, is swing cases. (a) wins a swing when rho has 4 diamonds and SA, about 11%. (b) wins a swing when diamonds 3-3 and sa off, about 18%. Note that when diamonds are 5-1 you can switch to spades, so no swing in that case.

We didn’t take into account that an expert lho may duck the SA (!) when you lead low to the K (if you do it early), hoping you have KQT and misguess later. The likelihood of this is very hard to evaluate.

Of course, it looks attractive to (c) cash your hearts+clubs before committing yourself. The percentages may change. You would come down to:

Dummy: x --- AKxx ---

Declarer: KT --- Qxx ----

and can still choose either option. The drawback to this is that when LHO shows out on the second round of diamonds, you can no longer switch gears (you’re cut off from spades,) so this line looks bad when diamonds are 5-1. You might therefore leave the 4th club uncashed. But cashing all your winners has an advantage: if RHO started with QJxx spades and 4 diamonds, he’ll be squeezed down to a stiff spade honor and you make it if you read the position, which I think you will: who is diabolical enough to pitch a spade honor and keep 2 small, holding such as Jxxxx xx Jxx xxx?

I love how this extremely simple-looking hand has so many wrinkles. Another diabolical falsecard opportunity that might occur is when RHO has the aforementioned QJxx xx JTxx xxx. When you cash hearts and clubs, what if he nonchalantly pitched a diamond and two spades (preferably diamond first,) unguarding diamonds? Wouldn’t you think he must have started with 5 diamonds, and play for the SA onside? Could any defender do that in real life, though? He doesn’t even know you have the ST.

My verdict is that I would cash all the winners (this is assuming hearts+clubs aren’t 5-1), then try to get the ending right – if RHO has even two fewer round cards than LHO, my calculations say the percentages shift enough to favor (a).

The real-life story? RHO had AJxx xx JTxx xxx. Both declarers tested hearts and clubs without cashing the 4th club, then despite the breaks took line (b), going down for a push. If they had cashed the last club they would have seen the SJ pitch and probably gone right whether or not they did the math. No falsecard opportunities with this hand; any other pitch leaves declarer only winning options.



4 comments:

Arik Perlmutter said...

I think I would play a S toward the K at trick 2, the reason being, partly as you rightly mentioned, that W might duck it with the SA.
But even if W wins the trick all is not lost.
Unless W has the SQ as well he in all likelihood won't play a second S back – declarer's ST makes it unsafe for W to lead away from the J and with some small spots in S he will be afraid to provide declarer with a free finesse of his partner's presumed J.
So on a non S play by W to the third trick declarer sill has time to test the Diamonds.
Moreover, if E turns out to have QJX(X...) in Spades and 4 Diamonds an automatic simple squeeze is developed and there is no need to read the position – simply cash Hearts and Clubs and poor E will succumb.

Jonathan Weinstein said...

Good point, I should have mentioned that. I do think if he has A-empty in spades and can see a 3-3 diamond break or an imminent squeeze against partner, LHO may well find the spade continuation. With AJ, much harder.

The Rambler said...

Zia would have led a spade to the K I'm sure. That's what I'd probably do too.

The auction might come into play, for the possibilities of LHO leading the SA if he had it.

For your swing calculations, isn't it relevant to know the opponent sitting in your seat and his likely line of play?

Jonathan Weinstein said...

When comparing two lines of play, by "swing case for a" I mean a case where you win a swing if you do a and the other guy does b. This is a fine way to compare two lines even if you don't know what he'll actually do.

The auction sounded like two balanced hands, so SA lead was unlikely.