Thursday, December 18, 2014

Doubling 3NT for a lead (part two)

Last time, we talked about the general subject of doubling 3NT for a lead. Now, let's talk about the most problematic of all calls: double after it goes 1NT pass 3NT. You could play that partner could lead any bad suit, but it won't be any surprise when both defenders are weak in a minor suit on this auction. So, to me it makes sense to restrict leader's choice to a major. Some pairs play that double asks for the lead of a specific major. But unless you play a lot with this particular partner, it will rarely come up.

So, what sort of suit do we need for the double to work? How about ♠AKQxx? At the recent NABC in Providence, RI, this exact situation came up in a match against Benito Garozzo on my right and Jan van Cleeff on my left. Was my suit good enough to double with? I didn't have forever to think about it (lest I pass UI to partner) so I had to make up my mind quickly. Yes, I decided. There followed several tortuous minutes while I waited for my opponents to consider their options and for my partner to lead (this last didn't take long). Benito redoubled to ask how opener's majors were and opener passed to say "pretty good." However, none of this was clear to me at the time. It appeared to me that they didn't have a clear system for this situation (I knew who RHO was of course, but not LHO). My partner, Vincent, put his card face down. "Turn it over", I said. The deuce of spades. Hallelujah! Dummy came down with two small spades and declarer asked a fatuous "what are your leads?", and played the ten at trick under my queen. This card, incidentally, caused quite an upset—to say the least—for the 87-year-old Garozzo. But it was all play acting by van Cleeff and my feeling of victory was very short-lived. Declarer started with JTxxx of spades and wrapped up 10 tricks to go +1400. We lost 13 IMPs on that deal.

Was my bid so very bad? or was I just a little bit unlucky? I determined to find out. This wasn't a trivial problem in probabilities and I had to write some Java code to figure it out. But now the results are in!

I set up the following conditions: LHO has at least two cards in every suit and RHO is nominally balanced (so at least one spade). For the five remaining spades, LHO has 5 vacant places, partner 13 and RHO 12. Additionally, LHO has fewer than six spades; RHO has fewer than five (no transfer) and, 80% of the time, fewer than four (he didn't use Stayman). I also adjusted for the case where partner has four or more spades, because he might not recognize that spades is our suit. With five I assumed, he will not lead spades and with four I assumed he will pick a spade half the time. Probability of success? 52%.

That's really not enough (as I discovered) to make the bid worth while. Let's see what we get as an expectation of IMP gain.

We assume that when we are successful, running our suit, they will run to a minor-suit half of the time (bidding game half of those times and making it half of those times); otherwise they will sit for the double. When we are destined to fail, we assume that they will redouble, as Garozzo did. We also assume for the sake of argument that they are vulnerable.

In the case of my AKQxx, we have the following outcomes (with probabilities and expectations of IMPs):

Bad game6.5%+12+0.78

Oh dear! Overall, the expected gain is negative! With so many possible things to go wrong, not to mention the fact that partner might happen on a spade lead all on his own, it's a bad idea to double. There's also the psychological factor to take into account when playing with humans rather than robots. Partner (not to mention doubler) may be so disheartened by this result that the rest of the set suffers. I don't think that happened in our case (although we netted minus 3 on the other six boards), but it easily might.

Let's take a look at some other cases:

HoldingP(success)Expectation of IMPs

The two middle situations are much better. Having the jack in the second case makes quite a big difference mainly because it increases the probability of success, but also because it prevents a redoubled overtrick. AKQTx would be better than my hand but obviously not as good as AKQJx. Adding a sixth card increases the probability of success and also the penalty when they sit. Note that AKxxxxx just isn't good enough. Basically, you have to catch partner with two and even then you need an even split. Having the jack would help in those cases where opener has a doubleton queen or dummy (or partner) has her. But even then, you're gambling quite a bit.

What about a topless solid suit such as KQJxxx with an outside ace? The overall probabilities and expectations are approximately the same as when you have AKQxxx. However, you will have to face the rather likely possibility that opener has 8 running tricks in addition to the ace of your suit.

There's another way this can backfire, as my partner and I learned a number of years ago at a sectional Swiss in Maine. Our non-vulnerable opponents were playing a weak no trump and the auction went 1NT—3NT.  I doubled with something like ♠xxxx KQJxxx x ♣Ax. Partner had something like ♠xx Ax in the majors and quite reasonably assumed my suit was spades. We learned then, due to an adverse swing of 12 IMPs, that it might be a good idea to cash a major suit ace first just to see partner's card.

So, here are my conclusions if you're thinking of doubling 1NT—3NT for a major suit lead (assuming you've discussed this situation with partner):

HoldingTo double or not to double?
AKxxxxxAbsolutely not!
KQJxxxMaybe but be ready to apologize

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