GNT part 2

Our teammates played terrific bridge and carried us into 4th qualifying place for tomorrow's head-to-head match.  Twenty-four of the twenty-five districts fielded teams and sixteen qualified for the knockout stage.  We started strongly today in the Swiss and then hit a couple of bumps in the road before the dinner break.  However, we ended well with three wins in the second session to give us 97 VPs.  Meanwhile, our C team ended third while our A team finished in pole position :)

There were really no very interesting hands today (well, a couple were interesting in the wrong way) so I will use a post that I had prepared earlier.

I've recently been re-reading the very excellent Human Bridge Errors -- volume 1 of Infinity by Chthonic (pronounced like tonic except with a lisp), the (fictional) bridge-playing robot.  In reality it is by Danny Kleinman and Nick Straguzzi.  I've made mention of this book before in this blog (Chthonic).  I think this book is one of the best bridge teaching books there is.  It covers 57 varieties (yes, really!) of bridge errors and the advice is pithy, humorous and, above all, sage.

While all of the chapters are excellent, there are three in the section on competitive bidding that seem to me to stand out above the others, viz. #29, 30 and 31.

Fear of Bidding a Non-Blackwood Four Notrump (29) is something of a diatribe on how, for most humans, 4NT = Blackwood, period.  But at Chthonic points out, in a competitive auction, this is rarely the most useful treatment.  When our side has not found a fit, 4NT should be considered accordingly: if it is logical for this to be natural, then it is natural.  Else if it is needed to show two places to play, then it is a two-suited takeout (I'm summarizing).  If and only if neither of these make sense, then it is ace (or key-card) asking. 

Reopening on Inappropriate Hands Using Negative Double (30) is the antidote to that advice that we all received at some point: always reopen after you open 1-something and that is overcalled on your left followed by two passes.  The logic is that your partner may be trap-passing.  The trouble is that he simply might not have a very good hand and if we have a rock-bottom minimum, we may get into a little trouble.  So, Chthonic believes that we should have extras for this call, just as we would with any double that might be passed for penalties.

Ignoring Clues from the Opponents' Temp and Mannerisms (31) reminds us that the pair we have never seen playing at the club is probably not an expert pair.  If they stop below game, it doesn't mean that they don't have a game, especially if your RHO takes for ever to think about it.  In such circumstances, if we reopen, they may be delighted to take another bid and propel their side into a game they were otherwise going to miss.

I love the humorous way Chthonic pokes fun at us humans.  As an exponent of artificial intelligence techniques myself, I have lot of empathy with Chthonic.

Looks simple

It's the first hand of the evening at one of last week's STAC games (only we are vulnerable). After partner opens 3♦ in second seat, we find ourselves in 3NT with no opposition bidding. The lead is the ♥2 (fourth best) and this is what we see:

Dummy
♠	9 4 2
♥	10 7
♦	A Q 10 9 8 6 3
♣	6

My hand
♠	A K Q 8
♥	Q J 3
♦	5 2
♣	K Q 10 3

The opponents clear the hearts, we lead a small diamond, LHO follows with the four and it's decision time. Well, the first thing you notice about the dummy is that it's totally entryless outside diamonds (it's a great preempt, isn't it?).  The defenders have taken two tricks already and have a heart and a club to cash. So, if we're playing IMPs, we need to bring in the entire suit, so must finesse the Q to give us the best chance (about 26%) of making. At first glance, you might think that the chance of making is 50% but in practice, if we finesse the Q and it wins, we must also have a 2-2 split or see the J drop on our right.  Though even then, there's the chance of a dastardly defender deliberately throwing us off holding KJ.

In a diamond contract, there are at least 9 tricks so in effect we aren't competing with the declarers in diamonds. In any case, of 17 tables, only two played in diamonds. So, how do we maximize the number of tricks we will take, keeping in mind that the number may well be less than nine? Finesse the 10 (8 or 9) on the first round, in keeping with the Principle of Least Commitment. This play either breaks even or loses a trick to the Q play when the honors are split. But it enjoys a big win in the case where KJx is on our left and x is on our right (since we have no outside entries to dummy this layout will kill the suit stone dead if we finesse the Q). The 10 play also has a minor win in the unfortunate case where KJxx are all on our left, although this will not be a big comfort at the time. Nothing works of course when KJ are guarded on the right. See the table below for the details.

Layout	Cases	Probability	Q tricks	T tricks	Q expect	T expect
KJxx -	1	4.78%	2	3	0.096	0.143
KJx – x	2	12.44%	2	7	0.249	0.871
Kxx – J	1	6.22%	7	6	0.435	0.373
Kx – Jx	2	13.56%	7	6	0.949	0.814
Jxx – K	1	6.22%	6	6	0.373	0.373
Jx – Kx	2	13.56%	6	6	0.814	0.814
xx – KJ	1	6.78%	6	6	0.407	0.407
x – KJx	2	12.44%	1	1	0.124	0.124
Total	12	76.00%	53	61	4.536	5.157
Approx					4.42	5.08

When the "books" take a look at a suit like this, they assume that entries are available wherever needed.  However, with the excellent SuitPlay program by Jeroen Warmerdam, you can explicitly tell it how many entries accompany the suit, etc.

Since everything must be decided on the two leads towards dummy, we effectively have four realistic lines of play: Q or 10 on the first lead, A or the remaining honor on the second.  My analysis assumes that we will always guess right on the second lead but this will be easier sometimes than at other times.  In particular, if the Q won on the first trick, the Kx-Jx layout will be picked up easily.  But if the Q loses to the K, and LHO plays small to the second trick, we won't know whether he started with xx or Jxx.  Against most defenders, the 10 play may make the second guess easier because players tend to win as economically as possible. So, in a way, playing that 10 first is something of a safety play.

The best matchpoint line, starting with a finesse of the 10 and the one which I happened to choose at the table, did not give me the best chance of making the contract.  But it did give me the maximum expectation of diamond tricks.  As it happens, I lost the first trick to the J.  I was fortunate in that the defender who won the last heart trick didn't have the club ace and chose to lead a spade.  I therefore made my contract exactly.  This was worth only 5.5 out of 16 (approx 33%), however.  I shouldn't really be surprised.  At a club pairs, players perceive a premium on making contracts (and don't typically worry about minimizing the set). Perhaps in the Blue Ribbons I'd have had more company.

The table above has two columns each for the Q and the T plays.  The first is the number of tricks yielded.  The second is the expectation of tricks (the number times the probability).  By summing the expectations, we can compare the overall expectations of the two lines.  However, we poor humans cannot do these kinds of calculations at the table in practice (Chthonic would have no problem of course).  There's another, simplified, method of comparing the lines that Eric Rodwell describes in The Rodwell Files.  He suggests assuming that all possible layouts are equally likely.  This isn't quite accurate of course because, due to considerations of vacant places, KJ74 in one hand is not as likely as, say, KJ opposite 74.  That's because once the K and J have been "placed" in one hand, there are two fewer vacant places in that hand to take the 7, and if the 7 does go with the KJ, there are now three fewer vacant places to accommodate the 4 in the same hand.  However, to a first approximation, we can assume equal likelihood of each layout.  When there are n outstanding cards, there are 2^n possible layouts.  In this case, four missing cards so there are 16 possible layouts.

Once LHO plays a small card (the 7 or 4 in this case) to the first diamond lead, we can immediately eliminate four of the 16 cases. In the table above, the bottom row, labeled Approx, shows the expectations when we use this simplified method of calculation.  The two approximate values are 53/12 and 61/12.  As you can see, the numbers are very close to the accurate values.

However, for a complex situation like this one, even this amount of calculation is too much.  That's why I find myself frequently falling back on the principle of least commitment.

Chthonic

Lately, I've been rereading the two Chthonic books, The Principle of Restricted Talent, and Human Bridge Errors, Vol 1 of infinity. They're great! If you haven't read them, you should. Somewhat in the tradition of Victor Mollo and David Bird, but better perhaps. Possibly because Chthonic is a more likable protagonist than either H.H. or the Abbott.