Sunday, May 21, 2017

Happy families are all alike; every unhappy family is unhappy in its own way.

The so-called Anna Karenina principle, quoted in the title, applies to so many walks of life. This weekend, playing with Symphony Pro Musica, I am reminded forcefully that, while music performance is not a perfect example of the AK principle--especially for professional musicians--nevertheless it is close. A perfect performance is indeed very much like another perfect performance. Again, I hasten to add that there is yet plenty of scope for differences among "perfect" performances at the highest levels of the art. But, for a non-professional orchestra, where mistakes can and do happen, there are many more ways to mar a performance than there are ways to play it perfectly. In ensemble playing, every note must be:
  • properly formed (not a squeak or croak) and with the appropriate degree of vibrato;
  • the correct note (duh!);
  • in tune (and an orchestra's domain is not the equi-tempered scale of keyboards so playing in tune requires constant attention);
  • in time (not more than a few milliseconds early or late);
  • at the proper dynamic level;
  • exhibiting the correct emphasis/style.
When you have forty or fifty independent players in a (non-professional) orchestra, each playing say a thousand notes, the chances of a perfect performance are obviously small. That's not to say that the performance cannot still be very much enjoyed by the audience. On the contrary, one of the most essential aspects of musical performance is the freshness and immediacy of the performance.

So, what does all this have to do with bridge? A hand of bridge is another endeavor in which perfection is possible, but the number of ways to achieve the perfect result (from both sides' point of view) is small, whereas the number of ways to err is vastly greater. In other words, a hand of bridge is another exemplar of AK. I note with interest that we bridge players have another thing in mind when we use the letters "AK."

One of my favorite tools for researching this idea is BBO's GIB analyzer. At each player's turn, you can check to see which cards are the correct ones to play and which the incorrect. The only flaw is that GIB will tell you the immediate ("proximal") effect of the play of a card, but it cannot (or doesn't) tell you the "distal" effect, taking into account the reaction of the player's partner (this in the case of a defender). As an example, defending a suit contract, partner opens with the appropriate card of his "AK" holding in a side suit. Dummy has two cards in the suit. You have both the queen and the jack and perhaps some other cards. From GIB's point of view the play of the Q or J is entirely equivalent. But which you choose can have a major difference to the result when partner leads to the next trick. Still, the GIB tool is an invaluable resource.

As an example, let me share this defensive problem (note that it wasn't necessary to ask GIB this time). It's the second board of the session and you hold 75 9432 AK65 982, not vulnerable vs. vulnerable, dealer. You pass and LHO opens 1NT (15-17). Partner passes and RHO bids 3NT, alerted. Opener now bids 4S which is passed out. Partner asks before leading and we are told that dummy has four spades and five hearts. "No," dummy says, 3NT means I want to play in 3NT.

Partner leads the deuce of diamonds (third and lowest) and dummy comes down with: T843 AKT T98 AT3. Well, he does have four spades. You can see that this is going to be a tough session. Even when the opponents have a major misunderstanding, they land on their feet. Anyway, you win the king and now contemplate your lead to trick two.

You have twelve cards in your hand and I can tell you now that there are only two correct cards to play (and they are absolutely alike) while there are ten possible errors to make. A perfect example of the AK principle.

This is how your thinking should be going. Partner has either one, three or five diamonds. Five is ruled out because LHO opened 1NT. That leaves one or three. If it's one, that means opener has five which is quite possible. We have no outside entry so it seems reasonable to cash the ace and give partner his ruff. Perhaps we should give him the ruff now as the diamond ace can't go to bed. What if he led from Qx2, which appears probabilistically to be the most likely holding (he wouldn't tend to lead from a xxx side suit after this auction)? Then we'll always get our three diamond tricks. This is true whether he started with three or one (where the Q will be replaced by a ruff). Does anything else jump out?

Could he also have Jxx of trumps? Yes, this is entirely possible (we expect opener to have four spades). If partner's trumps are any better than this, he'll be getting a spade trick anyway, whatever we do. Providing that we are on lead at trick four, that hypothetical trump trick can be promoted by playing the thirteenth diamond!

The problem might have been easier at IMPs where all that matters is defeating the contract. At MPs, it's important not to give away silly overtricks, chasing some chimera. Yet, this problem is no harder than playing a scale in a major key. Unfortunately, I didn't think it through quite as well as I've shown here. I picked one of the ten unhappy cards (A) instead of either of the two happy cards: the five or six of diamonds.

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