Monday, December 27, 2010

Abiding by the law

My previous blog on pressure bidding prompted another look at the so-called Law of Total Tricks and, especially, I fought the law by Mike Lawrence and Anders Wirgren.

One of the first things I realized twenty years ago when I first read about the "law" was of course that at best it is a rule of thumb.  It is no more a true law (and perhaps even less so) than Bode's law.  Some people, if I am to believe the L&W book, seem to believe that it is absolutely true, in the same way that certain fundamentalist religious people think that their "book" is literally  true.  I say this because Lawrence and Wirgren devote a large part of the book to debunking the myths of the LOTT.  Would they bother if there weren't true believers?

Of course the "law" isn't literally true. Every bridge player knows that, including and especially Larry Cohen. And so do I.  Yet, one of my bridge friends still chides me for quoting the law when making general statements about competitive bidding, as if I was one of the devoted followers, believing every word of the gospel.

Nevertheless, the "law" does, in a very general sense, show how the total number of tricks available (ours at our best trump suit plus theirs at their best trump suit) increase with the combined lengths of the two best trump suits (ours plus theirs).  That's to say, on the whole, each additional trump (of ours) in one of our hands, or their trump in one of their hands, will result in an additional trick (either for us or for them).  It doesn't state this as a categorical fact.  It simply says that, in general, total tricks increases in step with total trumps.

Although it's never a true law, as mentioned above (in the majority of hands exact equality is the exception rather than the rule), it works best under the following conditions:
  • high card points are more or less evenly divided between the two opposing pairs (the usual range is quoted as 17-23 but this is of course an arbitrary boundary);
  • total trumps are nearer to 17/18 rather than the extremes of 14/21;
  • shortness and length are more or less in harmony (long suits beget short suits/voids);
  • you are willing to be off by one trick either way;
  • if you have a choice of trump suits of equal length, you choose the best one;
  • defense and declarer play at your table are perfect (double-dummy);
  • the layout doesn't contain too many short-suit honors, such as K, Qx, Jxx.
So, what use is the "law"?  It can be useful when you have to make a competitive decision to bid on, pass or double and it is not completely obvious from bridge logic and experience what to do.  This generally involves higher-level contracts, because an experienced player will be familiar with the lower level situations (should I bid 3♠ over their 3, for instance).  Newer players can use it of course at all levels because they won't have developed the appropriate judgment yet.

As noted, it won't always be right.  But bridge, especially matchpoints, is a game where we try to maximize our score in the long run without worrying too much about the occasional hand where things don't work out. For example, with no enemy bidding, no special avoidance requirements, and holding three small trumps in dummy (with outside entries) and AQT9x in our hand we will play low from dummy, playing the 9 if RHO plays low.  Generally speaking, we expect to lose one trick only.  But in fact, this favorable outcome will only occur 76% of the time.  Do we feel hard done by if occasionally we lose two tricks?  Of course not.  Bridge is not normally a game of absolutes.

Now, you might be wondering what "long suits beget short suits/voids" was supposed to mean.  What I mean by that is that as you get longer suits in your hand, you expect, or at least hope for, short suits to go with them, if not in your hand, then perhaps in partner's.  For example, you pick up a 7-card suit.  If the other suits are 2-2-2, this feels a little unnatural, and a bit of a disappointment, doesn't it?  You'd be much less surprised by the 7-3-2-1 pattern.  In fact, the 7-3-2-1 shape is three-and-one-half times more common than 7-2-2-2.  And, as Lawrence and Wirgren tell us, it is really shortness rather than length that is most indicative of the number of tricks we can take.  All things being equal, we'll take more tricks with a 7-3-2-1 hand than a 7-2-2-2 hand.  But the "law" only takes into account the length of the trumps, in this case, presumably the seven-card suit.  That's one of the obvious reasons why the law can't possibly be the gospel truth.

So, going back to my earlier question "what use is the law?", I do believe that it can help you decide what to do in a high-level competitive auction.  Here's an example from a recent club game.  You pick up in second seat, vulnerable versus not, ♠T7 93KQT4 ♣97653.  RHO passes, as do you, and LHO opens the proceedings with 2♠.  Partner bids 4♣ (showing a good hand and at least 5-5 in hearts and clubs) and RHO bids 4♠.  Now what?  Let's try to do a "law" calculation.  Given that LHO opened a weak two at favorable vulnerability in third seat, he probably has only five spades.  I doubt if RHO has five spades with shape because he'd probably have jumped straight to 5♠.  But he might have five spades without any shortness.  It looks like we have a ten-card club fit and they have a nine-card spade fit so we're guessing 19, or possibly only 18 tricks.  We don't have much in the way of points, but it does seem to be our hand, based on the auction so far, though perhaps not by a lot.  If they can make 4♠ (-420), we could be -500 or even -800 in 5♣ so that doesn't look good.  OTOH, if we can make 5♣ (600), they might be only -500 or -300 when doubled.  We decide to pass smoothly (ah, there's the rub!) hoping that given partner's quasi-game-forcing bid, our pass will be considered forcing.

Partner comes in now with 5 which strongly suggests 6-5 in the round suits since he'd probably just double with the 5-5 he originally promised.  RHO takes the push to 5♠ (perhaps he did have five spades after all) and we revise our idea of the hand now.  It looks like they have 10 spades and we have 10 clubs with an 8-card heart fit.  So I'm guessing we might have 20 total tricks.  However, given that all our honors are in what appears to be a short suit in partner's hand (at most a doubleton), I'm going to be conservative and estimate 19 total tricks as before.  So we decide to double expecting to gain 100, 300 or 500 as against (for 6♣) -800, -500, or -200.  If we're wrong and there are 20 total tricks, we will be spectacularly wrong in the two extreme cases: they make 850 (pass would be best) or we could make 1370; but still doing fine in the middle (and perhaps more likely) cases: 100, 300 instead of -500, -200.

How did we do in practice?  Both sides can take 10 tricks in their black suit, so it was right not to let them play 4♠. Their RHO made the all-too-common error of going to the well twice and falling down it the second time. We score +100 for about average (somewhat as we'd expect).  However, there were no other pairs our way scoring 100 for 5♠X.  Some pairs managed to set 5♠X two tricks but this must have been careless declarer play.

I think the law was helpful here, keeping us at average despite a difficult competitive board.  It was difficult because a) our balanced and poorly fitting hand suggested fewer total tricks than there were; and b) the other side can make game on only 17 high-card points.  For the full hand, look up board 18 from the Newton-Wellesley game on Christmas Eve.  I was not playing, by the way, so all my thinking described above was fictional, but reasonable.

1 comment:

  1. Are you referring to Board 18? If "yes", I object to several comments. I would object strongly to the 4C call: the leaping Michaels call might deliver 6 clubs, but should always deliver exactly five hearts. Here the big hand held x, AKQJxx, x, AKJxx ... not only too many hearts for 4C but also way too much strength to make a nongame forcing call. At the table, I bid 6H, and despite the wicked awesome results (pard had neither of the missing two aces, and I had a sure club loser as our ten card club fit ran into 3-0 split offisde. I would do the same again and can justify the choice by pointing out that if the hands of passing opener and passing partner were exchanged for one another, 6H would roll.
    Further objection to the comment about 4C being quasi-forcing. Why should that be the case?
    The only alternative I would consider is to double 2S and bid 4H (or 5H, if necessary) on the next round. I prefer 6H directly because it might induce 6S call and might make even when I am missing two aces ... provided I do not disclose my side club suit.