Tuesday, December 22, 2009

Suit Combinations and the Principle of Least Commitment

Are you one of those people who has learned all 656 of the bridge encyclopedia's suit combinations?  And you know how to extend the methods to all those that it doesn't cover?

Neither am I.

That's why I have been tinkering over the last few years with something I call the Principle of Least Commitment.  Basically, it works like this.  Instead of trying to remember the proper play at the table, just make sure that you take advantage of any useful sequences that you have.  Choosing a card from a sequence means you aren't committing yourself as much as if you play an isolated card.  Failing any useful sequences, finesse the lower of two significant cards first.  Again, you don't make such a big commitment at your first try.  For the full discussion, follow this link.

For example, you have a suit laid out thus: AQT2 opposite 753 and you are in a normal contract wanting to take the most tricks at matchpoints.  It may not seem to matter much whether you finesse the Q or T first, but it does.  If both honors are wrong you're going to lose two tricks in the suit.  If the honors are divided and you guess wrong then you'll lose one trick.  But if the honors are both on your left, then everything's roses, you say?  Well not quite.  Suppose you finesse the Q.  It wins.  Now you come back to finesse the T.  LHO has the K and J and can happily split his honors.  But if you finesse the T first, it too win and now when you come back to finesse the Q, it also will win and you've now got three tricks (four if the enemy cards split evenly) from the suit.

A suit combination came up the other evening at the club like this: 9 opposite AQT7643.  The contract was a part-score at our table and this was the trump suit.  It was a very normal contract so it was important to take the most tricks.  There is a sequence here: the T9.  But is it significant?  Well, the 8 is a significant card in the defenders' hands so it seems reasonable that the sequence is significant.  But is it sufficiently significant to outweigh the fact that we have only one chance to finesse and therefore should take the "obvious" finesse of the Q?

A careful analysis shows that it is better to run the 9 than to finesse the Q, but only slightly.  Here are the layouts that matter with the number of tricks from this suit (layouts assume that the length is in hand, the 9 is in dummy):

LHO/RHO layout
Probability
Q tricks
9 tricks
Jx – K8x
6.8%
6
5
J8 – Kxx
3.4%
6
5
K – J8xx
2.8%
4
5
Kx – J8x
6.8%
5
6
K8 – Jxx
3.4%
5
6
KJ8x – x
5.7%
4
5

As you can see, what you do only matters in 37.5% of the situations.  The top two cases both favor the finesse of the Q, while the lower four cases all favor running the nine.  Running the nine will win overall 8.5% of the time and is the right strategy for making the maximum number of tricks (your expectation overall is 5.47 tricks).

Unfortunately, I wasn't able to apply my principle of least commitment at the table because these hands were held by my opponents.  And even more unfortunately, the declarer was someone who knew his business.  But, fortunately, it was one of those times when the optimum play failed (it was in fact the first case mentioned in the table above).  Every other declarer must have finessed the Q because we were the only pair sitting our way to take four tricks.  And the defense on the hand is relatively obvious (the long hand was always going to be declarer and the opening leader is always going to start with his AKxx in a side suit).

Watch this space for more exciting developments in the principle of least commitment!

No comments:

Post a Comment