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A Suitable Study
By: Fred Gitelman

Originally Published in Canadian Master Point, April, 1996

A hand came up in the recent Macallan Tournament in London (formerly the Sunday Times Pairs) that interested me. At 3 of the eight tables the contract was 6. In order to make the slam, it was necessary to play this trump suit:

for one loser.

The three declarers were Americans Bob Hamman and Jeff Meckstroth, and Paul Chemla from France, certainly three of the very best players in the world.

Chemla, playing against George Mittelman and myself, finessed the Q on the first round. This lost to George's K. Next he cashed the A, dropping my J and was able to use the 10 to draw George's last trump. The entire layout was:

Hamman played low to his 8 on the first round and had to lose two trump tricks. Meckstroth started with dummy's 10. When the famous player holding J7 made the mistake of not covering, the defense was held to one trump trick and Meckstroth made his slam.

I thought it was highly unusual that three players of this calibre would all play a suit combination differently.

My first bridge mentor was Ted Horning. Over 10 years ago, Ted suggested that it would be highly benificial for me to study the vast tables of suit combinations in The Official Encyclopedia of Bridge. I decided that if Ted thought that knowing how to play suit combinations was important, I was going to learn how to play every one of them properly.

I was disappointed to find out that I was no better at studying long boring bridge tables than I was at studying long boring university textbooks. The fact that there were so many combinations made this task very painful. The fact that very few bridge hands contain "pure problems", the way the Encycopedia presents them, made it difficult to re-inforce what I was trying to learn. I gave up trying to memorize suit combinations and decided to teach myself how to figure out these problems at the table.

As the deal from London illustrates, not even the very best players in the world "know" how to play every suit combination. What they do have is the capacity to work out a reasonably good (if not the best) line of play.

It is not very difficult to figure out how to play some suit combinations. Here is the general approach:

  • Step 1: Think of all "reasonable" lines of play
  • Step 2: Figure out which line of play will work the greatest percentage of the time.

The word "percentage" might scare you. In fact, many of these problems can be solved without any mathematical calculation. For example:

You need 4 tricks from:

Here are some "reasonable" lines of play:

  1. Cash the A and lead the J next. This play will work whenever the suit is 3-3 or either opponent has KQ.
  2. Lead low to the J, later cash the A. This play will work whenever the suit is 3-3, either defender has KQ, or RHO has honour doubleton. This is clearly better than line 1.
  3. Cash the A and lead low next. This play will work whenever the suit is 3-3, either defender has KQ, or either defender has honour doubleton. This is best of all.

The presense of the 8 changes everything (and makes the computation more difficult):

Since all reasonable lines of play pick up all 3-3 breaks and both doubleton KQs, I will simplify this calculation by not mentioning these layouts. Here are some reasonable plays:

  1. Cash the A and lead the J next. In addition to the trivial layouts just mentioned this also picks up 9x in either hand. It also picks up K9 or Q9 in either hand.
  2. Lead low to the J and cash the A next. This also picks up both 9x and all K9 or Q9 combinations. It gains over line 1 in that it picks up Kx or Qx in RHO's hand. Line 2 is thus better than line 1.
  3. Cash the A and lead low next. Once again you will pick up all K9 or Q9 combinations. This time you lose to both 9x combinations that line 2 picks up. You still pick up Kx or Qx with RHO (as you did with line 2) and also pick up Kx or Qx with LHO (which line 2 loses to). Thus, in order to chose between lines 2 and 3 you have to answer this question:

What is more likely, that either defender started with 9x or that LHO started with Kx or Qx? If the former is true, line 2 is better. If the latter is true, line 3 is better. Perhaps the simplest way to answer this question is to list all of the relevant holdings in which lines 2 and 3 gain against each other:

Line 2 gains:

  • 95 KQ76
  • 96 KQ75
  • 97 KQ65
  • KQ76 95
  • KQ75 96
  • KQ65 97

Line 3 gains:

  • Q5 K976
  • Q6 K975
  • Q7 K965
  • K5 Q976
  • K6 Q975
  • K7 Q976

Each line gains against the other on six layouts. Since all of these layouts are equally likely, lines 2 and 3 have equal chances of success. Both are better than line 1 but neither is as good as:

4) Lead low to the 8. Cash the A next. Line 4 works whenever line 3 does. It gains over line 3 when RHO has 9x or KQ9x. Simple logic tells us that since line 4 is better than line 3 and line 3 is equal to line 2, line 4 is also better than line 2. Line 4 is the correct line.

I have shown this suit combination to various international stars none of whom "knew" the right answer. They were all surprised when I told them it was right to play low to the 8. For some reason this play does not look "intuitive".

Here is another combination with a non-intuitive answer:

You need four tricks:

Here are three reasonable lines:

  1. Cash the A and lead the 2. If RHO follows small, play the 10. The critical winning case is when LHO has Kxx.
  2. Cash the A and lead the 2. If RHO follows small, play the Q. This play works when LHO has Jxx or Jx. It is thus better than line 1. Most experts would play this suit combination this way. They would succeed almost 39% of the time.
  3. The right answer is very non-intuitive: start by leading the Q and passing it if LHO does not cover. This loses to KJx with RHO (which lines 1 and 2 pick up) but wins when LHO has KJx. These combinations cancel out. Line 3 picks up Jx in either hand (like line 2) but also picks up Kx with LHO. Line 3 will succeed over 44% of the time.

The calculations involved in solving some suit combination problems (like the one from London) are too difficult for all but the very best players to solve at the table. Most of those that have the capacity to solve this problem would not bother going to the trouble. This is largely a matter of practicality - in a bridge tournament you have limited amounts of time and concentration. Finding a line of play that is 5% better than the "normal looking play" will only make a difference in one such hand in 20. On the other 19 hands your play will not matter and your calculations will leave you with less time and mental energy for the "easy hands" (yes, I have been told some bridge hands are easy).

Another downside in trying to figure out every suit combination at the table is that sometimes there is no answer:

You need 5 tricks holding:

 opposite a void.

Here are the reasonable lines:

  1. Lead the A followed by the Q. This loses to Kx in either hand which lines 2 and 3 pick up.
  2. Lead the A followed by the 10. This loses to Jx in either hand which lines 1 and 3 pick up.
  3. Lead the A followed by a small card. This loses to 9x in either hand which lines 1 and 2 pick up.

Since Kx, Jx, and 9x are all equally likely, lines 1, 2 and 3 are all equally likely to succeed. Wouldn't you feel silly spending five minutes figuring this out at the table only to discover that you would have to rely on your table presense instead of your brilliant technique?

Back to London, your trump suit in 6 is:

My computer tells me that neither Hamman, Meckstroth, nor Chemla played the suit correctly. It says that you should cash the A first, then lead low towards the Q and guess whether or not to duck. I am not completely confident the computer is correct and have not checked the calculations myself.

The computer also says that Hamman's play was the best of the three. He was the only declarer to go down. Meckstroth made the technically worst play but was able to capitalize on an error by the defense. Defensive errors are impossible to factor into the play of suit combinations. Meckstroth may be the best player in the world at inducing his opponents to make mistakes. In terms of winning bridge, this quality is far more important than perfect technique.

I started this article by claiming that it was not practical to memorize tables of suit combinations. I have tried to demonstrate that it is not practical (in most cases) to figure out these problems at the table. Does this mean that I think my old mentor was wrong and that it is a waste of time to consider such problems?

In retrospect, I think Ted was after something else besides my actually memorizing every suit combination. Ted wanted me to see the entire scope of what plays were possible in a single suit. By reading these tables (and by doing formal analyses) a player can learn some very sound general principles even if they are only able to memorize a small percentages of the thousands of combinations.

When players like Hamman, Meckstroth, and Chelma each play the same trump suit differently, it illustrates that perfect suit combination play is not a critical factor in winning bridge. The second best play usually gets the job done. Your bridge goals should not include perfection - that is impractical. They should be to avoid completely ridiculous plays and to be aware of some of the "non-intuitive" plays. Studying suit combinations (either through tables or through formal analyses) can help you achieve these goals.

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