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Suit Combinations
getting the most from your cards

When you haven't been playing long, declaring a contract can be a confusing and scary experience. There are a lot of things to consider. To make it easier, you should probably start by looking at each suit individually—the total number of tricks you take is the sum of the number in each suit (counting ruffs as trump tricks). Therefore, the best way to start improving your play is to try to take more tricks in each suit.

Looked at like this, you will see four suit combinations to play. To simplify things, we start by assuming we can lead to each trick from whichever hand we want to, and then once we have looked at all the suits in this way we consider the more practical problems of how to deal with constraints like having to lead from the hand that won the previous trick [insert advert for Directors' revenge here – Ed].

How to play a suit combination:

When you look at a suit combination, you should consider:

  1. which cards might take your tricks
  2. the cards in the opponents' hands
  3. how these might be divided
  4. how you can take advantage of favourable positions
Example:
 S x x  [W E]  S A Q 
This is a fairly simple example that you have probably seen before. There are nine outstanding cards. Your only hopes of winning tricks are the ace and the queen. The ace will always win a trick. Therefore, the only card that matters is the king. You need to make sure it isn't played on your queen. Obviously if you play the queen, the opponent with the king will play it if he is still to play in this trick. To avoid his doing this, there are two things you can try:
  1. Play the ace and hope that he is forced to play the king under it, when your queen will take the next trick.
  2. Try to play the queen at some stage in the trick after the person with the king has already played (a small card). To do this you usually lead from the hand without the queen and then play the queen if second hand doesn't play the king.
Which of these should you do? Well, sometimes one will work, and sometimes the other will work. There may be clues to help you decide, but these will be covered in a later article. For the moment we assume that you can only see the cards in the chosen suit, and you haven't heard the bidding, so you have no idea which will work. In this case, all you can do is go for the play that is more likely to work. To do this, you need to be able to estimate the chance of success in each case. This is easily done as follows:
  1. Work out which hands the line succeeds against.
  2. Estimate how likely these hands are.
For (2), there is a simple way of getting a good estimate. There are some number n cards outstanding in the suit. Each card can be in either hand, so there are 2n possible layouts. These are mostly approximately equally likely, so just count how many of the 2n layouts your line succeeds against.

In our example line (a) succeeds whenever the king is singleton. This is just two hands (singleton in the North hand and singleton in the South hand). Meanwhile, line (b) succeeds when the king is in the North hand. This occurs in 28 of the layouts (once the king is placed in the North hand the remaining 8 cards can be distrbuted in any way between the two hands). Line (b) (called a finesse) is therefore significantly better than line (a).

Now lets look at a more complicated example:
 H K J T 9 x  [W E]  H A x x 
There are now many lines:
  1. Cash the ace and king and hope the queen falls.
  2. Finesse the ten (then the jack).
  3. Cash the ace then finesse the ten (then finesse the jack).
  4. Run the jack (then the ten)
  5. Cash the king then run the jack (i.e. lead it and play low from East if North plays low)
After some thought we see that the situations in which these lines work are as follows:
  1. Queen doubleton in either hand: 8 out of 32 possibilities
  2. Queen in the South hand: 16 out of 32 possibilities ... except that if South has all five outstanding cards his queen will beat the nine on the last trick! so only 15 out of 32 possibilities.
  3. Queen in the South hand (and not to 5) or singleton queen in the North hand: 15 + 1 = 16 possibilities.
  4. Queen in the North hand and not to 5: 15 possibilities
  5. Singleton queen in the South hand or queen in the North hand and not to 4 or 5 (you can now only finesse once): 12 possibilities
Thus we see that the best line is line (3) which offers approximately a 50% chance of taking all 5 tricks.

Safety plays

In the previous two examples, there were only two possible numbers of tricks we could sensibly win, so we simply needed to work out which line gives us the best chance of taking the larger number. However, in real-life situations the number of tricks we take may vary by a lot, and the best chance of taking one number of tricks may be a different line from the best chance of taking another number of tricks. Consider the following example:
 D x x x x  [W E]  D A Q x x x 
The only way to take all 5 tricks is to find a doubleton king onside (finessing the queen on the first round). However, if 4 tricks in this suit are sufficient to make your contract, the best chance of taking these is to win the ace on the first round, then lead a low one towards the queen. This is an example of a safety play, where you reduce your expected number of tricks in order to minimise the chance of losing too many (it's like buying insurance—you are paying with your overtrick to protect yourself against something really bad [Toby is assuming IMPs or rubber bridge, where making your contract is all-important – Ed]). What this means is that whenever you are looking at a suit combination you should ask yourself "how many tricks do I need to win in this suit?". If the answer is less than the number of tricks you might be able to win, you should perhaps look for a safety play.

Here are some examples of suit combinations where safety plays can be used—see if you can find them:
 C x x x    [W E]  C A K J x   (3 tricks needed)
 S K 9       [W E]  S A J 7 x   (3 tricks needed)
 H A 9 x x  [W E]  H K J x x  (3 tricks needed)


When you've decided how to play, click here for the answers.

In the next article, I'll explain what to do once you have decided how many tricks you have in each suit.