home site map Bridge October 2005 email

# Best play in a suit – I

This is one of a series of analyses of the play of the hand that I did in rec.games.bridge newsgroup during the late 80’s (that would be the 1980’s, not the 1880’s.)

<!– PAGE TEXT GOES HERE –!>

### The original problem

Given J876 in dummy and AT32 in hand, what is the best line for 3 tricks in the suit. Assume that entries are no problem.

### Analysis

Probability of split of five cards:

```    3-2  156/230 = 67.8% (20 cases)
4-1   65/230 = 28.3% (10 cases)
5-0    9/230 =  3.9% ( 2 cases)
```
The best lines of play, as far as I can see are:

A: Lead low from the board to the T, and playing the A on the second round. This wins in the following cases:

3-2 splits: RHO has 954 KQ9 KQ5 KQ4 Q5 Q4 K5 K4 Q9 K9 KQ = 11 cases
4-1 splits: RHO has K Q KQ54 = 3 cases

pr = (11/20)*67.8% + (3/10)*28.3% = 45.8%

B: Lead the J on the first round. If covered, lead the 8 on the second round and finesse for the 9. If it is not covered, play to the T on the second round. This wins in the following cases:

3-2 splits: RHO has Q94 Q95 K94 K95 Q54 K54 KQ9 Q9 K9 KQ = 10 cases
4-1 splits: RHO has KQ54 KQ94 KQ95 = 3 cases
5-0 splits: RHO has KQ954

pr = (10/20)*67.8% + (3/10)*28.3% +(1/2)*3.9% = 44.3%

C: Lead the J on the first round. Finesse for the 9 on the second round regardless of whether the J is covered. This wins in the following cases:

3-2 splits: RHO has Q94 Q95 KQ9 Q9 K9 KQ = 8 cases
4-1 splits: RHO has KQ54 KQ95 KQ94 Q954 K954 = 5 cases
5-0 splits: RHO has KQ954 = 1 case

pr = (8/20)*67.8% + (5/10)*28.3% + (1/2)*3.9% = 43.2%

Note: If RHO has Q54 or K54 and covers the J line C gains 6.8%. In addition, if it is known that RHO always covers in this situation, failure to cover is a cue to play the A on the second round. This picks up an additional 3.4% in lines B and C.
So Line A by a whisker (1.5%). However that is not the whole story. Quite often it happens that we can get information about the distribution in a suit by playing other suits, so that we know which opponent is more likely to have length in the suit in question. As it happens line A works best if RHO is short and lines B and C work best if RHO is long. We have these percentages (calculated by eliminating cases)
```     Line:        A     B     C
RHO long:  32.8% 68.3% 66.1%
LHO long:  58.8% 20.3% 20.3%
```
So: If no information about the suit can be obtained, play line A. If it is determined that LHO is probably long, play line A. If it is determined that RHO is probably long, play line B. If RHO can be counted for 4 or more cards play line C. In practice, one should be able to do better than 50%.

One final consideration is the issue of errors and deception. On the lead of the J, covering from Q54 is considered to be an error. I.e. suppose you sit over the dummy with Q54 and J is lead from J876. Do you cover? Well, no. If declarer has AT932 and partner has K, partner is not going to be too happy. In the given hand covering is not pleasant. Suppose, however, that declarer has AT3 or K32; now failure to cover gives up a trick. Bridge is not a simple game.