Join Bridge Winners
Computer Bridge: Playing a Deceptive Winner
(Page of 7)

I. Introduction

This article presents thoughts on how a computer-bridgeplayer, often called a "bridge robot" (and which I will call, "Robot"), might discern on defense (as Declarer's RHO, in our discussion) that winning a trick with an unnecessarily high card could induce Declarer to select a line that would fail on the actual layout.

Robot would come to this realization by contemplating (1) for Declarer, various holdings and the consequential single-dummy suit-play attempts available to the declaring side; and (2) how Robot's previous play might influence the Declarer-perceived likelihood of success of these various suit-play attempts. This will be carried out by the following steps (which the reader might wish to skip on first reading, being that they will be presented less tersely later):

  1. Generate hands for Declarer that are consistent with the inferences Robot has made thus far.
  2. For each hand generated in step 1, enumerate the sensible ways* for Robot to play to the current trick and if applicable, to lead to the next trick.
  3. For each play plan enumerated in step 2, identify the plausible layouts* of the most dangerous suit(s) from Declarer's single-dummy perspective.
  4. For each dangerous-suit layout identified in step 3, identify the line of play that from Declarer's single-dummy perspective gives the best chance of making the contract, and then determine whether it would succeed on the actual layout.
  5. Based on the possibilities generated in steps 1 through 4, determine what Robot should play to the current trick (and if applicable, lead to the next trick) in order to give the best chance of setting the contract owing to Declarer's choice of line.

 

Robot is assumed to have access to a catalog of suit combinations (discussed previously at https://bridgewinners.com/article/view/computer-bridge-inferences-from-the-play-to-a-trick/) that includes the plays and layouts that could satisfy a given trick-taking objective (in terms of a minimum number of winners established for the leading side or a maximum number of winners established for the non-leading side, for example).

(This article does not address how the above scheme might be incorporated into the overall card-play arsenal of a computer-bridgeplayer.)

* For this discussion, Robot is presumed able to "enumerate the sensible ways" and "identify the plausible layouts." Future articles might address how these skills could be implemented in a computer-bridgeplayer.

II. Step 1: Generating Hands for Declarer that Are Consistent with Robot's Inferences

We examine the thought process of Robot at its turn to play to Trick 2:

West
Dummy
AJ943
74
K6
9753
Robot
KQ106
KJ5
832
QJ4
South
W
N
E
S
1
P
1
P
2NT
P
3
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
Q
6
2
A
3
1
0
2
5
9
2

Step 1

Assuming that Robot allows for 1-point upgrades and downgrades of balanced hands by other players, then one hand for Declarer that would be consistent with the inferences available to Robot is

Declarer (?)
2x
AQ10xx
Axx
AKx

where "(?)" in South's name is meant to convey that the hand is constructed.

This hand will be the focus of the rest of the article, but in practice, other consistent hands for Declarer would also need to be generated and subject to analogous processing.

III. Step 2: Identifying Sensible Plays and Continuations for Robot

Below is the full layout implied by the hand chosen for Declarer in step 1:

West
5x
xxx
QJ10xx
xxx
North
AJ943
74
K6
9753
Robot
KQ106
KJ5
832
QJ4
Declarer (?)
2x
AQ10xx
Axx
AKx
W
N
E
S
1
P
1
P
2NT
P
3
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
Q
6
2
A
3
1
0
2
5
9
2

Step 2

Given the auction, the play thus far, and the possible Declarer hand generated in the previous section, Robot would have available the following sensible continuations:

  • Win with the T and lead the 3.
  • Win with the Q and lead the 3.
  • Win with the K and lead the 3.

We'll start with the first one.

IV. Step 3: Identifying Plausible Layouts of the Suit(s) Most Dangerous for Declarer's Possible Hands

This is the hypothetical single-dummy setting where Declarer holds the constructed hand from step 1, RHO wins Trick 2 with the T (from step 2), and the 3 is led to Trick 3 (also from step 2).

West
North
AJ943
74
K6
9753
East
Declarer (?)
2x
AQ10xx
Axx
AKx
W
N
E
S
1
P
1
P
2NT
P
3
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
Q
6
2
A
3
1
0
2
5
9
10
2
1
1
3
3

Step 3

From Declarer's perspective, one dangerous suit layout would be if LHO started with QJTxx and East started with x32. (In practice, Robot would consider others also.)

V. Step 4: Identifying Best Source(s) of Winners, Given Declarer's Possible Hand, Robot's Having Won the T at Trick 2, and a Hypothetical Dangerous Suit Layout

Below is the hypothetical single-dummy setting (where Declarer holds the constructed hand, RHO wins Trick 2 with the T, and the 3 is led to Trick 3) augmented by the hypothetical dangerous suit layout.

West
5
QJ10xx
North
AJ943
74
K6
9753
Robot
10
32x
Declarer (?)
2x
AQ10xx
Axx
AKx
W
N
E
S
1
P
1
P
2NT
P
3
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
Q
6
2
A
3
1
0
2
5
9
10
2
1
1
3
3

Step 4

The declaring side would have six top tricks and would need to establish three more winners to make the contract. The defenders would have established three diamonds, would have taken one spade winner, and would need one more winner for a set.

Robot now searches the catalog of card combinations for single-suit, single-dummy layouts that match the declaring side's holdings and could in principle yield the declaring side at least three winners without losing a trick in the suit(s). The catalog would indicate that with x opposite AJ43 and the defenders' still holding KQxx, establishing even one winner would necessarily entail losing a trick in the suit.

However, the catalog would also indicate that with 74 opposite AQTxx, it is possible to establish at least three tricks without losing a trick in the suit, provided that there are two entries for leading the suit and RHO holds KJx. The present hypothetical layout after winning the K at Trick 3 would provide the entries, and RHO's holding KJx would not conflict with inferences available to Declarer. Finally, Robot would calculate the percentage that the full layout would allow hearts to be brought in for at least three winners (not counting the A, which was a master to start with).

Robot's conclusion would be that if the T were won at Trick 2 and a diamond returned, Declarer's only chance would be to finesse RHO for both heart honors, which would succeed as the cards lie.

VI. How a Different Choice at Step 2 Can Influence Step 4: Identifying Best Source(s) of Winners Given Declarer's Possible Hand, Robot's Having Won the Q at Trick 2, and a Hypothetical Dangerous-suit Layout

Below is the hypothetical single-dummy setting where Declarer holds the constructed hand from step 1, RHO wins Trick 2 with the Q (which is a different choice at step 2), and the 3 is led to Trick 3, augmented by the same hypothetical dangerous-suit layout as in the previous instance of step 3.

West
5
QJ10xx
North
AJ943
74
K6
9753
Robot
Q
32x
Declarer (?)
2x
AQ10xx
Axx
AKx
W
N
E
S
1
P
1
P
2NT
P
3
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
Q
6
2
A
3
1
0
2
5
9
Q
2
1
1
3
3

The exercise in the previous section is now repeated for where Robot wins Trick 2 with the Q rather than the T.

Step 4 (based on a different choice at step 2)

Robot now searches the catalog of card combinations for single-suit, single-dummy layouts that match the declaring side's holdings and could in principle yield the declaring side at least three winners without losing a trick in the suit(s). The catalog would indicate that with x opposite AJ43, the defenders' still holding KTxx, and LHO holding Kx, three winners could be established without losing a trick. The above hypothetical layout would provide the entries, and LHO's holding KT would not conflict with inferences available to Declarer (although Kx would, being that the catalog would indicate that RHO should have won Trick 2 with the T if that card were held). Finally, Robot would calculate the percentage* that the full layout would allow spades to be brought in for three winners (not counting the A, which was a master to start with).

The catalog would also be consulted for prospects to establish three winners from the heart suit, as was discussed previously. Robot would calculate the percentage* that the full layout would allow hearts to be brought in for at least three winners (not counting the A, which was a master to start with).

Robot's conclusion would be that if Declarer held the hypothetical hand, the Q were won at Trick 2, RHO led a diamond to Trick 3, and Declarer were contemplating a 5=3 diamond break, attacking spades at Trick 4 should appear at minimum quite reasonable to Declarer.

* How Robot would calculate such percentages is beyond the scope of this article.

VII. Robot's Tentative Conclusion about What to Do at Tricks 2 and 3

The previous sections indicate that if South were dealt x2 AQTxx Axx AKx and was contemplating a 5=3 diamond split, then Robot's winning the Q at Trick 2 and continuing diamonds is far more likely to induce Declarer to take the losing line of continuing spades than if Robot were to win the T at Trick 2 and continue diamonds.

At the table, this analysis would need to be extended to cover winning the K at Trick 2 and continuing diamonds, as well as other combinations of plausible hands for Declarer and plausible (from Declarer's perspective) breaks in the defenders' diamonds. Once that was done, Robot could compare the overall merit of various Trick 2 plays and continuation and select the best one.

2 Comments
Getting Comments... loading...
.

Bottom Home Top