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Computer Bridge: The "More Dangerous" Opponent
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I. Introduction

In some situations where the defenders could set the contract once they regain possession, leading the suit that accomplishes this might appear safe to one defender but risky to the other. Declarer can attempt to exploit this by selecting a line of play in which if possession is lost before the contract is made, the defender in greater doubt would be on lead.

This article presents thoughts on how a computer-bridgeplayer (often called a "bridge robot," and which I have been calling, "Robot") could determine which defender this probably is.

II. Terminology

I have adapted from American football the following terms and assigned them bridge meanings:

  • Possession—one or more consecutive tricks in which the same side leads
  • Series—one or more consecutive tricks in which the same side leads a given suit

III. Single-suit Layout Where Either Opponent Could Cash out

Suppose that Robot is declaring 3N and that the first trick is as follows (where bold indicates cards played to this trick):

                      963 (Dummy)

5 (LHO)                                    J (RHO)

                      KQ (Declarer)

Assume that Robot has used the card-combination catalog to infer that RHO's play of the jack denies the ten, as discussed in "Computer Bridge: Inferences from the Play to a Trick" (https://bridgewinners.com/article/view/computer-bridge-inferences-from-the-play-to-a-trick/). Depending on the defenders' agreements, the following might be a plausible layout.

                      963 (Dummy)

ATx5x (LHO)                             Jxx (RHO)

                     KQ (Declarer)

The play to Trick 1 would leave

                       96 (Dummy)

ATxx (LHO)                               xx (RHO)

                        Q (Declarer)

As discussed in "Computer Bridge: Card Combinations in Notrump" (https://bridgewinners.com/article/view/computer-bridge-card-combinations-in-notrump/), the card-combination catalog would reflect the effective promotion of the honors appearing in this nine-card layout, yielding

                       xx (Dummy)

AQxx (LHO)                              xx (RHO)

                       K (Declarer)

Suppose that (1) to establish enough winners for the contract might entail giving up possession once, and (2) Declarer might be able to influence which defender would win that trick. How might Robot discern which opponent is the "more dangerous"?

IV. Single-dummy Dangerous-suit Layout as Viewed by West

Let's first suppose that West might gain the lead. (For the moment, continue assuming that West led from ATx5x.) From West's perspective, the outstanding cards in the suit are the Q and two x's, and the original holdings for Declarer that would be consistent with everyone's actions thus far are KQxx, KQx, Kxx, KQ, and Kx.

Declarer's starting with KQx would imply the following nine-card layout (after promotion):

                        xx (Dummy)

AQxx (LHO)                              x (RHO)

                        Kx (Declarer)

In pondering this possible layout, West could conclude that (1) West's leading the suit would give the opposition a winner that Declarer otherwise could not have created, and (2) East's leading the suit would allow West to take the ace and three tricks with original non-masters.

Robot could discern this by searching the card-combination catalog for this layout, which would tell Robot the result of various players' leading (for example, how many winners gained by the leading side, how many winners gained by the non-leading side, whether possession would be lost).

Robot would perform similar steps for Declarer's other holdings that would appear plausible to West (given in this page's opening paragraph). Robot would conclude that from West's perspective, (1) leading the ace would produce three winners if Declarer started with Kxx, KQ, or Kx; (2) the defenders could not immediately produce any winners if Declarer was dealt KQxx; and (3) the defenders could run the suit if East were to lead the second round and Declarer was dealt any feasible holding but KQxx.

Robot would perform similar analysis for other holdings consistent with West's opening lead.

V. Single-dummy Dangerous-suit Layout as Viewed by East

Let's now consider that East might gain the lead. (For the moment, continue assuming that East followed from Jxx.) From East's perspective, the original holdings for Declarer that would be consistent with everyone's actions thus far are AKx, KQx, KTx, Kxx, AK, KQ, or Kx. Robot could infer this through the defenders' opening-lead agreements.

In pondering the various layouts implied by these holdings for Declarer, East could conclude that East's leading the suit (1) would produce whatever winners the defenders were entitled to, and (2) would not produce for the declaring side any winners that it wasn't entitled to.

Robot could discern this by searching the card-combination catalog for the various layouts implied by Declarer's plausible holdings (as viewed by East). This would tell Robot the result of various players' leading. Robot would infer that East would perceive no risk in leading this suit. Robot would therefore conclude that surrendering possession to East would be hopeless.

Robot would perform similar analysis for other holdings consistent with East's play at Trick 1.

VI. Single-dummy Layout in Which There Is a More Dangerous Opponent

The following deal illustrates how Robot might apply this type of analysis.

West
North
963
873
KJ3
AQ104
East
South
KQ
AK5
765
KJ863
W
N
E
S
1NT
2
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
1

Assume that the opponents' bidding and carding agreements would allow Robot to interpret the opening lead as being from five cards headed by the ace. For each spade layout (using x's where feasible) that could accordingly be constructed from the defenders' cards, Robot would use the opening-lead catalog to identify holdings in other suits that would have appeared more attractive to West, as discussed in "Computer Bridge: Single-suit Plans in Notrump" (https://bridgewinners.com/article/view/computer-bridge-single-suit-plans-in-notrump/). Any more-attractive holdings found would be inferred as not dealt to West. (On this occasion, the search for more attractive holdings wouldn't yield any.)

Then, as discussed in "Computer Bridge: Single-suit Plans in Notrump II" (https://bridgewinners.com/article/view/computer-bridge-single-suit-plans-in-notrump-ii/), Robot would use the card-combination catalog to obtain single-suit plans and would use them to construct scenarios for building winners—one winner for the declaring side in this case. These scenarios would incorporate the opponents' plans for when they gain possession.

Given that West was inferred to have led from a five-carder headed by the ace, Robot would realize that whenever diamonds were led, the defenders could take the ace and cash out for a set. In desperation, Robot would apply the type of analysis discussed earlier in this article and conclude that East is the "more dangerous" opponent.

West
North
963
873
KJ3
AQ104
East
South
KQ
AK5
765
KJ863
W
N
E
S
1NT
2
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
3
J
K
3
1
0
1

Robot would revise the above calculations according to East's play at Trick 1 and its implications for what spade layouts can be ruled out. On this deal, Robot would infer that West led from ATx4x.

This would enable Robot to conclude that leading a diamond toward the king offers the best chance of creating a winner without allowing East, the more dangerous opponent, to gain possession.

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