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Computer Bridge: Opening Lead vs. Notrump
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I. Introduction

This article presents thoughts on how a computer-bridgeplayer, often called a "bridge robot" (and which I will call, "Robot"), could select an opening lead against a notrump contract using a decision process that would enable Robot's partner to draw inferences from what Robot failed to lead.

Such a decision process might need to consider the following:

  • Whether Robot holds enough winners to cash out for a set
  • The likely extent of trick sources for the declaring side
  • Whether the defenders' assets seem to be concentrated in one hand
  • Which of the hidden hands likely holds length in a given suit (which we define as at least four pieces)
  • Whether Partner has made an explicitly lead-directing call
  • Robot's holding in each suit

Robot would then access an opening-leads catalog that would provide the relative merit of Robot's various holdings for opening lead, taking into account all of the above.

The assumed form of scoring is IMPs.

II. Determining the Likely Extent of Trick Sources for the Declaring Side

If Robot does not hold enough winners to cash out for a set. Robot would use the auction and its holdings to determine the likely extent of trick sources for the declaring side. This would be one of the following:

  • "Lush"—the auction and Robot's holdings imply copious running tricks for the declaring side
  • "Barren"—both opponents' hands are narrowly defined, and suits are breaking poorly for Declarer
  • "Fertile"—the declaring side, given time, can probably establish enough winners

Here are working criteria for "lush":

  • The Declaring side has shown a suit (or suits) whose length (or combined length) is not lower than two fewer than the contracted number of tricks,
  • In this suit (or each of these suits), the declaring side is inferred to hold the top three honors, and
  • Robot lacks a stopper in it (or them).

Here are working criteria for "barren":

  • The strength of each opponent is within a two-point range,
  • Neither has shown a six-card suit,
  • Robot has HH-fourth or better behind Declarer's inferred 4+ card suit(s),
  • Robot has stiff or void in front of Dummy's inferred five-card suit(s) (if any), and
  • Robot has doubleton or shorter in front of Dummy's inferred four-card suit(s).

"Lush" would suggest that the opening leader attack, preferably by cashing tricks or leading from honor sequences. "Barren" would suggest that the opening leader try to avoid losing a trick that Declarer might not otherwise earn.

If the criteria for neither "lush" nor "barren" are met, then the deal would be presumed "fertile" for the declaring side.

III. Considering Whether the Defenders' Assets Are Likely Concentrated in One Hand

If the deal is deemed "fertile," then Robot would need to consider whether the defenders' assets seem to be concentrated in one hand. (If the deal qualifies as "lush" or "barren," that would seem to fix the defense's strategy irrespective of how the defenders' strength is distributed.) This would be done using the declaring side's strength range and would yield one of the following:

  • "Bulk"—Robot holds all but possibly a couple of the defenders' HCP
  • "Broke"—Robot holds at most 2 HCP
  • "Shared"—Something between these two extremes

IV. Considering Which Player(s) Has Implied Length in a Given Suit

Assuming that Robot was drawing inferences during the auction, it will have determined which of the other players (if any) is inferred to hold length in a given suit. If we disregard the distinction between not being inferred to hold length and denying holding length, then there are eight possibilities as to which of the hidden hands holds length:

  • No one (which isn't saying that a given player doesn't necessarily hold length)
  • Partner only
  • Dummy only
  • Declarer only
  • Partner and Dummy
  • Partner and Declarer
  • Dummy and Declarer
  • Partner, Dummy, and Declarer

V. Considering Whether Partner Has Called for a Given Suit to Be Led

Partner's calling for a given suit to be led would have to be explicit, such as a lead-directing double.

VI. Organizing a Catalog of Opening Leads versus Notrump

Robot's holding in a suit would be the last piece of information needed to find a unique match in the opening-leads catalog.

The following summarizes the search criteria:

  • Trick-source availability / defense-strength concentration (if applicable), yielding five possibilties: lush, barren, fertile/bulk, fertile/broke, fertile/shared
  • Whether Dummy is inferred to hold length in the suit
  • Whether Partner is inferred to hold length in the suit
  • Whether Declarer is inferred to hold length in the suit
  • Whether Partner has called for the suit to be led
  • A particular suit holding for the opening leader

The matching item would have a score (say, from 1 to 99), where the higher the number, the better the chance that the lead would result in defeating the contract. If the highest score is shared among two or more holdings in Robot's hand, a tiebreak would be needed. (A tiebreak regimen could start with major over minor.)

VII. Sample Robot Hand and Auction

Here's an illustration of the above-presented lead-selection method.

West (Robot)
A87
1094
KJ4
J862
W
N
E
S
1
P
1
P
1
P
1NT
P
3NT
P
P
P

Here's how Robot would apply the methods described.

1. Robot would recognize that it lacks the winners to set the contract immediately.

2. Based on the auction and Robot's HCP, this deal would be assessed as fertile/shared.

3. Robot would use the following to find the match in the opening-lead catalog for spades:

3a. Deal is fertile/shared

3b. Dummy is inferred to hold length in spades

3c. Partner isn't inferred to hold length in spades

3d. Declarer is inferred not to hold length in spades (which is treated as "isn't inferred...")

3e. Partner has not called for spades to be led

3f. Robot's spade holding is Axx

4. The match in the opening-lead catalog for the criteria in #3 carries a score of 21. (This score was picked arbitrarily and is not based on analysis.)

5. Robot would apply the equivalent of step 3 to hearts.

6. Robot would apply the criteria in #5 to search the opening-lead catalog.

7. Robot would apply the equivalent of step 3 to diamonds.

8. Robot would apply the criteria in #7 to search the opening-lead catalog.

9. Robot would apply the equivalent of step 3 to clubs.

10. Robot would apply the criteria in #9 to search the opening-lead catalog.

11. Robot would compare the scores obtained for all suits, and it would lead the highest-scoring.

VIII. Open Questions

Here are some open questions regarding an opening-lead catalog.

  1. Is there a reasonable way for the scores taken from the opening-lead catalog to be adjusted so as to account for matchpoints or other forms of scoring besides IMPs?
  2. If at least two suits share the highest score from the opening-leads catalog, are definitive tiebreaks necessary, or should Robot choose one at random if the tiebreaking does not yield a clear favorite?
  3. Could the opening-lead catalog be abbreviated by identifying circumstances/holdings from which one would never lead? Would it be worth the effort?
  4. Should a given player's "expected" length in a suit be accounted for?
  5. How should the X's in the opening-lead catalog be worked out?

IX. Sources

The hand and auction on page 7 are from The Bridge World, April 2007, Master Solvers' Club Problem H (rotated).

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