Join Bridge Winners
Computer Bridge: Opening-lead Inferences versus NT II
(Page of 19)

(These "Computer Bridge" articles present techniques that might enable a computer-bridgeplayer to emulate certain qualities of human players, such as drawing inferences from actions taken or not taken, or imagining how a layout might be perceived by another player.)

I. Introduction

This article's predecessor, "Computer Bridge: Opening-lead Inferences versus NT" (https://bridgewinners.com/article/view/computer-bridge-opening-lead-inferences-versus-nt/), described how a computer-bridgeplayer (often called a "bridge robot," and which I have been calling, "Robot") in third seat at Trick 1 might identify layouts that meet each of these criteria:

  • The opening leader's hand is consistent with that player's auction.
  • None of Partner's other suits would have presented a more desirable opening lead than the one actually made.
  • Declarer's holding would be consistent with that player's auction.
  • Declarer's holding in the opening-led suit would be consistent with Dummy's play to Trick 1.

The present article extends the deal given in the earlier one, by enumerating hand types for Partner whose implied layouts would meet the above criteria. Future articles would address how Robot might use this set of hand types to assess the defenders' prospects and decide on a play to Trick 1.

II. Terminology

Some of these Computer Bridge articles use the following homegrown terms:

  • 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
  • Meldoid—set of two or more equals in a given suit in a given hand, or a single card in a given hand that has no equals in that suit in that hand

III. Partner's Single-suit Holdings that Are Consistent with the Opening Lead

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

This article's predecessor noted that the following spade holdings for Partner could be constructed from cards held neither by Dummy nor Robot and would be consistent with the opening lead and the defenders' agreement.

  • KJ94x, KJx4x, K1094x, K10x4x, K9x4x, J10x4x, J9x4x, 109x4
  • KJ94, KJx4, K10x4, K9x4, J10x4, J9x4, 109x4
  • KJ4, K104, K94, Kx4, J94, Jx4, 10x4
  • doubleton 4x
  • singleton 4

(This pair's agreement is assumed to call for leading the jack from KJ10x(x) and the ten from K109x; hence these holdings are omitted.)

We will assume that for a given length and set of court card(s)* in the suit, Robot will at first exclude all holdings except the strongest one, up to and including the suit's third-highest card. The rationale is that if even a hand with the highest available spot(s) wouldn't set the contract, time will have been saved by Robot's not having examined hands containing at least some weaker spots.**

Repeating the above list but with the "weaker" holdings in bold gives

  • KJ94x, KJx4x, K1094x, K10x4x, K9x4x, J10x4x, J9x4x, 109x4x
  • KJ94, KJx4, K10x4, K9x4, J10x4, J9x4, 109x4
  • KJ4, K104, K94, Kx4, J94, Jx4, 10x4
  • doubleton 4x
  • singleton 4

Omitting the bold holdings yields the following:

  • KJ94x, K1094x, J10x4x, 109x4x
  • KJ94, K10x4, J10x4, 109x4
  • KJ4, K104, J94, 10x4
  • doubleton 4x
  • singleton 4

---------------

* A, K, Q, or J.

** I'm deferring consideration of where the defenders' holdings' being weaker could increase the chance of a set, by giving Declarer a guess. This can be seen in (1) Partner has Q109 over Declarer's Kxx and under Dummy's AJx, versus (2) Partner has Q9x over Declarer's K10x and under Dummy's AJx.

IV. Opening-lead Priorities for the Given Auction

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

Assume that for this auction, the opening-leads catalog (see "Computer Bridge: Opening Lead vs. Notrump", https://bridgewinners.com/article/view/computer-bridge-opening-lead-vs-notrump/, Dec. 20, 2018) would reflect the following priorities, recommended by Richard Pavlicek at http://www.rpbridge.net/4g00.htm.

  1. Five-card or longer suit
  2. Safe honor sequence (which, based on Richard's examples, I understand to mean a holding headed by at least three equals, or a doubleton consisting of two equals, and I'll assume that either must contain at least one card higher than the nine and that AK-tight would be an exception)
  3. Four cards with neither ace nor king
  4. Worthless three cards
  5. Worthless doubleton
  6. Unsafe honor sequence
  7. Four cards with ace and/or king

 

Within a category, Richard suggests choosing a major suit over a minor suit.

To prioritize between two five-card suits or between two four-card suits with neither ace nor king, the opening-leads catalog is assumed to reflect the result of comparing the rank of each suit's highest card, the next-highest card if the highest cards are equal, etc. As soon as the corresponding cards differ, the suit with the higher card would take priority.

V. King-Jack-Nine-Four-X—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds KJ94x, that leaves room for West to hold 2 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 2 HCP as follows:

  • Q
  • J J
  • Q
  • Q

These honor combinations, combined with the constraints from the auction (such as that Partner would have intervened with 5=6 in the majors) and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

5=5=3=0:

  • KJ94x Q109xx xxx void
  • KJ94x J109xx Jxx void
  • KJ94x 1098xx Qxx void

5=5=2=1:

  • KJ94x Q109xx xx x
  • KJ94x J109xx Jx x
  • KJ94x 1098xx Qx x
  • KJ94x 1098xx xx Q

5=5=1=2:

  • KJ94x Q109xx x xx
  • KJ94x J109xx J xx
  • KJ94x 1098xx Q xx
  • KJ94x 1098xx x Qx

5=5=0=3:

  • KJ94x Q109xx void xxx
  • KJ94x 1098xx void Qxx

5=4=3=1:

  • KJ94x Q109x xxx x
  • KJ94x J109x Jxx x
  • KJ94x 1098x Qxx x
  • KJ94x 1098x xxx Q

5=4=2=2:

  • KJ94x Q109x xx xx
  • KJ94x J109x Jx xx
  • KJ94x 1098x Qx xx
  • KJ94x 1098x xx Qx

5=4=1=3:

  • KJ94x Q109x x xxx
  • KJ94x J109x J xxx
  • KJ94x 1098x Q xxx
  • KJ94x 1098x x Qxx

VI. King-Ten-Nine-Four-X—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds K1094x, that leaves room for West to hold 3 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 3 HCP as follows:

  • Q J
  • Q J
  • J Q
  • J Q
  • Q J
  • J Q

These honor combinations, combined with the constraints from the auction (such as that Partner would have intervened with 5=6 in the majors) and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

5=5=3=0:

  • K1094x QJ10xx xxx void
  • K1094x Q109xx Jxx void
  • K1094x J109xx Qxx void
  • K1094x 1098xx QJx void

5=5=2=1:

  • K1094x QJ10xx xx x
  • K1094x Q109xx Jx x
  • K1094x J109xx Qx x
  • K1094x J109xx xx Q
  • K1094x 1098xx QJ x
  • K1094x 1098xx Jx Q

5=5=1=2:

  • K1094x QJ10xx x xx
  • K1094x Q109xx J xx
  • K1094x J109xx Q xx
  • K1094x J109xx x Qx
  • K1094x 1098xx J Qx

5=5=0=3:

  • K1094x QJ10xx void xxx
  • K1094x J109xx void Qxx

5=4=3=1:

  • K1094x QJ10x xxx x
  • K1094x Q109x Jxx x
  • K1094x J109x Qxx x
  • K1094x J109x xxx Q
  • K1094x 1098x QJx x
  • K1094x 1098x Jxx Q

5=4=2=2:

  • K1094x QJ10x xx xx
  • K1094x Q109x Jx xx
  • K1094x J109x Qx xx
  • K1094x J109x xx Qx
  • K1094x 1098x QJ xx
  • K1094x 1098x Jx Qx

5=4=1=3:

  • K1094x QJ10x x xxx
  • K1094x Q109x J xxx
  • K1094x J109x Q xxx
  • K1094x J109x x Qxx
  • K1094x 1098x J Qxx

VII. Jack-Ten-X-Four-X—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds J10x4x, that leaves room for West to hold 5 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 5 HCP as follows:

  • A J
  • A J
  • Q J Q
  • Q J Q
  • Q Q J
  • Q J Q
  • J Q Q
  • J A
  • Q J Q
  • J A

These honor combinations, combined with the constraints from the auction (such as that Partner would have intervened with 5=6 in the majors) and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

5=5=3=0:

None. (To reach 6 HCP requires at least 2 HCP in hearts, but this would make Partner's hearts "stronger" than Partner's spades and therefore a higher-priority lead.)

5=5=2=1:

  • J10x4x J10xxx Qx Q
  • J10x4x J10xxx xx A
  • J10x4x 109xxx QJ Q
  • J10x4x 109xxx Jx A

5=5=1=2:

  • J10x4x J10xxx Q Qx
  • J10x4x J10xxx x Ax
  • J10x4x 109xxx J Ax

5=5=0=3:

  • J10x4x J10xxx void Axx

5=4=3=1:

  • J10x4x AJ10x xxx x
  • J10x4x A109x Jxx x
  • J10x4x QJ10x Qxx x
  • J10x4x QJ10x xxx Q
  • J10x4x Q109x QJx x
  • J10x4x Q109x Jxx Q
  • J10x4x J109x Qxx Q
  • J10x4x J109x xxx A
  • J10x4x 1098x QJx Q
  • J10x4x 1098x Jxx A

5=4=2=2:

  • J10x4x AJ10x xx xx
  • J10x4x A109x Jx xx
  • J10x4x QJ10x Qx xx
  • J10x4x QJ10x xx Qx
  • J10x4x Q109x QJ xx
  • J10x4x Q109x Jx Qx
  • J10x4x J109x Qx Qx
  • J10x4x J109x xx Ax
  • J10x4x 1098x QJ Qx
  • J10x4x 1098x Jx Ax

5=4=1=3:

  • J10x4x AJ10x x xxx
  • J10x4x A109x J xxx
  • J10x4x QJ10x Q xxx
  • J10x4x QJ10x x Qxx
  • J10x4x Q109x J Qxx
  • J10x4x J109x Q Qxx
  • J10x4x J109x x Axx
  • J10x4x 1098x J Axx

VIII. Ten-Nine-X-Four-X—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds 109x4x, that leaves room for West to hold 6 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 6 HCP as follows:

  • A Q
  • A J J
  • A Q
  • A Q
  • Q J Q J
  • Q J J Q
  • Q Q Q
  • Q A
  • J Q J Q
  • J J A
  • Q A
  • A Q

These honor combinations, combined with the constraints from the auction (such as that Partner would have intervened with 5=6 in the majors) and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

5=5=3=0:

None. (To reach 6 HCP requires at least 3 HCP in hearts, but this would make Partner's hearts "stronger" than Partner's spades and therefore a higher-priority lead.)

5=5=2=1:

  • 109x4x 109xxx Qx A

5=5=1=2:

  • 109x4x 109xxx Q Ax
  • 109x4x 109xxx x AQ

5=5=0=3:

  • 109x4x 109xxx void AQx

5=4=3=1:

  • 109x4x AQ10x xxx x
  • 109x4x AJ10x Jxx x
  • 109x4x A109x Qxx x
  • 109x4x A109x xxx Q
  • 109x4x QJ10x QJx x
  • 109x4x QJ10x Jxx Q
  • 109x4x Q109x Qxx Q
  • 109x4x Q109x xxx A
  • 109x4x J109x QJx Q
  • 109x4x J109x Jxx A
  • 109x4x 1098x Qxx A

5=4=2=2:

  • 109x4x AQ10x xx xx
  • 109x4x AJ10x Jx xx
  • 109x4x A109x Qx xx
  • 109x4x A109x xx Qx
  • 109x4x QJ10x QJ xx
  • 109x4x QJ10x Jx Qx
  • 109x4x Q109x Qx Qx
  • 109x4x Q109x xx Ax
  • 109x4x J109x QJ Qx
  • 109x4x J109x Jx Ax
  • 109x4x 1098x Qx Ax
  • 109x4x 1098x xx AQ

5=4=1=3:

  • 109x4x AQ10x x xxx
  • 109x4x AJ10x J xxx
  • 109x4x A109x Q xxx
  • 109x4x A109x x Qxx
  • 109x4x QJ10x J Qxx
  • 109x4x Q109x Q Qxx
  • 109x4x Q109x x Axx
  • 109x4x J109x J Axx
  • 109x4x 1098x Q Axx
  • 109x4x 1098x x AQx

IX. King-Jack-Nine-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds KJ94, that leaves room for West to hold 2 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 2 HCP as follows:

  • Q
  • J J
  • Q
  • Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

4=4=3=2:

None. (With Partner's having only 2 HCP outside of spades, hearts would be headed by at most the queen and therefore would take lead-priority over spades.)

4=4=2=3:

None. (Ditto.)

X. King-Ten-X-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds K10x4, that leaves room for West to hold 3 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 3 HCP as follows:

  • Q J
  • Q J
  • J Q
  • J Q
  • Q J
  • J Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

4=4=3=2:

None. (With Partner's having only 3 HCP outside of spades, hearts would be headed by at most the queen and therefore would take lead-priority over spades.)

4=4=2=3:

None. (Ditto.)

XI. Jack-Ten-X-Four—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds J10x4, that leaves room for West to hold 5 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 5 HCP as follows:

  • A J
  • A J
  • Q J Q
  • Q J Q
  • Q Q J
  • Q J Q
  • J Q Q
  • J A
  • Q J Q
  • J A

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand:

4=4=3=2:

  • J10x4 AJ10x xxx xx
  • J10x4 A109x Jxx xx
  • J10x4 J10xx Qxx Qx
  • J10x4 J10xx xxx Ax
  • J10x4 109xx QJx Qx
  • J10x4 109xx Jxx Ax

4=4=2=3:

  • J10x4 AJ10x xx xxx
  • J10x4 A109x Jx xxx
  • J10x4 J10xx Qx Qxx
  • J10x4 J10xx xx Axx
  • J10x4 109xx QJ Qxx
  • J10x4 109xx Jx Axx

XII. Ten-Nine-X-Four—Strongest Holdings for Each Honor Allocation

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds 109x4, that leaves room for West to hold 6 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 6 HCP as follows:

  • A Q
  • A J J
  • A Q
  • A Q
  • Q J Q J
  • Q J J Q
  • Q Q Q
  • Q A
  • J Q J Q
  • J J A
  • Q A
  • A Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

4=4=3=2:

  • 109x4 AQ10x xxx xx
  • 109x4 AJ10x Jxx xx
  • 109x4 A109x Qxx xx
  • 109x4 A109x xxx Qx
  • 109x4 109xx Qxx Ax
  • 109x4 109xx xxx AQ

4=4=2=3:

  • 109x4 AQ10x xx xxx
  • 109x4 AJ10x Jx xxx
  • 109x4 A109x Qx xxx
  • 109x4 A109x xx Qxx
  • 109x4 109xx Qx Axx
  • 109x4 109xx xx AQx

XIII. King-Jack-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds KJ4, that leaves room for West to hold 2 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 2 HCP as follows:

  • Q
  • J J
  • Q
  • Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Three cards headed by two non-touching honors doesn't make Richard's list and therefore has lower lead priority than does any four-card holding.)

XIV. King-Ten-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds K104, that leaves room for West to hold 3 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 3 HCP as follows:

  • Q J
  • Q J
  • J Q
  • J Q
  • Q J
  • J Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Three cards headed by two non-touching honors doesn't make Richard's list and therefore has lower lead priority than does any four-card holding.)

XV. Jack-Nine-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds J94, that leaves room for West to hold 5 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 5 HCP as follows:

  • A J
  • A J
  • Q J Q
  • Q J Q
  • Q Q J
  • Q J Q
  • J Q Q
  • J A
  • Q J Q
  • J A

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Three cards headed by an honor doesn't make Richard's list and therefore has lower lead priority than does any four-card holding.)

XVI. Ten-X-Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds 10x4, that leaves room for West to hold 6 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 6 HCP as follows:

  • A Q
  • A J J
  • A Q
  • A Q
  • Q J Q J
  • Q J J Q
  • Q Q Q
  • Q A
  • J Q J Q
  • J J A
  • Q A
  • A Q

These honor combinations, combined with the constraints from the auction and play thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Three cards headed by an honor doesn't make Richard's list and therefore has lower lead priority than does any four-card holding.)

XVII. Doubleton Four-X—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds doubleton 4x, that leaves room for West to hold 6 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 6 HCP as follows:

  • A Q
  • A J J
  • A Q
  • A Q
  • Q J Q J
  • Q J J Q
  • Q Q Q
  • Q A
  • J Q J Q
  • J J A
  • Q A
  • A Q

These honor combinations, combined with the constraints from the auction and play (such as that Partner would have instead led from a suit of five cards or longer) thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Partner would have at most three cards in each minor and therefore at least five hearts, which would give that suit lead-priority.)

XVIII. Singleton Four—No Consistent Layouts

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

If West holds singleton 4, that leaves room for West to hold 6 HCP outside of spades if Declarer is at the low end of 14–16 HCP.

The available honors outside of spades (AQJ, QJ, AQ) can be combined for 6 HCP as follows:

  • A Q
  • A J J
  • A Q
  • A Q
  • Q J Q J
  • Q J J Q
  • Q Q Q
  • Q A
  • J Q J Q
  • J J A
  • Q A
  • A Q

These honor combinations, combined with the constraints from the auction and play (such as that Partner would have instead led from a suit of five cards or longer) thus far, would yield the following strongest holdings for Partner's various shapes that would be consistent with Declarer's having a balanced or semi-balanced hand.

None. (Partner would have at most three cards in each minor and therefore at least six hearts, which would give that suit lead-priority.)

XIX. Summary of Consistent Spade Holdings

West
Dummy
Q75
K5
AK1062
952
Robot
A82
42
987
KJ1073
South
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT South
NS: 0 EW: 0
4
5
1

The following spade holdings for Partner were found to be consistent with the auction and play up to Robot's turn:

  • KJ94x, K1094x, J10x4x, 109x4x
  • J10x4, 109x4

How Robot might apply this list of holdings and their accompanying consistent layouts identified in previous sections is yet to be addressed.

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