Join Bridge Winners
Computer Bridge: Counting Winners versus NT II
(Page of 8)

(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

The article "Computer Bridge: Counting Winners versus NT" (https://bridgewinners.com/article/view/computer-bridge-counting-winners-versus-nt/, March 21, 2019) discussed how a defending computer-bridgeplayer (often called a "bridge robot," and which I have been calling, "Robot") might count its side's possible winners against notrump and select a play accordingly.

Part of that piece addressed how to identify layouts where the declaring side would have enough sure winners for the contract. This article goes further by identifying layouts in which (1) the declaring side would already possess or could establish on power on any distribution of the defenders' cards, enough cashable winners to make the contract in its first possession; and (2) the defense, in its first possession, could neither set the contract nor strand the contract-making winner. Robot as defender would dismiss such layouts as "hopeless."

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

I have adopted from other bridge communities the following term:

  • Court Card—ace, king, queen, or jack

III. Hand Types for Partner that Are Consistent with the Auction, the Play, and the Partnerships' Agreements

The article "Computer Bridge: Opening-lead Inferences versus NT II" (https://bridgewinners.com/article/view/computer-bridge-opening-lead-inferences-versus-nt-ii/, May 20, 2019) considered the following deal:

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

Robot had inferred that the following spade holdings for Partner would be consistent with the auction and the play up to Robot's turn and would incorporate the highest available spots up to the third-highest card in the suit (based on the rationale that if Declarer would have enough winners even if denied these spots, Robot would be justified in dismissing all other layouts involving the same distribution and allocation of court cards):

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

Robot had also inferred the following hand types for Partner (a long list, sorry):

KJ94x

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

K1094x

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

J10x4x

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

109x4x

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

J10x4

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

109x4

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

IV. Identifying Layouts Where the Defenders Cannot Prevent the Contract's Being Fulfilled in the Declaring Side's First Possession through Masters and Guaranteed Promotion of Long Cards

Such layouts are those that meet all of these criteria:

  1. If East ducks Trick 1, the declaring side would already possess or could generate on power on any distribution of the defenders' cards, enough winners to fulfill the contract and be able to take them in its first possession.
  2. If East wins Trick 1, the card-combination catalog provides no possibility for the defenders to set the contract in its first possession (even by giving Declarer a guess).
  3. If East wins Trick 1, no return would prevent Declarer from (a) generating on power on any distribution of the defenders' cards, enough winners to fulfill the contract; and (b) taking them in the declaring side's first possession.

 

The next three sections will determine the layouts meeting these criteria, by identifying the layouts for which at least one criterion isn't satisfied. Layouts failing at least one criterion would remain on Robot's radar. Layouts meeting all three criteria would be dismissed by Robot at "hopeless."

V. Identification of Layouts that Fail Criterion #1 (East's Ducking Trick 1 Would Give the Declaring Side at Least Nine Cashable Winners)

Robot would now examine each of the layouts from page 3 for whether they would give Declarer nine cashable winners if East ducked at Trick 1.

In the following list of holdings for West (with Declarer's implied holding in parentheses), regular font indicates that the implied layout wouldn't give Declarer at least nine cashable winners (whether because Declarer would lack or couldn't generate enough winners, or because not enough of those winners would be cashable). Italic font means that the layout would provide Declarer at least nine cashable winners and therefore would need to be tested against the criterion on the next page.

For example, the first layout below (West: KJ94x Q109xx xxx void, South: 10x AJxx QJ AQxxx) meets the first criterion for "hopeless" because East's ducking Trick 1 would give the declaring side nine winners (one spade, two hearts, five diamonds, one club) irrespective of the defenders' distribution. The second layout below (West: KJ94x J109xx Jxx void, South: 10x AQxx Qx AQxxx) would be considered as not "hopeless," because single-dummy, Declarer could see only eight certain winners (one spade, three hearts, three diamonds, one club) and no way to establish a ninth winner in the declaring side's first possession that would succeed in all legal layouts. Although in the latter layout, Declarer should still succeed because cashing three diamonds and keeping the club finesse in reserve dominates taking the club finesse immediately, this reasoning might not apply if Declarer's spade holding provided a second stopper (for example, if Declarer were dealt K9). Robot's consideration of such factors in Declarer's planning would be complex and therefore is deferred to a future article.

KJ94x

5=5=3=0:

  • KJ94x Q109xx xxx void (10x AJxx QJ AQxxx)
  • KJ94x J109xx Jxx void (10x AQxx Qx AQxxx)
  • KJ94x 1098xx Qxx void (10x AQJx Jx AQxxx)

5=5=2=1:

  • KJ94x Q109xx xx x (10x AJxx QJx AQxx)
  • KJ94x J109xx Jx x (10x AQxx Qxx AQxx)
  • KJ94x 1098xx Qx x (10x AQJx Jxx AQxx)
  • KJ94x 1098xx xx Q (10x AQJx QJx Axxx)

5=5=1=2:

  • KJ94x Q109xx x xx (10x AJxx QJxx AQx)
  • KJ94x J109xx J xx (10x AQxx Qxxx AQx)
  • KJ94x 1098xx Q xx (10x AQJx Jxxx AQx)
  • KJ94x 1098xx x Qx (10x AQJx QJxx Axx)

5=5=0=3:

  • KJ94x Q109xx void xxx (10x AJxx QJxxx AQ)
  • KJ94x 1098xx void Qxx (10x AQJx QJxxx Ax)

5=4=3=1:

  • KJ94x Q109x xxx x (10x AJxxx QJ AQxx)
  • KJ94x J109x Jxx x (10x AQxxx Qx AQxx)
  • KJ94x 1098x Qxx x (10x AQJxx Jx AQxx)
  • KJ94x 1098x xxx Q (10x AQJxx QJ Axxx)

5=4=2=2:

  • KJ94x Q109x xx xx (10x AJxxx QJx AQx)
  • KJ94x J109x Jx xx (10x AQxxx Qxx AQx)
  • KJ94x 1098x Qx xx (10x AQJxx Jxx AQx)
  • KJ94x 1098x xx Qx (10x AQJxx QJx Axx)

5=4=1=3:

  • KJ94x Q109x x xxx (10x AJxxx QJxx AQ)
  • KJ94x J109x J xxx (10x AQxxx Qxxx AQ)
  • KJ94x 1098x Q xxx (10x AQJxx Jxxx AQ)
  • KJ94x 1098x x Qxx (10x AQJxx QJxx Ax)

K1094x

5=5=3=0:

  • K1094x QJ10xx xxx void (Jx A9xx QJ AQxxx)
  • K1094x Q109xx Jxx void (Jx AJxx Qx AQxxx)
  • K1094x J109xx Qxx void (Jx AQxx Jx AQxxx)
  • K1094x 1098xx QJx void (Jx AQJx xx AQxxx)

5=5=2=1:

  • K1094x QJ10xx xx x (Jx A9xx QJx AQxx)
  • K1094x Q109xx Jx x (Jx AJxx Qxx AQxx)
  • K1094x J109xx Qx x (Jx AQxx Jxx AQxx)
  • K1094x J109xx xx Q (Jx AQxx QJx Axxx)
  • K1094x 1098xx QJ x (Jx AQJx xxx AQxx)
  • K1094x 1098xx Jx Q (Jx AQJx Qxx Axxx)

5=5=1=2:

  • K1094x QJ10xx x xx (Jx A9xx QJxx AQx)
  • K1094x Q109xx J xx (Jx AJxx Qxxx AQx)
  • K1094x J109xx Q xx (Jx AQxx Jxxx AQx)
  • K1094x J109xx x Qx (Jx AQxx QJxx Axx)
  • K1094x 1098xx J Qx (Jx AQJx Qxxx Axx)

5=5=0=3:

  • K1094x QJ10xx void xxx (Jx A9xx QJxxx AQ)
  • K1094x J109xx void Qxx (Jx AQxx QJxxx Ax)

5=4=3=1:

  • K1094x QJ10x xxx x (Jx A9xxx QJ AQxx)
  • K1094x Q109x Jxx x (Jx AJxxx Qx AQxx)
  • K1094x J109x Qxx x (Jx AQxxx Jx AQxx)
  • K1094x J109x xxx Q (Jx AQxxx QJ Axxx)
  • K1094x 1098x QJx x (Jx AQJxx xx AQxx)
  • K1094x 1098x Jxx Q (Jx AQJxx Qx Axxx)

5=4=2=2:

  • K1094x QJ10x xx xx (Jx A9xxx QJx AQx)
  • K1094x Q109x Jx xx (Jx AJxxx Qxx AQx)
  • K1094x J109x Qx xx (Jx AQxxx Jxx AQx)
  • K1094x J109x xx Qx (Jx AQxxx QJx Axx)
  • K1094x 1098x QJ xx (Jx AQJxx xxx AQx)
  • K1094x 1098x Jx Qx (Jx AQJxx Qxx Axx)

5=4=1=3:

  • K1094x QJ10x x xxx (Jx A9xxx QJxx AQ)
  • K1094x Q109x J xxx (Jx AJxxx Qxxx AQ)
  • K1094x J109x Q xxx (Jx AQxxx Jxxx AQ)
  • K1094x J109x x Qxx (Jx AQxxx QJxx Ax)
  • K1094x 1098x J Qxx (Jx AQJxx Qxxx Ax)

J10x4x

5=5=2=1:

  • J10x4x J10xxx Qx Q (K9 AQ9x Jxx Axxx)
  • J10x4x J10xxx xx A (K9 AQ9x QJx Qxxx)
  • J10x4x 109xxx QJ Q (K9 AQJx xxx Axxx)
  • J10x4x 109xxx Jx A (K9 AQJx Qxx Qxxx)

5=5=1=2:

  • J10x4x J10xxx Q Qx (K9 AQ9x Jxxx Axx)
  • J10x4x J10xxx x Ax (K9 AQ9x QJxx Qxx)
  • J10x4x 109xxx J Ax (K9 AQJx Qxxx Qxx)

5=5=0=3:

  • J10x4x J10xxx void Axx (K9 AQ9x QJxxx Qx)

5=4=3=1:

  • J10x4x AJ10x xxx x (K9 Q9xxx QJ AQxx)
  • J10x4x A109x Jxx x (K9 QJxxx Qx AQxx)
  • J10x4x QJ10x Qxx x (K9 A9xxx Jx AQxx)
  • J10x4x QJ10x xxx Q (K9 A9xxx QJ Axxx)
  • J10x4x Q109x QJx x (K9 AJxxx xx AQxx)
  • J10x4x Q109x Jxx Q (K9 AJxxx Qx Axxx)
  • J10x4x J109x Qxx Q (K9 AQxxx Jx Axxx)
  • J10x4x J109x xxx A (K9 AQxxx QJ Qxxx)
  • J10x4x 1098x QJx Q (K9 AQJxx xx Axxx)
  • J10x4x 1098x Jxx A (K9 AQJxx Qx Qxxx)

5=4=2=2:

  • J10x4x AJ10x xx xx (K9 Q9xxx QJx AQx)
  • J10x4x A109x Jx xx (K9 QJxxx Qxx AQx)
  • J10x4x QJ10x Qx xx (K9 A9xxx Jxx AQx)
  • J10x4x QJ10x xx Qx (K9 A9xxx QJx Axx)
  • J10x4x Q109x QJ xx (K9 AJxxx xxx AQx)
  • J10x4x Q109x Jx Qx (K9 AJxxx Qxx Axx)
  • J10x4x J109x Qx Qx (K9 AQxxx Jxx Axx)
  • J10x4x J109x xx Ax (K9 AQxxx QJx Qxx)
  • J10x4x 1098x QJ Qx (K9 AQJxx xxx Axx)
  • J10x4x 1098x Jx Ax (K9 AQJxx Qxx Qxx)

5=4=1=3:

  • J10x4x AJ10x x xxx (K9 Q9xxx QJxx AQ)
  • J10x4x A109x J xxx (K9 QJxxx Qxxx AQ)
  • J10x4x QJ10x Q xxx (K9 A9xxx Jxxx AQ)
  • J10x4x QJ10x x Qxx (K9 A9xxx QJxx Ax)
  • J10x4x Q109x J Qxx (K9 AJxxx QJxx Ax)
  • J10x4x J109x Q Qxx (K9 AQxxx Jxxx Ax)
  • J10x4x J109x x Axx (K9 AQxxx QJxx Qx)
  • J10x4x 1098x J Axx (K9 AQJxx Qxxx Qx)

109x4x

5=5=2=1:

  • 109x4x 109xxx Qx A (KJ AQJx Jxx Qxxx)

5=5=1=2:

  • 109x4x 109xxx Q Ax (KJ AQJx Jxxx Qxx)
  • 109x4x 109xxx x AQ (KJ AQJx QJxx xxx)

5=5=0=3:

  • 109x4x 109xxx void AQx (KJ AQJx QJxxx xx)

5=4=3=1:

  • 109x4x AQ10x xxx x (KJ J9xxx QJ AQxx)
  • 109x4x AJ10x Jxx x (KJ Q9xxx Qx AQxx)
  • 109x4x A109x Qxx x (KJ QJxxx Jx AQxx)
  • 109x4x A109x xxx Q (KJ QJxxx QJ Axxx)
  • 109x4x QJ10x QJx x (KJ A9xxx xx AQxx)
  • 109x4x QJ10x Jxx Q (KJ A9xxx Qx Axxx)
  • 109x4x Q109x Qxx Q (KJ AJxxx Jx Axxx)
  • 109x4x Q109x xxx A (KJ AJxxx QJ Qxxx)
  • 109x4x J109x QJx Q (KJ AQxxx xx Axxx)
  • 109x4x J109x Jxx A (KJ AQxxx Qx Qxxx)
  • 109x4x 1098x Qxx A (KJ AQJxx Jx Qxxx)

5=4=2=2:

  • 109x4x AQ10x xx xx (KJ J9xxx QJx AQx)
  • 109x4x AJ10x Jx xx (KJ Q9xxx Qxx AQx)
  • 109x4x A109x Qx xx (KJ QJxxx Jxx AQx)
  • 109x4x A109x xx Qx (KJ QJxxx QJx Axx)
  • 109x4x QJ10x QJ xx (KJ A9xxx xxx AQx)
  • 109x4x QJ10x Jx Qx (KJ A9xxx Qxx Axx)
  • 109x4x Q109x Qx Qx (KJ AJxxx Jxx Axx)
  • 109x4x Q109x xx Ax (KJ AJxxx QJx Qxx)
  • 109x4x J109x QJ Qx (KJ AQxxx xxx Axx)
  • 109x4x J109x Jx Ax (KJ AQxxx Qxx Qxx)
  • 109x4x 1098x Qx Ax (KJ AQJxx Jxx Qxx)
  • 109x4x 1098x xx AQ (KJ AQJxx QJx xxx)

5=4=1=3:

  • 109x4x AQ10x x xxx (KJ J9xxx QJxx AQ)
  • 109x4x AJ10x J xxx (KJ Q9xxx Qxxx AQ)
  • 109x4x A109x Q xxx (KJ QJxxx Jxxx AQ)
  • 109x4x A109x x Qxx (KJ QJxxx QJxx Ax)
  • 109x4x QJ10x J Qxx (KJ A9xxx Qxxx Ax)
  • 109x4x Q109x Q Qxx (KJ AJxxx Jxxx Ax)
  • 109x4x Q109x x Axx (KJ AJxxx QJxx Qx)
  • 109x4x J109x J Axx (KJ AQxxx Qxxx Qx)
  • 109x4x 1098x Q Axx (KJ AQJxx Jxxx Qx)
  • 109x4x 1098x x AQx (KJ AQJxx QJxx xx)

J10x4

4=4=3=2:

  • J10x4 AJ10x xxx xx (K9x Q9xxx QJ AQx)
  • J10x4 A109x Jxx xx (K9x QJxxx Qx AQx)
  • J10x4 J10xx Qxx Qx (K9x AQ9xx Jx Axx)
  • J10x4 J10xx xxx Ax (K9x AQ9xx QJ Qxx)
  • J10x4 109xx QJx Qx (K9x AQJxx xx Axx)
  • J10x4 109xx Jxx Ax (K9x AQJxx Qx Qxx)

4=4=2=3:

  • J10x4 AJ10x xx xxx (K9x Q9xxx QJx AQ)
  • J10x4 A109x Jx xxx (K9x QJxxx Qxx AQ)
  • J10x4 J10xx Qx Qxx (K9x AQ9xx Jxx Ax)
  • J10x4 J10xx xx Axx (K9x AQ9xx QJx Qx)
  • J10x4 109xx QJ Qxx (K9x AQJxx xxx Ax)
  • J10x4 109xx Jx Axx (K9x AQJxx Qxx Qx)

109x4

4=4=3=2:

  • 109x4 AQ10x xxx xx (KJx J9xxx QJ AQx)
  • 109x4 AJ10x Jxx xx (KJx Q9xxx Qx AQx)
  • 109x4 A109x Qxx xx (KJx QJxxx Jx AQx)
  • 109x4 A109x xxx Qx (KJx QJxxx QJ Axx)
  • 109x4 109xx Qxx Ax (KJx AQJxx Jx Qxx)
  • 109x4 109xx xxx AQ (KJx AQJxx QJ xxx)

4=4=2=3:

  • 109x4 AQ10x xx xxx (KJx J9xxx QJx AQ)
  • 109x4 AJ10x Jx xxx (KJx Q9xxx Qxx AQ)
  • 109x4 A109x Qx xxx (KJx QJxxx Jxx AQ)
  • 109x4 A109x xx Qxx (KJx QJxxx QJx Ax)
  • 109x4 109xx Qx Axx (KJx AQJxx Jxx Qx)
  • 109x4 109xx xx AQx (KJx AQJxx QJx xx)

VI. Identification of Layouts that Fail Criterion #2 (East's Winning Trick 1 Doesn't Give the Defenders a Way to Possibly Set in Its First Possession)

Robot would now examine each of the layouts that meets the criterion from page 5 (that is, that give Declarer at least nine cashable winners on any distribution of the defenders' cards) for whether East's winning Trick 1 would give the defenders any means to try to set the contract in their first possession (possibly requiring Declarer to misguess but not to make a play that could succeed on no legal layout).

In the following list of holdings for West, regular font preceded by a single n-dash means that the layout failed criterion #1 and therefore had appeared in regular font on page 5, regular font without a leading n-dash means that the layout fails the present exclusion criterion (meaning that it gives the chance for a set in the defenders' first possession and therefore will remain on Robot's radar), and italic means that the layout would await the criterion on the next page.

KJ94x

5=5=3=0:

  • KJ94x Q109xx xxx void (10x AJxx QJ AQxxx)
  • KJ94x J109xx Jxx void (10x AQxx Qx AQxxx)
  • KJ94x 1098xx Qxx void (10x AQJx Jx AQxxx)

5=5=2=1:

  • KJ94x Q109xx xx x (10x AJxx QJx AQxx)
  • KJ94x J109xx Jx x (10x AQxx Qxx AQxx)
  • KJ94x 1098xx Qx x (10x AQJx Jxx AQxx)
  • KJ94x 1098xx xx Q (10x AQJx QJx Axxx)

5=5=1=2:

  • KJ94x Q109xx x xx (10x AJxx QJxx AQx)
  • KJ94x J109xx J xx (10x AQxx Qxxx AQx)
  • KJ94x 1098xx Q xx (10x AQJx Jxxx AQx)
  • KJ94x 1098xx x Qx (10x AQJx QJxx Axx)

5=5=0=3:

  • KJ94x Q109xx void xxx (10x AJxx QJxxx AQ)
  • KJ94x 1098xx void Qxx (10x AQJx QJxxx Ax)

5=4=3=1:

  • KJ94x Q109x xxx x (10x AJxxx QJ AQxx)
  • KJ94x J109x Jxx x (10x AQxxx Qx AQxx)
  • KJ94x 1098x Qxx x (10x AQJxx Jx AQxx)
  • KJ94x 1098x xxx Q (10x AQJxx QJ Axxx)

5=4=2=2:

  • KJ94x Q109x xx xx (10x AJxxx QJx AQx)
  • KJ94x J109x Jx xx (10x AQxxx Qxx AQx)
  • KJ94x 1098x Qx xx (10x AQJxx Jxx AQx)
  • KJ94x 1098x xx Qx (10x AQJxx QJx Axx)

5=4=1=3:

  • KJ94x Q109x x xxx (10x AJxxx QJxx AQ)
  • KJ94x J109x J xxx (10x AQxxx Qxxx AQ)
  • KJ94x 1098x Q xxx (10x AQJxx Jxxx AQ)
  • KJ94x 1098x x Qxx (10x AQJxx QJxx Ax)

K1094x

5=5=3=0:

  • K1094x QJ10xx xxx void (Jx A9xx QJ AQxxx)
  • K1094x Q109xx Jxx void (Jx AJxx Qx AQxxx)
  • K1094x J109xx Qxx void (Jx AQxx Jx AQxxx)
  • K1094x 1098xx QJx void (Jx AQJx xx AQxxx)

5=5=2=1:

  • K1094x QJ10xx xx x (Jx A9xx QJx AQxx)
  • K1094x Q109xx Jx x (Jx AJxx Qxx AQxx)
  • K1094x J109xx Qx x (Jx AQxx Jxx AQxx)
  • K1094x J109xx xx Q (Jx AQxx QJx Axxx)
  • K1094x 1098xx QJ x (Jx AQJx xxx AQxx)
  • K1094x 1098xx Jx Q (Jx AQJx Qxx Axxx)

5=5=1=2:

  • K1094x QJ10xx x xx (Jx A9xx QJxx AQx)
  • K1094x Q109xx J xx (Jx AJxx Qxxx AQx)
  • K1094x J109xx Q xx (Jx AQxx Jxxx AQx)
  • K1094x J109xx x Qx (Jx AQxx QJxx Axx)
  • K1094x 1098xx J Qx (Jx AQJx Qxxx Axx)

5=5=0=3:

  • K1094x QJ10xx void xxx (Jx A9xx QJxxx AQ)
  • K1094x J109xx void Qxx (Jx AQxx QJxxx Ax)

5=4=3=1:

  • K1094x QJ10x xxx x (Jx A9xxx QJ AQxx)
  • K1094x Q109x Jxx x (Jx AJxxx Qx AQxx)
  • K1094x J109x Qxx x (Jx AQxxx Jx AQxx)
  • K1094x J109x xxx !CQ (Jx AQxxx QJ Axxx)
  • K1094x 1098x QJx x (Jx AQJxx xx AQxx)
  • K1094x 1098x Jxx Q (Jx AQJxx Qx Axxx)

5=4=2=2:

  • K1094x QJ10x xx xx (Jx A9xxx QJx AQx)
  • K1094x Q109x Jx xx (Jx AJxxx Qxx AQx)
  • K1094x J109x Qx xx (Jx AQxxx Jxx AQx)
  • K1094x J109x xx Qx (Jx AQxxx QJx Axx)
  • K1094x 1098x QJ xx (Jx AQJxx xxx AQx)
  • K1094x 1098x Jx Qx (Jx AQJxx Qxx Axx)

5=4=1=3:

  • K1094x QJ10x x xxx (Jx A9xxx QJxx AQ)
  • K1094x Q109x J xxx (Jx AJxxx Qxxx AQ)
  • K1094x J109x Q xxx (Jx AQxxx Jxxx AQ)
  • K1094x J109x x Qxx (Jx AQxxx QJxx Ax)
  • K1094x 1098x J Qxx (Jx AQJxx Qxxx Ax)

J10x4x

5=5=2=1:

  • J10x4x J10xxx Qx Q (K9 AQ9x Jxx Axxx)
  • J10x4x J10xxx xx A (K9 AQ9x QJx Qxxx)
  • J10x4x 109xxx QJ Q (K9 AQJx xxx Axxx)
  • J10x4x 109xxx Jx A (K9 AQJx Qxx Qxxx)

5=5=1=2:

  • J10x4x J10xxx Q Qx (K9 AQ9x Jxxx Axx)
  • J10x4x J10xxx x Ax (K9 AQ9x QJxx Qxx)
  • J10x4x 109xxx J Ax (K9 AQJx Qxxx Qxx)

(The second layout in the above list fails the present exclusion criterion because if East shifts to a low club at Trick 2, Declarer must guess whether to play the Q [which holds if East led from the AK] or a x [which causes the suit to block if East led from A-fifth or K-fifth].)

5=5=0=3:

  • J10x4x J10xxx void Axx (K9 AQ9x QJxxx Qx)

5=4=3=1:

  • J10x4x AJ10x xxx x (K9 Q9xxx QJ AQxx)
  • J10x4x A109x Jxx x (K9 QJxxx Qx AQxx)
  • J10x4x QJ10x Qxx x (K9 A9xxx Jx AQxx)
  • J10x4x QJ10x xxx Q (K9 A9xxx QJ Axxx)
  • J10x4x Q109x QJx x (K9 AJxxx xx AQxx)
  • J10x4x Q109x Jxx Q (K9 AJxxx Qx Axxx)
  • J10x4x J109x Qxx Q (K9 AQxxx Jx Axxx)
  • J10x4x J109x xxx A (K9 AQxxx QJ Qxxx)
  • J10x4x 1098x QJx Q (K9 AQJxx xx Axxx)
  • J10x4x 1098x Jxx A (K9 AQJxx Qx Qxxx)

5=4=2=2:

  • J10x4x AJ10x xx xx (K9 Q9xxx QJx AQx)
  • J10x4x A109x Jx xx (K9 QJxxx Qxx AQx)
  • J10x4x QJ10x Qx xx (K9 A9xxx Jxx AQx)
  • J10x4x QJ10x xx Qx (K9 A9xxx QJx Axx)
  • J10x4x Q109x QJ xx (K9 AJxxx xxx AQx)
  • J10x4x Q109x Jx Qx (K9 AJxxx Qxx Axx)
  • J10x4x J109x Qx Qx (K9 AQxxx Jxx Axx)
  • J10x4x J109x xx Ax (K9 AQxxx QJx Qxx)
  • J10x4x 1098x QJ Qx (K9 AQJxx xxx Axx)
  • J10x4x 1098x Jx Ax (K9 AQJxx Qxx Qxx)

5=4=1=3:

  • J10x4x AJ10x x xxx (K9 Q9xxx QJxx AQ)
  • J10x4x A109x J xxx (K9 QJxxx Qxxx AQ)
  • J10x4x QJ10x Q xxx (K9 A9xxx Jxxx AQ)
  • J10x4x QJ10x x Qxx (K9 A9xxx QJxx Ax)
  • J10x4x Q109x J Qxx (K9 AJxxx QJxx Ax)
  • J10x4x J109x Q Qxx (K9 AQxxx Jxxx Ax)
  • J10x4x J109x x Axx (K9 AQxxx QJxx Qx)
  • J10x4x 1098x J Axx (K9 AQJxx Qxxx Qx)

109x4x

5=5=2=1:

  • 109x4x 109xxx Qx A (KJ AQJx Jxx Qxxx)

5=5=1=2:

  • 109x4x 109xxx Q Ax (KJ AQJx Jxxx Qxx)
  • 109x4x 109xxx x AQ (KJ AQJx QJxx xxx)

5=5=0=3:

  • 109x4x 109xxx void AQx (KJ AQJx QJxxx xx)

5=4=3=1:

  • 109x4x AQ10x xxx x (KJ J9xxx QJ AQxx)
  • 109x4x AJ10x Jxx x (KJ Q9xxx Qx AQxx)
  • 109x4x A109x Qxx x (KJ QJxxx Jx AQxx)
  • 109x4x A109x xxx Q (KJ QJxxx QJ Axxx)
  • 109x4x QJ10x QJx x (KJ A9xxx xx AQxx)
  • 109x4x QJ10x Jxx Q (KJ A9xxx Qx Axxx)
  • 109x4x Q109x Qxx Q (KJ AJxxx Jx Axxx)
  • 109x4x Q109x xxx A (KJ AJxxx QJ Qxxx)
  • 109x4x J109x QJx Q (KJ AQxxx xx Axxx)
  • 109x4x J109x Jxx A (KJ AQxxx Qx Qxxx)
  • 109x4x 1098x Qxx A (KJ AQJxx Jx Qxxx)

5=4=2=2:

  • 109x4x AQ10x xx xx (KJ J9xxx QJx AQx)
  • 109x4x AJ10x Jx xx (KJ Q9xxx Qxx AQx)
  • 109x4x A109x Qx xx (KJ QJxxx Jxx AQx)
  • 109x4x A109x xx Qx (KJ QJxxx QJx Axx)
  • 109x4x QJ10x QJ xx (KJ A9xxx xxx AQx)
  • 109x4x QJ10x Jx Qx (KJ A9xxx Qxx Axx)
  • 109x4x Q109x Qx Qx (KJ AJxxx Jxx Axx)
  • 109x4x Q109x xx Ax (KJ AJxxx QJx Qxx)
  • 109x4x J109x QJ Qx (KJ AQxxx xxx Axx)
  • 109x4x J109x Jx Ax (KJ AQxxx Qxx Qxx)
  • 109x4x 1098x Qx Ax (KJ AQJxx Jxx Qxx)
  • 109x4x 1098x xx AQ (KJ AQJxx QJx xxx)

5=4=1=3:

  • 109x4x AQ10x x xxx (KJ J9xxx QJxx AQ)
  • 109x4x AJ10x J xxx (KJ Q9xxx Qxxx AQ)
  • 109x4x A109x Q xxx (KJ QJxxx Jxxx AQ)
  • 109x4x A109x x Qxx (KJ QJxxx QJxx Ax)
  • 109x4x QJ10x J Qxx (KJ A9xxx Qxxx Ax)
  • 109x4x Q109x Q Qxx (KJ AJxxx Jxxx Ax)
  • 109x4x Q109x x Axx (KJ AJxxx QJxx Qx)
  • 109x4x J109x J Axx (KJ AQxxx Qxxx Qx)
  • 109x4x 1098x Q Axx (KJ AQJxx Jxxx Qx)
  • 109x4x 1098x x AQx (KJ AQJxx QJxx xx)

J10x4

4=4=3=2:

  • J10x4 AJ10x xxx xx (K9x Q9xxx QJ AQx)
  • J10x4 A109x Jxx xx (K9x QJxxx Qx AQx)
  • J10x4 J10xx Qxx Qx (K9x AQ9xx Jx Axx)
  • J10x4 J10xx xxx Ax (K9x AQ9xx QJ Qxx)
  • J10x4 109xx QJx Qx (K9x AQJxx xx Axx)
  • J10x4 109xx Jxx Ax (K9x AQJxx Qx Qxx)

4=4=2=3:

  • J10x4 AJ10x xx xxx (K9x Q9xxx QJx AQ)
  • J10x4 A109x Jx xxx (K9x QJxxx Qxx AQ)
  • J10x4 J10xx Qx Qxx (K9x AQ9xx Jxx Ax)
  • J10x4 J10xx xx Axx (K9x AQ9xx QJx Qx)
  • J10x4 109xx QJ Qxx (K9x AQJxx xxx Ax)
  • J10x4 109xx Jx Axx (K9x AQJxx Qxx Qx)

109x4

4=4=3=2:

  • 109x4 AQ10x xxx xx (KJx J(xxx QJ AQx)
  • 109x4 AJ10x Jxx xx (KJx Q9xxx Qx AQx)
  • 109x4 A109x Qxx xx (KJx QJxxx Jx AQx)
  • 109x4 A109x xxx Qx (KJx QJxxx QJ Axx)
  • 109x4 109xx Qxx Ax (KJx AQJxx Jx Qxx)
  • 109x4 109xx xxx AQ (KJx AQJxx QJ xxx)

4=4=2=3:

  • 109x4 AQ10x xx xxx (KJx J9xxx QJx AQ)
  • 109x4 AJ10x Jx xxx (KJx Q9xxx Qxx AQ)
  • 109x4 A109x Qx xxx (KJx QJxxx Jxx AQ)
  • 109x4 A109x xx Qxx (KJx QJxxx QJx Ax)
  • 109x4 109xx Qx Axx (KJx AQJxx Jxx Qx)
  • 109x4 109xx xx AQx (KJx AQJxx QJx xx)

VII. Identification of Layouts that Fail Criterion #3 (East's Winning Trick 1 Gives the Defenders No Continuation that Would Prevent Declarer's Taking Enough Winners to Fulfill the Contract in the Declaring Side's First Possession)

Robot would now examine each of the layouts that meets the criterion from page 6 (that is, that doesn't give the defenders a chance to set in its first possession) for whether East's winning Trick 1 would give the defenders any means to prevent Declarer's cashing enough winners in the declaring side's first possession.

In the following list of holdings for West, regular font preceded by a single n-dash means that the layout failed criterion #2 and therefore had appeared in regular font on page 6. Regular font preceded by two n-dashes means that the layout failed criterion #1 and therefore had appeared in regular font with one preceding n-dash on page 6. Regular font without a leading n-dash means that the layout fails this criterion (meaning that it gives the defenders at least one way to win Trick 1 and then prevent Declarer from cashing enough winners for the contract in its first possession). Bold means that the layout meets all three criteria for dismissal from Robot's radar, owing to offering the defenders "no chance."

KJ94x

5=5=3=0:

  • KJ94x Q109xx xxx void (10x AJxx QJ AQxxx)
  • ——KJ94x J109xx Jxx void (10x AQxx Qx AQxxx)
  • ——KJ94x 1098xx Qxx void (10x AQJx Jx AQxxx)

5=5=2=1:

  • KJ94x Q109xx xx x (10x AJxx QJx AQxx)
  • ——KJ94x J109xx Jx x (10x AQxx Qxx AQxx)
  • ——KJ94x 1098xx Qx x (10x AQJx Jxx AQxx)
  • KJ94x 1098xx xx Q (10x AQJx QJx Axxx)

5=5=1=2:

  • KJ94x Q109xx x xx (10x AJxx QJxx AQx)
  • ——KJ94x J109xx J xx (10x AQxx Qxxx AQx)
  • ——KJ94x 1098xx Q xx (10x AQJx Jxxx AQx)
  • KJ94x 1098xx x Qx (10x AQJx QJxx Axx)

5=5=0=3:

  • KJ94x Q109xx void xxx (10x AJxx QJxxx AQ)
  • KJ94x 1098xx void Qxx (10x AQJx QJxxx Ax)

5=4=3=1:

  • KJ94x Q109x xxx x (10x AJxxx QJ AQxx)
  • ——KJ94x J109x Jxx x (10x AQxxx Qx AQxx)
  • ——KJ94x 1098x Qxx x (10x AQJxx Jx AQxx)
  • KJ94x 1098x xxx Q (10x AQJxx QJ Axxx)

5=4=2=2:

  • KJ94x Q109x xx xx (10x AJxxx QJx AQx)
  • ——KJ94x J109x Jx xx (10x AQxxx Qxx AQx)
  • ——KJ94x 1098x Qx xx (10x AQJxx Jxx AQx)
  • KJ94x 1098x xx Qx (10x AQJxx QJx Axx)

5=4=1=3:

  • KJ94x Q109x x xxx (10x AJxxx QJxx AQ)
  • ——KJ94x J109x J xxx (10x AQxxx Qxxx AQ)
  • ——KJ94x 1098x Q xxx (10x AQJxx Jxxx AQ)
  • KJ94x 1098x x Qxx (10x AQJxx QJxx Ax)

K1094x

5=5=3=0:

  • K1094x QJ10xx xxx void (Jx A9xx QJ AQxxx)
  • ——K1094x Q109xx Jxx void (Jx AJxx Qx AQxxx)
  • ——K1094x J109xx Qxx void (Jx AQxx Jx AQxxx)
  • ——K1094x 1098xx QJx void (Jx AQJx xx AQxxx)

5=5=2=1:

  • K1094x QJ10xx xx x (Jx A9xx QJx AQxx)
  • ——K1094x Q109xx Jx x (Jx AJxx Qxx AQxx)
  • ——K1094x J109xx Qx x (Jx AQxx Jxx AQxx)
  • K1094x J109xx xx Q (Jx AQxx QJx Axxx)
  • ——K1094x 1098xx QJ x (Jx AQJx xxx AQxx)
  • K1094x 1098xx Jx Q (Jx AQJx Qxx Axxx)

5=5=1=2:

  • K1094x QJ10xx x xx (Jx A9xx QJxx AQx)
  • ——K1094x Q109xx J xx (Jx AJxx Qxxx AQx)
  • ——K1094x J109xx Q xx (Jx AQxx Jxxx AQx)
  • K1094x J109xx x Qx (Jx AQxx QJxx Axx)
  • K1094x 1098xx J Qx (Jx AQJx Qxxx Axx)

5=5=0=3:

  • K1094x QJ10xx void xxx (Jx A9xx QJxxx AQ)
  • K1094x J109xx void Qxx (Jx AQxx QJxxx Ax)

5=4=3=1:

  • K1094x QJ10x xxx x (Jx A9xxx QJ AQxx)
  • ——K1094x Q109x Jxx x (Jx AJxxx Qx AQxx)
  • ——K1094x J109x Qxx x (Jx AQxxx Jx AQxx)
  • K1094x J109x xxx Q (Jx AQxxx QJ Axxx)
  • ——K1094x 1098x QJx x (Jx AQJxx xx AQxx)
  • K1094x 1098x Jxx Q (Jx AQJxx Qx Axxx)

5=4=2=2:

  • K1094x QJ10x xx xx (Jx A9xxx QJx AQx)
  • ——K1094x Q109x Jx xx (Jx AJxxx Qxx AQx)
  • ——K1094x J109x Qx xx (Jx AQxxx Jxx AQx)
  • K1094x J109x xx Qx (Jx AQxxx QJx Axx)
  • ——K1094x 1098x QJ xx (Jx AQJxx xxx AQx)
  • K1094x 1098x Jx Qx (Jx AQJxx Qxx Axx)

5=4=1=3:

  • K1094x QJ10x x xxx (Jx A9xxx QJxx AQ)
  • ——K1094x Q109x J xxx (Jx AJxxx Qxxx AQ)
  • ——K1094x J109x Q xxx (Jx AQxxx Jxxx AQ)
  • K1094x J109x x Qxx (Jx AQxxx QJxx Ax)
  • K1094x 1098x J Qxx (Jx AQJxx Qxxx Ax)

J10x4x

5=5=2=1:

  • ——J10x4x J10xxx Qx Q (K9 AQ9x Jxx Axxx)
  • J10x4x J10xxx xx A (K9 AQ9x QJx Qxxx)
  • ——J10x4x 109xxx QJ Q (K9 AQJx xxx Axxx)
  • ——J10x4x 109xxx Jx A (K9 AQJx Qxx Qxxx)

5=5=1=2:

  • ——J10x4x J10xxx Q Qx (K9 AQ9x Jxxx Axx)
  • J10x4x J10xxx x Ax (K9 AQ9x QJxx Qxx)
  • ——J10x4x 109xxx J Ax (K9 AQJx Qxxx Qxx)

5=5=0=3:

  • J10x4x J10xxx void Axx (K9 AQ9x QJxxx Qx)

5=4=3=1:

  • ——J10x4x AJ10x xxx x (K9 Q9xxx QJ AQxx)
  • ——J10x4x A109x Jxx x (K9 QJxxx Qx AQxx)
  • ——J10x4x QJ10x Qxx x (K9 A9xxx Jx AQxx)
  • J10x4x QJ10x xxx Q (K9 A9xxx QJ Axxx)
  • ——J10x4x Q109x QJx x (K9 AJxxx xx AQxx)
  • ——J10x4x Q109x Jxx Q (K9 AJxxx Qx Axxx)
  • ——J10x4x J109x Qxx Q (K9 AQxxx Jx Axxx)
  • J10x4x J109x xxx A (K9 AQxxx QJ Qxxx)
  • ——J10x4x 1098x QJx Q (K9 AQJxx xx Axxx)
  • ——J10x4x 1098x Jxx A (K9 AQJxx Qx Qxxx)

5=4=2=2:

  • ——J10x4x AJ10x xx xx (K9 Q9xxx QJx AQx)
  • ——J10x4x A109x Jx xx (K9 QJxxx Qxx AQx)
  • ——J10x4x QJ10x Qx xx (K9 A9xxx Jxx AQx)
  • J10x4x QJ10x xx Qx (K9 A9xxx QJx Axx)
  • ——J10x4x Q109x QJ xx (K9 AJxxx xxx AQx)
  • ——J10x4x Q109x Jx Qx (K9 AJxxx Qxx Axx)
  • ——J10x4x J109x Qx Qx (K9 AQxxx Jxx Axx)
  • J10x4x J109x xx Ax (K9 AQxxx QJx Qxx)
  • ——J10x4x 1098x QJ Qx (K9 AQJxx xxx Axx)
  • ——J10x4x 1098x Jx Ax (K9 AQJxx Qxx Qxx)

5=4=1=3:

  • ——J10x4x AJ10x x xxx (K9 Q9xxx QJxx AQ)
  • ——J10x4x A109x J xxx (K9 QJxxx Qxxx AQ)
  • ——J10x4x QJ10x Q xxx (K9 A9xxx Jxxx AQ)
  • J10x4x QJ10x x Qxx (K9 A9xxx QJxx Ax)
  • ——J10x4x Q109x J Qxx (K9 AJxxx QJxx Ax)
  • ——J10x4x J109x Q Qxx (K9 AQxxx Jxxx Ax)
  • J10x4x J109x x Axx (K9 AQxxx QJxx Qx)
  • ——J10x4x 1098x J Axx (K9 AQJxx Qxxx Qx)

109x4x

5=5=2=1:

  • ——109x4x 109xxx Qx A (KJ AQJx Jxx Qxxx)

5=5=1=2:

  • ——109x4x 109xxx Q Ax (KJ AQJx Jxxx Qxx)
  • 109x4x 109xxx x AQ (KJ AQJx QJxx xxx)

5=5=0=3:

  • 109x4x 109xxx void AQx (KJ AQJx QJxxx xx)

5=4=3=1:

  • ——109x4x AQ10x xxx x (KJ J9xxx QJ AQxx)
  • ——109x4x AJ10x Jxx x (KJ Q9xxx Qx AQxx)
  • ——109x4x A109x Qxx x (KJ QJxxx Jx AQxx)
  • ——109x4x A109x xxx Q (KJ QJxxx QJ Axxx)
  • ——109x4x QJ10x QJx x (KJ A9xxx xx AQxx)
  • ——109x4x QJ10x Jxx Q (KJ A9xxx Qx Axxx)
  • ——109x4x Q109x Qxx Q (KJ AJxxx Jx Axxx)
  • ——109x4x Q109x xxx A (KJ AJxxx QJ Qxxx)
  • ——109x4x J109x QJx Q (KJ AQxxx xx Axxx)
  • ——109x4x J109x Jxx A (KJ AQxxx Qx Qxxx)
  • ——109x4x 1098x Qxx A (KJ AQJxx Jx Qxxx)

5=4=2=2:

  • ——109x4x AQ10x xx xx (KJ J9xxx QJx AQx)
  • ——109x4x AJ10x Jx xx (KJ Q9xxx Qxx AQx)
  • ——109x4x A109x Qx xx (KJ QJxxx Jxx AQx)
  • ——109x4x A109x xx Qx (KJ QJxxx QJx Axx)
  • ——109x4x QJ10x QJ xx (KJ A9xxx xxx AQx)
  • ——109x4x QJ10x Jx Qx (KJ A9xxx Qxx Axx)
  • ——109x4x Q109x Qx Qx (KJ AJxxx Jxx Axx)
  • ——109x4x Q109x xx Ax (KJ AJxxx QJx Qxx)
  • ——109x4x J109x QJ Qx (KJ AQxxx xxx Axx)
  • ——109x4x J109x Jx Ax (KJ AQxxx Qxx Qxx)
  • ——109x4x 1098x Qx Ax (KJ AQJxx Jxx Qxx)
  • 109x4x 1098x xx AQ (KJ AQJxx QJx xxx)

 5=4=1=3:

  • ——109x4x AQ10x x xxx (KJ J9xxx QJxx AQ)
  • ——109x4x AJ10x J xxx (KJ Q9xxx Qxxx AQ)
  • ——109x4x A109x Q xxx (KJ QJxxx Jxxx AQ)
  • ——109x4x A109x x Qxx (KJ QJxxx QJxx Ax)
  • ——109x4x QJ10x J Qxx (KJ A9xxx Qxxx Ax)
  • ——109x4x Q109x Q Qxx (KJ AJxxx Jxxx Ax)
  • ——109x4x Q109x x Axx (KJ AJxxx QJxx Qx)
  • ——109x4x J109x J Axx (KJ AQxxx Qxxx Qx)
  • ——109x4x 1098x Q Axx (KJ AQJxx Jxxx Qx)
  • 109x4x 1098x x AQx (KJ AQJxx QJxx xx)

J10x4

4=4=3=2:

  • ——J10x4 AJ10x xxx xx (K9x Q9xxx QJ AQx)
  • ——J10x4 A109x Jxx xx (K9x QJxxx Qx AQx)
  • ——J10x4 J10xx Qxx Qx (K9x AQ9xx Jx Axx)
  • J10x4 J10xx xxx Ax (K9x AQ9xx QJ Qxx)
  • ——J10x4 109xx QJx Qx (K9x AQJxx xx Axx)
  • ——J10x4 109xx Jxx Ax (K9x AQJxx Qx Qxx)

4=4=2=3:

  • ——J10x4 AJ10x xx xxx (K9x Q9xxx QJx AQ)
  • ——J10x4 A109x Jx xxx (K9x QJxxx Qxx AQ)
  • ——J10x4 J10xx Qx Qxx (K9x AQ9xx Jxx Ax)
  • J10x4 J10xx xx Axx (K9x AQ9xx QJx Qx)
  • ——J10x4 109xx QJ Qxx (K9x AQJxx xxx Ax)
  • ——J10x4 109xx Jx Axx (K9x AQJxx Qxx Qx)

109x4

4=4=3=2:

  • ——109x4 AQ10x xxx xx (KJx J(xxx QJ AQx)
  • ——109x4 AJ10x Jxx xx (KJx Q9xxx Qx AQx)
  • ——109x4 A109x Qxx xx (KJx QJxxx Jx AQx)
  • ——109x4 A109x xxx Qx (KJx QJxxx QJ Axx)
  • ——109x4 109xx Qxx Ax (KJx AQJxx Jx Qxx)
  • 109x4 109xx xxx AQ (KJx AQJxx QJ xxx)

4=4=2=3:

  • ——109x4 AQ10x xx xxx (KJx J9xxx QJx AQ)
  • ——109x4 AJ10x Jx xxx (KJx Q9xxx Qxx AQ)
  • ——109x4 A109x Qx xxx (KJx QJxxx Jxx AQ)
  • ——109x4 A109x xx Qxx (KJx QJxxx QJx Ax)
  • ——109x4 109xx Qx Axx (KJx AQJxx Jxx Qx)
  • 109x4 109xx xx AQx (KJx AQJxx QJx xx)

VIII. Roster of Layouts Where the Contract Is Not Assured

The following lists all of the non-bold layouts from page 7. The next step might be for Robot to identify the layouts where Declarer could hardly misguess in accumulating enough winners for the contract on the declaring side's first possession. This could be the subject of a future article.

KJ94x

5=5=3=0:

  • KJ94x Q109xx xxx void (10x AJxx QJ AQxxx)
  • ——KJ94x J109xx Jxx void (10x AQxx Qx AQxxx)
  • ——KJ94x 1098xx Qxx void (10x AQJx Jx AQxxx)

5=5=2=1:

  • KJ94x Q109xx xx x (10x AJxx QJx AQxx)
  • ——KJ94x J109xx Jx x (10x AQxx Qxx AQxx)
  • ——KJ94x 1098xx Qx x (10x AQJx Jxx AQxx)

5=5=1=2:

  • KJ94x Q109xx x xx (10x AJxx QJxx AQx)
  • ——KJ94x J109xx J xx (10x AQxx Qxxx AQx)
  • ——KJ94x 1098xx Q xx (10x AQJx Jxxx AQx)

5=5=0=3:

  • KJ94x Q109xx void xxx (10x AJxx QJxxx AQ)

5=4=3=1:

  • KJ94x Q109x xxx x (10x AJxxx QJ AQxx)
  • ——KJ94x J109x Jxx x (10x AQxxx Qx AQxx)
  • ——KJ94x 1098x Qxx x (10x AQJxx Jx AQxx)

5=4=2=2:

  • KJ94x Q109x xx xx (10x AJxxx QJx AQx)
  • ——KJ94x J109x Jx xx (10x AQxxx Qxx AQx)
  • ——KJ94x 1098x Qx xx (10x AQJxx Jxx AQx)

5=4=1=3:

  • KJ94x Q109x x xxx (10x AJxxx QJxx AQ)
  • ——KJ94x J109x J xxx (10x AQxxx Qxxx AQ)
  • ——KJ94x 1098x Q xxx (10x AQJxx Jxxx AQ)

K1094x

5=5=3=0:

  • K1094x QJ10xx xxx void (Jx A9xx QJ AQxxx)
  • ——K1094x Q109xx Jxx void (Jx AJxx Qx AQxxx)
  • ——K1094x J109xx Qxx void (Jx AQxx Jx AQxxx)
  • ——K1094x 1098xx QJx void (Jx AQJx xx AQxxx)

5=5=2=1:

  • K1094x QJ10xx xx x (Jx A9xx QJx AQxx)
  • ——K1094x Q109xx Jx x (Jx AJxx Qxx AQxx)
  • ——K1094x J109xx Qx x (Jx AQxx Jxx AQxx)
  • ——K1094x 1098xx QJ x (Jx AQJx xxx AQxx)
  • K1094x 1098xx Jx Q (Jx AQJx Qxx Axxx)

5=5=1=2:

  • K1094x QJ10xx x xx (Jx A9xx QJxx AQx)
  • ——K1094x Q109xx J xx (Jx AJxx Qxxx AQx)
  • ——K1094x J109xx Q xx (Jx AQxx Jxxx AQx)
  • K1094x 1098xx J Qx (Jx AQJx Qxxx Axx)

5=5=0=3:

  • K1094x QJ10xx void xxx (Jx A9xx QJxxx AQ)

5=4=3=1:

  • K1094x QJ10x xxx x (Jx A9xxx QJ AQxx)
  • ——K1094x Q109x Jxx x (Jx AJxxx Qx AQxx)
  • ——K1094x J109x Qxx x (Jx AQxxx Jx AQxx)
  • K1094x 1098x QJx x (Jx AQJxx xx AQxx)
  • K1094x 1098x Jxx Q (Jx AQJxx Qx Axxx)

5=4=2=2:

  • K1094x QJ10x xx xx (Jx A9xxx QJx AQx)
  • ——K1094x Q109x Jx xx (Jx AJxxx Qxx AQx)
  • ——K1094x J109x Qx xx (Jx AQxxx Jxx AQx)
  • ——K1094x 1098x QJ xx (Jx AQJxx xxx AQx)
  • K1094x 1098x Jx Qx (Jx AQJxx Qxx Axx)

5=4=1=3:

  • K1094x QJ10x x xxx (Jx A9xxx QJxx AQ)
  • ——K1094x Q109x J xxx (Jx AJxxx Qxxx AQ)
  • ——K1094x J109x Q xxx (Jx AQxxx Jxxx AQ)
  • K1094x 1098x J Qxx (Jx AQJxx Qxxx Ax)

J10x4x

5=5=2=1:

  • ——J10x4x J10xxx Qx Q (K9 AQ9x Jxx Axxx)
  • ——J10x4x 109xxx QJ Q (K9 AQJx xxx Axxx)
  • ——J10x4x 109xxx Jx A (K9 AQJx Qxx Qxxx)

5=5=1=2:

  • ——J10x4x J10xxx Q Qx (K9 AQ9x Jxxx Axx)
  • J10x4x J10xxx x Ax (K9 AQ9x QJxx Qxx)
  • ——J10x4x 109xxx J Ax (K9 AQJx Qxxx Qxx)

5=5=0=3:

  • J10x4x J10xxx void Axx (K9 AQ9x QJxxx Qx)

5=4=3=1:

  • ——J10x4x AJ10x xxx x (K9 Q9xxx QJ AQxx)
  • ——J10x4x A109x Jxx x (K9 QJxxx Qx AQxx)
  • ——J10x4x QJ10x Qxx x (K9 A9xxx Jx AQxx)
  • ——J10x4x Q109x QJx x (K9 AJxxx xx AQxx)
  • ——J10x4x Q109x Jxx Q (K9 AJxxx Qx Axxx)
  • ——J10x4x J109x Qxx Q (K9 AQxxx Jx Axxx)
  • ——J10x4x 1098x QJx Q (K9 AQJxx xx Axxx)
  • ——J10x4x 1098x Jxx A (K9 AQJxx Qx Qxxx)

5=4=2=2:

  • ——J10x4x AJ10x xx xx (K9 Q9xxx QJx AQx)
  • ——J10x4x A109x Jx xx (K9 QJxxx Qxx AQx)
  • ——J10x4x QJ10x Qx xx (K9 A9xxx Jxx AQx)
  • ——J10x4x Q109x QJ xx (K9 AJxxx xxx AQx)
  • ——J10x4x Q109x Jx Qx (K9 AJxxx Qxx Axx)
  • ——J10x4x J109x Qx Qx (K9 AQxxx Jxx Axx)
  • J10x4x J109x xx Ax (K9 AQxxx QJx Qxx)
  • ——J10x4x 1098x QJ Qx (K9 AQJxx xxx Axx)
  • ——J10x4x 1098x Jx Ax (K9 AQJxx Qxx Qxx)

5=4=1=3:

  • ——J10x4x AJ10x x xxx (K9 Q9xxx QJxx AQ)
  • ——J10x4x A109x J xxx (K9 QJxxx Qxxx AQ)
  • ——J10x4x QJ10x Q xxx (K9 A9xxx Jxxx AQ)
  • ——J10x4x Q109x J Qxx (K9 AJxxx QJxx Ax)
  • ——J10x4x J109x Q Qxx (K9 AQxxx Jxxx Ax)
  • J10x4x J109x x Axx (K9 AQxxx QJxx Qx)
  • ——J10x4x 1098x J Axx (K9 AQJxx Qxxx Qx)

109x4x

5=5=2=1:

  • ——109x4x 109xxx Qx A (KJ AQJx Jxx Qxxx)

5=5=1=2:

  • ——109x4x 109xxx Q Ax (KJ AQJx Jxxx Qxx)
  • 109x4x 109xxx x AQ (KJ AQJx QJxx xxx)

5=5=0=3:

  • 109x4x 109xxx void AQx (KJ AQJx QJxxx xx)

5=4=3=1:

  • ——109x4x AQ10x xxx x (KJ J9xxx QJ AQxx)
  • ——109x4x AJ10x Jxx x (KJ Q9xxx Qx AQxx)
  • ——109x4x A109x Qxx x (KJ QJxxx Jx AQxx)
  • ——109x4x A109x xxx Q (KJ QJxxx QJ Axxx)
  • ——109x4x QJ10x QJx x (KJ A9xxx xx AQxx)
  • ——109x4x QJ10x Jxx Q (KJ A9xxx Qx Axxx)
  • ——109x4x Q109x Qxx Q (KJ AJxxx Jx Axxx)
  • ——109x4x Q109x xxx A (KJ AJxxx QJ Qxxx)
  • ——109x4x J109x QJx Q (KJ AQxxx xx Axxx)
  • ——109x4x J109x Jxx A (KJ AQxxx Qx Qxxx)
  • ——109x4x 1098x Qxx A (KJ AQJxx Jx Qxxx)

5=4=2=2:

  • ——109x4x AQ10x xx xx (KJ J9xxx QJx AQx)
  • ——109x4x AJ10x Jx xx (KJ Q9xxx Qxx AQx)
  • ——109x4x A109x Qx xx (KJ QJxxx Jxx AQx)
  • ——109x4x A109x xx Qx (KJ QJxxx QJx Axx)
  • ——109x4x QJ10x QJ xx (KJ A9xxx xxx AQx)
  • ——109x4x QJ10x Jx Qx (KJ A9xxx Qxx Axx)
  • ——109x4x Q109x Qx Qx (KJ AJxxx Jxx Axx)
  • ——109x4x Q109x xx Ax (KJ AJxxx QJx Qxx)
  • ——109x4x J109x QJ Qx (KJ AQxxx xxx Axx)
  • ——109x4x J109x Jx Ax (KJ AQxxx Qxx Qxx)
  • ——109x4x 1098x Qx Ax (KJ AQJxx Jxx Qxx)
  • 109x4x 1098x xx AQ (KJ AQJxx QJx xxx)

5=4=1=3:

  • ——109x4x AQ10x x xxx (KJ J9xxx QJxx AQ)
  • ——109x4x AJ10x J xxx (KJ Q9xxx Qxxx AQ)
  • ——109x4x A109x Q xxx (KJ QJxxx Jxxx AQ)
  • ——109x4x A109x x Qxx (KJ QJxxx QJxx Ax)
  • ——109x4x QJ10x J Qxx (KJ A9xxx Qxxx Ax)
  • ——109x4x Q109x Q Qxx (KJ AJxxx Jxxx Ax)
  • ——109x4x Q109x x Axx (KJ AJxxx QJxx Qx)
  • ——109x4x J109x J Axx (KJ AQxxx Qxxx Qx)
  • ——109x4x 1098x Q Axx (KJ AQJxx Jxxx Qx)
  • 109x4x 1098x x AQx (KJ AQJxx QJxx xx)

J10x4

4=4=3=2:

  • ——J10x4 AJ10x xxx xx (K9x Q9xxx QJ AQx)
  • ——J10x4 A109x Jxx xx (K9x QJxxx Qx AQx)
  • ——J10x4 J10xx Qxx Qx (K9x AQ9xx Jx Axx)
  • J10x4 J10xx xxx Ax (K9x AQ9xx QJ Qxx)
  • ——J10x4 109xx QJx Qx (K9x AQJxx xx Axx)
  • ——J10x4 109xx Jxx Ax (K9x AQJxx Qx Qxx)

4=4=2=3:

  • ——J10x4 AJ10x xx xxx (K9x Q9xxx QJx AQ)
  • ——J10x4 A109x Jx xxx (K9x QJxxx Qxx AQ)
  • ——J10x4 J10xx Qx Qxx (K9x AQ9xx Jxx Ax)
  • J10x4 J10xx xx Axx (K9x AQ9xx QJx Qx)
  • ——J10x4 109xx QJ Qxx (K9x AQJxx xxx Ax)
  • ——J10x4 109xx Jx Axx (K9x AQJxx Qxx Qx)

109x4

4=4=3=2:

  • ——109x4 AQ10x xxx xx (KJx J(xxx QJ AQx)
  • ——109x4 AJ10x Jxx xx (KJx Q9xxx Qx AQx)
  • ——109x4 A109x Qxx xx (KJx QJxxx Jx AQx)
  • ——109x4 A109x xxx Qx (KJx QJxxx QJ Axx)
  • ——109x4 109xx Qxx Ax (KJx AQJxx Jx Qxx)
  • 109x4 109xx xxx AQ (KJx AQJxx QJ xxx)

4=4=2=3:

  • ——109x4 AQ10x xx xxx (KJx J9xxx QJx AQ)
  • ——109x4 AJ10x Jx xxx (KJx Q9xxx Qxx AQ)
  • ——109x4 A109x Qx xxx (KJx QJxxx Jxx AQ)
  • ——109x4 A109x xx Qxx (KJx QJxxx QJx Ax)
  • ——109x4 109xx Qx Axx (KJx AQJxx Jxx Qx)
  • 109x4 109xx xx AQx (KJx AQJxx QJx xx)
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