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The opening leads (conclusion)
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Using selected hands to support or refute claims that a pair is cheating is generally inconclusive. Every pair will take its share of apparently unorthodox actions, and some of these will succeed. If one carefully selected the right hands, one could use these hands to demonstrate that just about any pair is cheating.

In order to make a proper analysis, it is necessary to look at all the hands from a given event. One must examine what signal might have been given, what the normal action with the other hand would be, and what action the other hand would take with the benefit of a signal.

When analyzing the results of Wladow-Elinescu, I chose to focus just on opening leads for several reasons. The claim was that they were signaling for opening leads. I wouldn't get involved with their bidding system or bidding judgment. Opening leads are often fairly clear as to which suit the partner of the opening leader would like to see. Finally, the opening lead is often important and the leader does not know whether or not his lead will make or break the contract, so if they are signaling it is less likely that they will pull their punches.

I looked at all the hands they played in the quarter-finals, semi-finals, and finals of the Senior World Championships in Bali, 2013. I documented every hand on which they were on defense in these matches, except for a couple where the vugraph operator did not record the bidding. There were close to 100 hands. All these matches were close going into the final segment, so there is no question that they would be trying their best at all times.

The majority of the hands are not relevant for one of several reasons. The opening leader might have had an automatic opening lead regardless of what partner is signaling. The suit which partner is signaling for and the suit which the opening leader is likely to lead might coincide. Or, it might not be at all clear which suit the partner of the opening leader would signal for if signals are being given.

An individual person analyzing the hands could make a subjective judgment about which hands are relevant. However, the judgment of the individual may create an unfair bias on an individual hand. To avoid this bias, I posed to the BridgeWinners readers three surveys on the hands in order to determine which hands are relevant for analysis of the leads. These surveys were:

Survey 1: I gave the reader the hand of the partner of the opening leader, and asked which suit (if any) they would signal for if they were permitted to give such a signal. They were assumed to know whether their partner had a short suit or was balanced, and that their partner had the same distributional information about their hand. There were 107 responses. You can see the results of this survey here.

Survey 2: I gave the reader the opening leader's hand, and asked which suit they would lead without any UI. There were 71 responses. You can see the results of this survey here.

Survey 3: I gave the reader the same opening lead problem, but this time with the additional information about which suit partner had signaled for (I chose that suit from the results of survey 1), as well as the distributional information about partner's hand. There were 43 responses. The dwindling number of responses was probably indicative of some readers getting tired of the surveys. You can see the results of this survey here.

From a theoretical point of view, these surveys are not particularly accurate. The size of people answering the surveys is relatively small. There is no attempt to get a cross-section of responders to the surveys. A responder may easily misclick and send the wrong answer. There is no real security, so a person could respond more than once.

Fortunately, accuracy is not needed for this type of survey. This isn't like an election poll where the difference between 48% and 52% is everything. All we need is a good approximation. If 75% of the responders say they would lead a heart on a given hand, we can be sure that a heart lead is the popular choice. We don't care if the true figure should be 70% or 80%, only that a heart lead is the clear majority choice.

Overall, I felt the results of the surveys were pretty good. I believe that the readers were a bit too conservative when deciding whether or not to give a signal, choosing no preference when it would be more profitable to give a signal. In a couple of cases, I believe the readers may have failed to take into account the distributional information about the hand which is assumed to be available to them when choosing which signal to give or what to lead with the knowledge of the signals. These factors may have skewed the results on a couple of the hands. But for the most part the results look accurate. I agreed with almost all of the choices which the readers found clear.

The purpose of the surveys is not to determine guilt or innocence. It is entirely to determine which hands we should be examining. We are looking for hands where it is fairly clear which suit would have been signaled for (if there were signaling), where that suit probably wouldn't have been led with no UI, and where that suit probably would have been led with the aid of the signal. For example, consider the following which was from the finals, segment 6, deal 20.

West
QJ6
A742
10952
62
North
10853
J3
AQ43
J85
East
AK
KQ1085
8
AK974
South
9742
96
KJ76
Q103
W
N
E
S
P
P
1
P
1
P
1
P
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

1: Strong

1: 0-7

According to the survey, 88% of the readers would have signaled for a diamond lead if they held the North hand. Holding the South hand, 10% of the readers would have led a diamond with no UI. However, 98% of the readers would have led a diamond if partner had signaled for a diamond lead.

From these results, whether or not a diamond was led is an indication of guilt or innocence. However, one hand by itself proves nothing. If the results of the survey are accurate, there is a 10% chance that an entirely honest pair would have stumbled onto the diamond lead, so if a diamond were in fact led that would not prove signaling. Similarly, if there were signaling there is a 12% chance that there would not have been a signal for a diamond lead, so if something else were led that would not prove there was no signal. It is merely an indication. Only by looking at all the relevant hands might we get real evidence as to whether or not signals were being given.

Below is a chart showing the percentage vote for the chosen signal, the percentage of voters who would have led that suit with no information, and the percentage of voters who would have led that suit with the information from the signal.

SegmentBoardSuitSignalLeadLead w/s
f6 18 66% 92% 100%
f6 19 No 50%
**f6 20 88% 9% 100%
**f6 21 59% 14% 100%
**f6 23 64% 8% 84%
f6 28 34% 29% 75%
f6 31 44% 65% 95%
f5 2 93% 52% 100%
**f5 3 64% 15% 89%
**f5 4 75% 6% 97%
f5 5 46% 8% 92%
f5 7 77% 82% 97%
f5 8 43% 57% 100%
f5 11 55% 66% 100%
f5 12 No 73%
f5 13 60% 83% 100%
**f3 4 81% 32% 97%
f3 5 93% 63% 97%
**f3 9 73% 38% 100%
f3 10 No 56%
f3 11 No 42%
**f3 12 59% 14% 97%
f3 13 57% 77% 92%
f3 16 50% 14% 49%
f2 18 84% 92% 100%
f2 20 57% 100% 100%
**f2 22 61% 25% 89%
f2 23 47% 82% 100%
**f2 24 91% 17% 100%
**f2 30 51% 5% 89%
f2 31 81% 98% 97%
**s6 18 70% 31% 97%
**s6 21 84% 6% 81%
s6 23 94% 72% 97%
**s6 24 59% 22% 95%
s6 26 41% 94% 70%
**s6 28 90% 38% 95%
s6 30 78% 88% 100%
s5 1 75% 62% 100%
s5 2 No 40%
**s5 4 79% 2% 57%
s5 10 95% 55% 97%
s5 14 77% 100% 95%
**s5 15 56% 6% 78%
s3 4 50% 42% 49%
**s3 8 98% 0% 54%
s3 9 No 46%
s3 11 No 60%
s3 13 40% 3% 32%
s3 14 45% 43% 89%
s3 16 57% 40% 86%
s2 18 57% 43% 62%
s2 19 92% 65% 92%
s2 22 91% 94% 100%
s2 24 67% 94% 100%
**s2 25 67% 3% 86%
**S2 29 70% 5% 84%
s2 30 No 49%
s2 32 69% 98% 100%
**q6 19 61% 42% 100%
**q6 22 65% 3% 70%
q6 23 98% 55% 100%
q6 24 79% 8% 14%
q6 25 45% 0% 19%
q6 26 85% 92% 100%
q6 27 77% 92% 100%
q6 28 53% 71% 97%
**q6 29 80% 20% 70%
**q6 31 55% 2% 81%
q6 32 80% 40% 89%
**q5 1 53% 15% 95%
**q5 2 99% 5% 78%
q5 5 No 70%
q5 8 No 60%
q5 14 37% 98% 100%
q5 15 No 73%
q4 18 No 85%
q4 20 44% 22% 70%
q4 21 70% 49% 97%
q4 22 72% 2% 46%
q4 24 No 78%
q4 25 48% 0% 38%
q4 26 No 68%
q4 27 99% 82% 100%
q4 31 98% 72% 100%
q4 32 60% 97% 100%
**q3 7 90% 0% 68%
q3 10 No 60%
**q3 11 98% 17% 95%
q3 12 48% 83% 100%
q3 14 No 66%
q3 15 90% 78% 100%

Which hands should we include? Whichever ones are to be included, it must be done on a totally objective basis depending on the results of the survey. I decided on the following conditions:

1) There had to be at least 50% votes for giving a signal for a specific suit.

2) There had to be at least a 50% difference between the votes for the lead of that suit with no information and for the lead of that suit with the information from the signal.

For the example hand discussed above, there was an 88% vote for the diamond signal, and a difference of 88% (98 - 10) between the diamond lead with no information and the diamond lead with the information from the signal. Thus, this hand would qualify easily. Other hands were more borderline and there were several which were close, but I had to draw the line somewhere and this is where I chose to draw it. The hands with ** in the chart are the hands which fit this criterion. 28 of the hands satisfied these conditions.

It is important to note that we haven't yet looked at what lead was actually made at the table. It is first necessary to determine in a totally objective manner which hands we should be considering for analysis without being biased about the lead that was made. I believe we have done this successfully.

Suppose a pair is honest. On what percentage of the deals which meet the above criterion would we expect them to stumble onto the lead of the suit which would have been signaled for if there were signaling? It would be fairly small, since our conditions specify that the lead is not a "popular" choice in the first place. If we average the percent of votes there were for the lead in question with no information from the survey on the hands we are examining, this comes to about 14.3%. Thus, on average we would expect an honest pair to make the signaled for lead only a little over 14% of the time.

As a sanity check, I chose to look at the results of Helgemo-Helness for their play in the knockout stages of the Bermuda Bowl. I found 24 deals where in my judgment a signal would have been made for suit A, I would have led something else with no signal, but I would have led suit A with the signal. Of course this is just a survey of 1 person, but it is reasonably accurate. On these 24 deals, they led the suit which would have been signaled for 2 times. This is on the order of what I would have expected for an honest pair. If the same analysis were made for any other pair on any of the teams which made it to the finals in the Bermuda Bowl, the Venice Cup, or the Senior championship, I would be surprised if for the relevant hands they hit the lead partner would be signaling for (if there were signaling) as much as 25% of the time, and I would expect usually a lot lower.

One might think that if a pair is signaling and we examined the hands in this manner that they would virtually always lead the suit which the survey said that partner would lead. If that were so, than the failure to lead the suit on a few hands would be pretty strong evidence that the pair is not signaling. But this is not the case. There are several reasons why a different lead might be chosen.

1) As we have seen from the survey, the suit one would signal for is not always clear. The signaler might have chosen a minority suit for his signal.

2) As we have seen from the survey, the opening leader doesn't always lead the suit signaled for. On any given hand, the actual opening leader might have chosen to override the signal even though a majority of the voters led the suit signaled for.

3) It is possible that there are secondary signals which we don't know about. Or, if the partner of the opening leader has bid a suit the agreement might be to signal strength in another suit even though his bid suit is stronger.

4) The opening leader might think that leading the suit signaled for would just look too suspicious.

5) Occasionally the signal might be missed.

Now it is time to examine the chosen hands and see what the actual opening lead was. Once again, I emphasize that the hands chosen to be analyzed had absolutely nothing to do with the opening lead chosen at the table. They were chosen in a totally objective basis based on the survey. This is the first time we have looked at the actual opening leads.

Below is a chart showing just these chosen hands.

SegmentBoardSuitSignalLeadLead w/sSuit ledVerdict
f6 20 88% 9% 100% Guilty
f6 21 59% 14% 100% Guilty
f6 23 64% 8% 84% Guilty
f5 3 64% 15% 89% Innocent
f5 4 75% 6% 97% Guilty
f3 4 81% 32% 97% Innocent
f3 9 73% 38% 100% Guilty
f3 12 59% 14% 97% Guilty
f2 22 61% 25% 89% Innocent
f2 24 91% 17% 100% Innocent
f2 30 51% 5% 89% Guilty
s6 18 70% 31% 97% Innocent
s6 21 84% 6% 81% Innocent
s6 24 59% 22% 95% Guilty
s6 28 90% 38% 95% Guilty
s5 4 79% 2% 57% Innocent
s5 15 56% 6% 78% Guilty
s3 8 98% 0% 54% Innocent
s2 25 67% 3% 86% Innocent
s2 29 70% 5% 84% Guilty
q6 19 61% 42% 100% Guilty
q6 22 65% 3% 70% Innocent
q6 29 80% 20% 70% Innocent
q6 31 55% 2% 81% Innocent
q5 1 53% 15% 95% Guilty
q5 2 99% 5% 78% Guilty
q3 7 90% 0% 68% Innocent
q3 11 98% 17% 95% Guilty

It is worth examining all of the 28 hands.

Finals, Segment 6, Board 20

West
QJ6
A742
10952
62
North
10853
J3
AQ43
J85
East
AK
KQ1085
8
AK974
South
9742
96
KJ76
Q103
W
N
E
S
P
P
1
P
1
P
1
P
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

1: Strong

1: 0-7

Survey:

Signal for lead: 88%

lead with no information: 9%

lead with signal: 100%

Actual opening lead:

A perfect prototype. The survey (and the hand) makes it clear that a diamond lead would have been signaled for. A diamond lead (with no signal) was possible, but not likely. A diamond lead with the signal was clear-cut.

Finals, Segment 6, Board 21

West
652
98
KJ765
Q54
North
KQ3
J3
108432
J102
East
A1084
AQ5
Q
AK963
South
J97
K107642
A9
87
W
N
E
S
P
1
1
X
P
2
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

1: Strong

Survey:

Signal for lead: 59%

lead with no information: 14%

lead with signal: 100%

Actual opening lead:

The voters did vote for a spade signal, which looks right with KQx of spades. A spade lead is understandably unpopular and is pretty much a shot in the dark. However, with the signal the voters all thought it was clear-cut. And the spade lead was made at the table.

Finals, Segment 6, Board 23

West
K
AKJ
Q109864
J102
North
864
6532
AK73
87
East
A109732
84
J
K963
South
QJ5
Q1097
52
AQ54
W
N
E
S
P
1
P
1
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

1: 11-15 2+ diamonds

Survey:

Signal for lead: 59%

lead with no information: 8%

lead with signal: 84%

Actual opening lead:

Holding the AK of diamonds, the voters made what I consider the right decision to vote signal even though dummy had bid diamonds, since the North hand can't stand anything else. Not surprisingly the diamond lead was unpopular with no information. The signal changed it topopular, and it was the actual lead.

Finals, Segment 5, Board 3

West
AQJ862
10952
K8
5
North
3
K43
73
KQJ8643
East
K1094
A7
AQ64
A109
South
75
QJ86
J10952
72
W
N
E
S
P
1
4
4NT
P
5
P
6
P
P
P
D
6 West
NS: 0 EW: 0

Survey:

Signal for lead: 64%

lead with no information: 15%

lead with signal: 89%

Actual opening lead:

With nothing in any other suit it looks reasonable that South might signal for a heart, which was the majority choice. However, with only QJ of hearts he might give no signal. The heart lead was unpopular without the signal, but with the signal it became understandably popular. However, the opening lead was a club. This could an example of where a heart lead might be thought to be too strange with the natural-looking club lead available.

Finals, Segment 5, Board 4

West
A1093
65
10932
A84
North
J42
K1092
87
K1062
East
Q5
AQ743
AJ6
Q97
South
K876
J8
KQ54
J53
W
N
E
S
P
P
1NT
P
2
P
2
P
2NT
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Survey:

Signal for lead: 75%

lead with no information: 6%

lead with signal: 97%

Actual opening lead:

This was a clear case. A large majority of the readers voted to signal for a club lead, which certainly looks right on the North hand. Naturally a club lead from Jxx with a much stronger diamond suit was picked by almost nobody. However, with the help of the signal almost everybody went for the club lead, which was found at the table.

Finals, Segment 3, Board 4

West
QJ962
J85
QJ1054
North
K87
Q
KQ10653
973
East
A105
AK1043
J874
A
South
43
9762
A92
K862
W
N
E
S
P
1
1
P
2
P
4
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Survey:

Signal for lead: 81%

lead with no information: 32%

lead with signal: 97%

Actual opening lead:

It is likely that North would signal for a diamond lead, but a case could be made for a spade signal. The diamond lead with no information was only moderately popular, but with a signal for a diamond lead it was near unanimous. This could be a case where a signal for a secondary suit is given when a suit has already been bid.

Finals, Segment 3, Board 9

West
QJ5
KJ9875
K9
65
North
K8642
Q4
76
Q872
East
1097
A10
AQ84
J1043
South
A3
632
J10532
AK9
W
N
E
S
P
1
P
1
P
1NT
P
2
P
2
P
2
P
P
P
D
2 West
NS: 0 EW: 0

2: Relay to 2 for invite

Survey:

Signal for lead: 73%

lead with no information: 38%

lead with signal: 100%

Actual opening lead:

It looks likely that South would signal for a club lead with AK of clubs. Without a signal, any lead but a heart could be right and the club lead was not a majority choice. With a signal, everybody led a club. And that was the lead made at the table.

 

Finals, Segment 3, Board `12

West
K43
QJ108
A3
K743
North
98
A54
J1094
QJ52
East
AJ752
K97
86
A98
South
Q106
632
KQ752
106
W
N
E
S
1
P
1
P
1NT
P
2
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

1: 11-15 2+ diamonds

2: Relay to 2 for invite

Survey:

Signal for lead: 59%

lead with no information: 14%

lead with signal: 97%

Actual opening lead:

The majority of the voters reasonably signaled for a club lead. With no signal, a club lead was quite unpopular. With a signal, the club lead became virtually automatic. And a club was led at the table.

Finals, Segment 2, Board 22

West
K1075
AJ
KQ862
62
North
A83
103
J3
AJ10953
East
Q942
KQ98
10
KQ84
South
J6
76542
A9754
7
W
N
E
S
 
2
P
2N
P
3
P
3
P
3N
P
4
P
4
P
4
P
P
P
D
4 West
NS: 0 EW: 0

2: Short diamonds

3: Minimum

3NT: 4-4-1-4

4: Forces 4, planned signoff

Survey:

Signal for lead: 61%

lead with no information: 25%

lead with signal: 89%

Actual opening lead:

The majority of the voters chose to signal for a club lead. I believe they are in error. I think they forgot that partner already knew about the singleton club from the distributional signal during the bidding. I would have signaled for a diamond lead, the lead actually made at the table. This allows South to shift to a heart or a club depending on what he sees in dummy. However, since the majority of the voters did signal for a club lead we had to follow the rules of the survey and present the lead problem having gotten the signal for the club lead. Not surprisingly, the club lead turned from a minority choice into a solid majority choice with that signal. But IMO the at the table signal would have been for a diamond, not a club.

Finals, Segment 2, Board 24

West
K
KJ108742
9
AK84
North
J93
96
Q8643
972
East
752
AQ5
AJ1075
QJ
South
AQ10864
3
K2
10653
W
N
E
S
1
P
4
P
P
P
D
4 West
NS: 0 EW: 0

4: Not necessarily preemptive

Survey:

Signal for lead: 91%

lead with no information: 17%

lead with signal: 100%

Actual opening lead:

This was perhaps the most unlikely result of all of the hands examined if signals were being given. It looks like South would almost certainly signal for a spade, and North would almost certainly lead a spade with such a signal. Yet North led a diamond. One of the players might simply have had a flight of fancy, or a signal might have been missed. If there had been several hands such as this, which there are for other pairs, then there would be considerably more doubt about their guilt.

Finals, Segment 2, Board 30

West
98762
QJ6
108
AJ3
North
Q10
K1085
542
K1054
East
AKJ5
A4
AJ93
Q76
South
43
9732
KQ76
982
W
N
E
S
2NT
P
3
P
3
P
3NT
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Survey:

Signal for lead: 51%

lead with no information: 5%

lead with signal: 89%

Actual opening lead:

A bare majority of the voters went for the heart signal, which by our standards puts the hand into the relevant category. Almost nobody led a heart with no signal, while almost everybody led a heart with the signal. And a heart was led at the table.

Semi-finals, Segment 6, Board 18

West
AQ10
10932
AKJ8
84
North
J843
85
Q1095
J103
East
K76
KQ76
64
AKQ7
South
952
AJ4
732
9652
W
N
E
S
1NT
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Survey:

Signal for lead: 70%

lead with no information: 31%

lead with signal: 97%

Actual opening lead:

A majority of the voters signaled for a diamond lead, but with such a weak hand and not a great diamond holding giving no signal looks quite reasonable. The lead is basically a 3-way tossup with no signal. With a signal for a diamond lead, almost everybody led a diamond. At the table a club was led, but if there were no signal given that wouldn't mean anything.

Semi-finals, Segment 6, board 21

West
KJ94
AJ1082
8
K95
North
A2
654
Q72
Q10864
East
1083
KQ7
104
AJ732
South
Q765
93
AKJ9653
W
N
E
S
P
P
1
1
2
X
3
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Survey:

Signal for lead: 84%

lead with no information: 6%

lead with signal: 81%

Actual opening lead:

The large majority signaled for a club lead with their void. As could be expected, a club lead was almost never made with no signal while it was a heavy favorite with a signal. At the table a diamond was led. Keep in mind that North supposedly knew that South was short in clubs, thus a signal for a club lead would almost certainly mean a void. While this would look like the best defense, leading a club from the North hand on this auction and hitting partner's void would almost be an admission of cheating. North might not have wanted to take that risk, and with his good club holding he may have felt that the trick might come back if he doesn't give partner the ruff.

Semi-finals, Segment 6, Board 24

West
Q3
KQ86432
Q763
North
A854
8765
7
J954
East
KJ1097
AJ92
J10
108
South
Q632
K104
A95
AK2
W
N
E
S
3
P
P
P
D
3 West
NS: 0 EW: 0

Survey:

Signal for lead: 59%

lead with no information: 22%

lead with signal: 95%

Actual opening lead:

The vote for a club signal wasn't overwhelming, but it was the majority vote and looks reasonable holding AK of clubs. North's opening lead with no signal isn't clear, but a club lead wasn't particularly popular. With the signal, the club lead became clear. And the lead at the table was a club.

Semi-finals, Segment 6, Board 28

West
A1052
A954
873
106
North
973
K1083
KJ104
98
East
KQJ86
92
AKQJ74
South
4
QJ762
AQ65
532
W
N
E
S
P
P
1
1
X
3
5
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Survey:

Signal for lead: 90%

lead with no information: 38%

lead with signal: 95%

Actual opening lead:

Signaling for a diamond lead holding AQ of diamonds is clear. A diamond lead is quite reasonable anyway, but it is risky, and only a minority of the voters chose the lead with no information. After a signal for a diamond lead, the lead was nearly unanimous. And North did find the risky diamond lead at the table.

Semi-finals, Segment 5, Board 4

West
KJ1093
Q9
KQ32
K8
North
872
J4
AJ654
A109
East
654
AK86
97
5432
South
AQ
107532
108
QJ76
W
N
E
S
1
P
1NT
P
2
P
2
P
P
P
D
2 West
NS: 0 EW: 0

Survey:

Signal for lead: 79%

lead with no information: 2%

lead with signal: 57%

Actual opening lead:

It does look reasonable for South to signal for a club lead. And a club lead is clearly absurd with no signal. A bare majority of the voters chose to lead a club with the signal, which pushes this hand into the relevant category. Personally I disagree with the voters here. I would lead a heart even if partner were signaling for a club lead. And a heart lead was the lead chosen at the table.

Semi-finals, Segment 5, Board 15

West
AJ865
Q
A3
AQ1062
North
1043
AJ76
KQ76
73
East
KQ2
K8532
104
J84
South
97
1094
J9852
K95
W
N
E
S
P
1
P
2
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Survey:

Signal for lead: 56%

lead with no information: 6%

lead with signal: 78%

Actual opening lead:

With South's only high honor in clubs, it looks pretty clear to me to signal for a club lead. I was surprised that only 56% of the voters agreed, but it was a majority which is sufficient to put this hand into the relevant category. Not surprisingly almost nobody led a club with no information, but with a signal the club lead became quite popular. And a club was led at the table.

Semi-finals, Segment 3, Board 8

West
A863
KQ8
QJ2
1062
North
1074
A107532
96
74
East
K5
94
K8754
Q985
South
QJ92
J6
A103
AKJ3
W
N
E
S
1
P
1NT
P
P
P
D
1NT East
NS: 0 EW: 0

Survey:

Signal for lead: 98%

lead with no information: 0%

lead with signal: 54%

Actual opening lead:

Clearly North would signal for a heart lead, and clearly South would never lead a heart without the signal. A bare majority of the voters chose to lead a heart with the signal. Personally I think they are nuts -- I wouldn't consider a heart lead even with partner signaling for hearts. At the table a spade was led, which makes a lot more sense to me. But the voters rule, so this hand comes into the relevant category.

Semi-finals, Segment 2, Board 25

West
A1042
Q9876
Q
AJ10
North
KQ75
K532
J3
KQ2
East
J86
A
A10765
9873
South
93
J104
K9842
654
W
N
E
S
1NT
P
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

2: majors

Survey:

Signal for lead: 67%

lead with no information: 3%

lead with signal: 86%

Actual opening lead:

The majority of the voters chose reasonably to signal for a club lead with the KQ. A club lead was unpopular with no signal, but of course became popular with a signal. However, a diamond was led at the table, which certainly wouldn't have been signaled for. North might have chosen to give no signal, since he would be happy with most leads. Still, one would not expect this result from a pair giving signals.  This type of result occurred only a couple of times.  

Semi-finals, Segment 2, Board 29

West
Q752
A754
QJ
KJ9
North
K103
106
K10985
754
East
J96
K2
A7632
A106
South
A84
QJ983
4
Q832
W
N
E
S
P
1
P
1
P
1NT
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Survey:

Signal for lead: 70%

lead with no information: 5%

lead with signal: 84%

Actual opening lead:

It is logical for North to signal for a spade lead with K10x in spades and xxx in clubs, the unbid suits. Clearly a spade lead from the South hand is unpopular with no information. After a signal for a spade lead, the lead becomes quite clear as the voters said. And the unorthodox spade was led at the table.

Quarter-finals, Segment 6, Board 19

West
KQJ86
Q65
K
AJ53
North
542
A8
Q10754
1042
East
10973
J103
AJ62
K7
South
A
K9742
983
Q986
W
N
E
S
P
1
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

3: Limit raise

Survey:

Signal for lead: 61%

lead with no information: 42%

lead with signal: 100%

Actual opening lead:

While not totally clear, the majority of the voters did choose to signal for a heart lead holding the king. Shooting out the heart lead from ace-doubleton isn't unreasonable anyway, and a good-sized minority chose that lead with no information. However with the signal the heart lead was unanimous, which was sufficient to put this hand into our relevant category. And a heart lead was chosen at the table.

Quarter-finals, Segment 6, Board 22

West
Q105
K76
8742
1032
North
AJ87
105
Q5
J9865
East
643
QJ94
KJ10
AK4
South
K92
A832
A963
Q7
W
N
E
S
1NT
P
P
P
D
1NT East
NS: 0 EW: 0

Survey:

Signal for lead: 65%

lead with no information: 3%

lead with signal: 70%

Actual opening lead:

The majority of the voters chose to signal for a club lead holding J98xx rather than a spade lead holding AJxx. Personally I think the voters were wrong on this. I would have signaled for a spade lead, and I don't think it is close. Needless to say, almost nobody voted for either black suit with no information. After a signal for a club lead, the majority naturally led a club. I'm sure that after a signal for a spade lead, the majority would have led a spade. The actual lead at the table was a spade instead of a more popular red-suit lead.

Quarter-finals, Segment 6, Board 29

West
K87543
10
108752
3
North
AQ
Q8762
QJ9
942
East
J10
AK3
K643
AKJ6
South
962
J954
A
Q10875
W
N
E
S
1
1NT
3
4
P
4NT
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Survey:

Signal for lead: 80%

lead with no information: 20%

lead with signal: 70%

Actual opening lead:

It certainly makes sense to signal for a diamond lead holding the stiff ace, which is what most of the voters did. With no signal, a diamond lead wasn't attractive. Enough voters went for the diamond lead after the signal to barely push this hand into the relevant category. However, I believe these voters forgot that with signals given North knew that his partner had diamond shortness and didn't notice this information when casting their votes. Had they noticed this, I am quite sure that the diamond lead would not have been chosen after the signal.

Quarter-finals, Segment 6, Board 31

West
5
J985
K9865
K64
North
K10982
AK4
73
A75
East
AJ43
Q2
J1042
QJ10
South
Q76
10763
AQ
9832
W
N
E
S
P
P
1
P
2
X
XX
3
P
P
P
D
3 East
NS: 0 EW: 0

Survey:

Signal for lead: 55%

lead with no information: 2%

lead with signal: 81%

Actual opening lead:

Clearly a heart lead would be unpopular with no signal and popular with a signal for a heart lead, as the survey shows. A bare majority voted to signal for a heart lead. That wouldn't have been my choice. Partner is presumably pretty weak, and may not be getting in again. Why do I need a heart lead to my AK? A spade lead through something in dummy looks to be much more important. I would signal for a spade lead. The normal spade lead was made at the table.

Quarter-finals, Segment 5, Board 1

West
K8
9764
1063
10942
North
Q952
AQJ5
42
Q86
East
1076
K2
AKJ87
A75
South
AJ43
1083
Q95
KJ3
W
N
E
S
1NT
X
P
2
P
P
X
P
P
P
D
2X West
NS: 0 EW: 0

Survey:

Signal for lead: 53%

lead with no information: 15%

lead with signal: 95%

Actual opening lead:

The signal wasn't clear, but a bare majority did vote to signal for a spade. The spade lead isn't totally unreasonable with no signal, but only 15% of the voters chose it. Naturally with the signal for the lead almost everybody voted for the spade lead, which was sufficient to put this hand into the relevant category. At the table, a spade was led.

Quarter-finals, Segment 5, Board 2

West
Q84
7
98765
J1064
North
7
K93
AKQ3
87532
East
AKJ106532
AJ2
2
A
South
9
Q108654
J104
KQ9
W
N
E
S
1
2
P
4
6
P
P
P
D
6 East
NS: 0 EW: 0

1: Strong

Survey:

Signal for lead: 99%

lead with no information: 5%

lead with signal: 78%

Actual opening lead:

Naturally virtually everybody signaled for a diamond lead with AKQ. The diamond lead wasn't popular with two other potentially attractive leads available. With the signal, the diamond lead became the clear choice. And the lead at the table was a diamond.

Quarter-finals, Segment 3, Board 7

West
A52
AQ972
KJ5
Q5
North
Q43
84
AQ932
A83
East
J86
KJ3
108
KJ1094
South
K1097
1065
764
762
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Survey:

Signal for lead: 90%

lead with no information: 0%

lead with signal: 68%

Actual opening lead:

Clearly South would signal for a spade lead. Equally clearly, North would never lead a spade with no signal. With the signal, the voters chose the spade lead. I think they are wrong. North can see the potential to defeat the contract is in diamonds, not spades, in spite of the signal. I would lead a diamond even with partner giving a signal for a spade lead. In addition, even if North thought a spade lead would be best this kind of lead would almost be an admission of cheating if it struck gold. At the table, North made the entirely normal diamond lead.

Quarter-finals, Segment 3, Board 11

West
1098
AKQ75
5
AKJ7
North
A63
108
742
109863
East
Q
96432
QJ1093
Q5
South
KJ7542
J
AK86
42
W
N
E
S
 
2
X
3
P
P
4
P
4
P
5
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Survey:

Signal for lead: 98%

lead with no information: 17%

lead with signal: 95%

Actual opening lead:

The signal for a diamond lead was clear with AK of diamonds. With no signal, a diamond lead was not popular. With the signal, almost everybody led a diamond. And at the table, a diamond was led.

 

As can be seen, out of the 28 relevant hands Wladow-Elinescu found the lead which would have been signaled for (and was not a popular lead with no information but was the lead of choice with the extra information) 15 times out of 28 hands. This isn't just high. It is off the charts. Keep in mind that these leads were on average chosen by only 14.3% of the readers when there was no information. Thus, for any given hand, if there were no signaling one could expect that the opening leader would hit the lead partner would want about 1/7 of the time.

To get a feel for what this means, suppose a friend handed you a die which he swore was an honest die -- each of the numbers from 1 to 6 would be equally likely to appear when the die is rolled. You roll the die 28 times, and on 15 of those tosses the number 6 appears. Would you believe that the die was honest, when for an honest die the probability of getting a 6 on an individual roll is 1/6? Or would you be willing to bet that the die was loaded even though your friend swore that it was an honest die? This is roughly the same situation we are facing here. It is possible that an honest die could show a 6 15 times out of 28, just as it is possible that an honest pair could happen to hit partner's preferred suit 15 times out of 28 when making unpopular leads. But that's not the way to bet.

How unlikely is such an occurrence with an honest pair? Mathematicians will have to check me out on this. By my calculations (which could be off by a lot), the chances are about 1 in a million. Whatever the true number is, it is definitely tiny.

This in itself is pretty convincing. However, in my judgment (and this is only my judgment), almost all the hands where the actual opening lead matched the suit signaled for were clear, while on many of the hands where the opening lead did not match the suit signaled for there was reason to question the accuracy of the survey or some other factor.

Statistics can never absolutely prove anything. They can simply show what the probability of an event occurring is under certain assumptions. It is then a matter of judgment as to whether these assumptions are accurate.

It is theoretically possible that by sheer luck Wladow-Elinsecu could have achieved these results playing honestly. However, I prefer to believe in Oswald Jacoby's law of unlikely events, which is: If an extremely unlikely event happened, it didn't!

I have stated that one deal can't by itself prove that a pair is cheating. However, there is one hand in particular which I believe the readers should see.

Quarter-finals, Segment 4, Board 26

West
AK532
QJ32
A96
7
North
974
K104
Q542
AJ3
East
J8
8765
KJ
KQ1094
South
Q106
A9
10873
8652
W
N
E
S
P
P
1
P
1NT
P
2
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

North led the ace of clubs. This was quite a surprise. A diamond lead got almost all the votes (with no signal), and nobody chose a club lead. However, it is clear that South wouldn't be signaling for a club lead and North does have to lead something. What followed was most interesting.

After having led the ace of clubs and seeing dummy, if this hand were presented to 100 experts as a defensive problem I am quite confident that there would be 100 votes for a diamnd shift. How could one possibly do anything else? If partner has the ace of diamonds this puts declarer on an immediate guess for his contract, and even if declarer guesses right all partner needs is the jack of hearts to defeat 4. Dummy's clubs are established, and if North doesn't shift to a diamond declarer will be able to pitch all of his losing diamonds on the clubs.

Instead of shifting to a diamond, North continued clubs. Declarer won, and led a heart to queen and king. North played a third round of clubs. Declarer won, and led a heart. South won the ace, and a fourth round of clubs promoted North's 10 for the setting trick.

How could this defense be possible? If there were signals for the opening lead and partner had the ace of diamonds, then it is 100% that partner would have signaled for a diamond lead. As Sherlock Holmes would say, since South didn't cough twice in the night he can't have the ace of diamonds, so a diamond shift is futile. Now the best chance to defeat the contract does appear to be to play partner for ace-doubleton of hearts and 4 clubs.

Now let's revisit the opening lead. The majority of the voters went for no signal. However, holding the ace of hearts it seems pretty reasonable to signal for a heart lead. I know that would have been my choice. So, suppose North did receive that signal. Might he not place his partner with the ace-doubleton of hearts? And might he not envision the trump promotion at the start of the hand and lead the ace of clubs in preparation for the promotion on the fourth round of clubs? Really a brilliant lead, which unfortunately appears to have been based on illegal information.

For completeness, below I am giving every hand in the survey. These hands can be found on the BBO vugraph archives. The URL for this is here.

Finals segment 6

Board 18

West
A109
J8732
Q2
1074
North
KJ4
Q65
AKJ93
KJ
East
Q86
AK4
104
AQ852
South
7532
109
8765
963
W
N
E
S
1NT
P
2
X
2
P
P
P
D
2 East
NS: 0 EW: 0

1NT: 14-16

2: Transfer

Board 19

West
K84
Q32
KQJ75
QJ
North
9753
J6
A832
982
East
AQ102
K97
4
A10743
South
J6
A10854
1096
K65
W
N
E
S
1
P
1
2
P
2
P
3
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Board 20

West
QJ6
A742
10952
62
North
10853
J3
AQ43
J85
East
AK
KQ1085
8
AK974
South
9742
96
KJ76
Q103
W
N
E
S
P
P
1
P
1
P
1
P
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

1: Strong

1: 0-7

Board 21

West
652
98
KJ765
Q54
North
KQ3
J3
108432
J102
East
A1084
AQ5
Q
AK963
South
J97
K107642
A9
87
W
N
E
S
P
1
1
X
P
2
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

1: Strong

Board 23

West
K
AKJ
Q109864
J102
North
864
6532
AK73
87
East
A109732
84
J
K963
South
QJ5
Q1097
52
AQ54
W
N
E
S
P
1
P
1
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

1: 11-15 2+ diamonds

Board 28

West
KJ6
A
K972
QJ1092
North
10743
K9653
3
A87
East
A9852
Q42
Q86
43
South
Q
J1087
AJ1054
K65
W
N
E
S
1
P
1
P
2
P
2
P
P
P
D
2 West
NS: 0 EW: 0

1: 11-15 2+ diamonds

Board 29

West
Q86542
2
KJ75
72
North
107
Q6
10632
KJ1084
East
AJ
KJ10953
Q84
A9
South
K93
A874
A9
Q653
W
N
E
S
P
1
P
1
P
3
P
P
P
D
3 East
NS: 0 EW: 0

Board 31

West
1094
K973
1084
A95
North
J763
J10
Q652
Q62
East
AQ8
Q82
AKJ7
874
South
K52
A654
93
KJ103
W
N
E
S
1
P
1
X
P
2
P
P
P
D
2 West
NS: 0 EW: 0

Finals segment 5

Board 2

West
QJ52
A2
A105
9742
North
9864
KQ105
94
AQ3
East
AK107
98
KQJ2
K106
South
3
J7643
8763
J85
W
N
E
S
1NT
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 3

West
AQJ862
10952
K8
5
North
3
K43
73
KQJ8643
East
K1094
A7
AQ64
A109
South
75
QJ86
J10952
72
W
N
E
S
P
1
4
4NT
P
5
P
6
P
P
P
D
6 West
NS: 0 EW: 0

Board 4

West
A1093
65
10932
A84
North
J42
K1092
87
K1062
East
Q5
AQ743
AJ6
Q97
South
K876
J8
KQ54
J53
W
N
E
S
P
P
1NT
P
2
P
2
P
2NT
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Board 5

West
A1073
K9732
10
1052
North
K6
5
AQ962
KQ864
East
Q4
AQ10864
J43
A73
South
J9852
J5
K875
J9
W
N
E
S
1
1
1
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 7

West
K985
AQ87643
Q2
North
A1062
K
K75432
KJ
East
Q4
10
AJ86
A108743
South
J73
J952
Q109
965
W
N
E
S
P
1
X
1NT
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 8

West
9532
Q9
9
A106532
North
1076
865
A543
Q97
East
KQJ84
A107
QJ6
J4
South
A
KJ432
K10872
K8
W
N
E
S
P
P
1
2
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

2: Hearts and a minor

Board 11

West
A72
KJ64
K8
K762
North
Q53
1073
976
10543
East
1084
Q985
AJ1042
J
South
KJ96
A2
Q53
AQ98
W
N
E
S
1
P
1
X
P
2
P
2
P
4
P
P
P
D
4 West
NS: 0 EW: 0

1: Strong

1: 0-8

2: 5+ diamonds, 4 hearts

Board 12

West
Q7432
A64
KQ72
Q
North
1086
KQ95
KJ10932
East
AKJ9
J10
AJ65
A85
South
5
8732
109843
764
W
N
E
S
 
1
3
4
P
4
P
4N
P
5
P
5
P
6
P
6
P
P
P
D
6 West
NS: 0 EW: 0

Board 13

West
108
9863
AJ1073
63
North
KJ7542
95
Q10985
East
3
KQJ752
K82
AKJ
South
AQ96
A104
Q64
742
W
N
E
S
P
1
P
1
2
3
3
4
4
P
P
5
P
P
P
D
5 East
NS: 0 EW: 0

Finals segment 3

Board 4

West
QJ962
J85
QJ1054
North
K87
Q
KQ10653
973
East
A105
AK1043
J874
A
South
43
9762
A92
K862
W
N
E
S
P
1
1
P
2
P
4
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 5

West
K2
AK72
K
AK7432
North
J1064
10653
QJ964
East
AQ98
QJ984
A7
J9
South
753
108532
Q10865
W
N
E
S
 
P
1N
P
2
P
2
P
4
P
5
P
7
X
P
P
7N
P
P
P
D
7NT East
NS: 0 EW: 0

4: RKC hearts

Board 9

West
QJ5
KJ9875
K9
65
North
K8642
Q4
76
Q872
East
1097
A10
AQ84
J1043
South
A3
632
J10532
AK9
W
N
E
S
P
1
P
1
P
1NT
P
2
P
2
P
2
P
P
P
D
2 West
NS: 0 EW: 0

2: Relay to 2 for invite

Board 10

West
865
J1082
KQJ5
Q9
North
Q942
K943
1082
A6
East
K10
AQ6
74
KJ7532
South
AJ73
75
A963
1084
W
N
E
S
2
P
P
P
D
2 East
NS: 0 EW: 0

Board 11

West
A3
875
AQJ64
K65
North
Q82
AJ103
K10953
2
East
KJ1064
K962
8
AQ8
South
975
Q4
72
J109743
W
N
E
S
P
1NT
P
2
X
2
P
3
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

3: 4 hearts, 5 spades

Board 12

West
K43
QJ108
A3
K743
North
98
A54
J1094
QJ52
East
AJ752
K97
86
A98
South
Q106
632
KQ752
106
W
N
E
S
1
P
1
P
1NT
P
2
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

1: 11-15 2+ diamonds

2: Relay to 2 for invite

Board 13

West
2
J10542
7
KQ8732
North
A943
K873
932
65
East
Q86
AKQJ10854
94
South
KJ1075
AQ96
6
AJ10
W
N
E
S
P
1
1
X
3
5
X
P
P
P
D
5X East
NS: 0 EW: 0

1: 11-15 2+ diamonds

Board 16

West
8
J109432
Q8
J973
North
J
A85
AJ10742
Q82
East
A1076432
KQ
653
10
South
KQ95
76
K9
AK654
W
N
E
S
P
2NT
P
3
P
3
3
X
P
P
P
D
3X East
NS: 0 EW: 0

2NT: Both minors or 6+ diamonds

3: Pass or correct

Finals segment 2

Board 18

West
K52
86
A87
KQ975
North
943
Q75
Q9542
43
East
10876
AJ4
K6
A1082
South
AQJ
K10932
J103
J6
W
N
E
S
1
1
2
2
3
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

1: 11-15 2+ diamonds

Board 20

West
AQ762
J104
J
A652
North
J953
Q62
AK1063
K
East
K1084
AK7
954
Q107
South
9853
Q872
J9843
W
N
E
S
1
2
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 22

West
K1075
AJ
KQ862
62
North
A83
103
J3
AJ10953
East
Q942
KQ98
10
KQ84
South
J6
76542
A9754
7
W
N
E
S
 
2
P
2N
P
3
P
3
P
3N
P
4
P
4
P
4
P
P
P
D
4 West
NS: 0 EW: 0

2: Short diamonds

3: Minimum

3NT: 4-4-1-4

4: Forces 4, planned signoff

Board 23

West
104
K632
AQ9
J965
North
9652
104
10754
K32
East
AKQJ7
Q97
K
A1087
South
83
AJ85
J8632
Q4
W
N
E
S
 
P
P
P
1
P
1
P
1
P
1N
P
2
P
3
P
3N
P
P
P
D
3NT West
NS: 0 EW: 0

Board 24

West
K
KJ108742
9
AK84
North
J93
96
Q8643
972
East
752
AQ5
AJ1075
QJ
South
AQ10864
3
K2
10653
W
N
E
S
1
P
4
P
P
P
D
4 West
NS: 0 EW: 0

4: Not necessarily preemptive

Board 30

West
98762
QJ6
108
AJ3
North
Q10
K1085
542
K1054
East
AKJ5
A4
AJ93
Q76
South
43
9732
KQ76
982
W
N
E
S
2NT
P
3
P
3
P
3NT
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 31

West
A732
J107
KQ63
72
North
Q10986
982
KQJ53
East
K5
KQ532
AJ7
A84
South
J4
A9864
1054
1096
W
N
E
S
P
P
P
1NT
P
3
X
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

3: Puppet Stayman

Semi finals segment 6

Board 18

West
AQ10
10932
AKJ8
84
North
J843
85
Q1095
J103
East
K76
KQ76
64
AKQ7
South
952
AJ4
732
9652
W
N
E
S
1NT
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 21

West
KJ94
AJ1082
8
K95
North
A2
654
Q72
Q10864
East
1083
KQ7
104
AJ732
South
Q765
93
AKJ9653
W
N
E
S
P
P
1
1
2
X
3
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 23

West
J43
K107542
A7
108
North
982
A8
J10643
A42
East
10
Q93
KQ5
KQ9653
South
AKQ765
J6
982
J7
W
N
E
S
 
2
P
P
3
P
3
3
4
P
P
4
P
P
5
X
P
P
P
D
5X West
NS: 0 EW: 0

Board 24

West
Q3
KQ86432
Q763
North
A854
8765
7
J954
East
KJ1097
AJ92
J10
108
South
Q632
K104
A95
AK2
W
N
E
S
3
P
P
P
D
3 West
NS: 0 EW: 0

Board 26

West
J103
A4
K9752
832
North
Q98765
Q832
8
QJ
East
42
KJ1096
QJ10
AK9
South
AK
75
A643
107654
W
N
E
S
1
P
1NT
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

Board 28

West
A1052
A954
873
106
North
973
K1083
KJ104
98
East
KQJ86
92
AKQJ74
South
4
QJ762
AQ65
532
W
N
E
S
P
P
1
1
X
3
5
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Board 30

West
J98642
A7642
K3
North
A107
K109
10853
964
East
KQ3
QJ
AJ92
AQ52
South
5
853
KQ764
J1087
W
N
E
S
 
1
P
1
P
2N
P
3
P
3
P
4
P
4
X
XX
P
4N
P
5
P
6
P
P
P
D
6 West
NS: 0 EW: 0

Semi-finals segment 5

Board 1

West
KQ1052
6
QJ54
A85
North
AJ63
K
K1098
KQ32
East
874
J10932
632
74
South
9
AQ8754
A7
J1096
W
N
E
S
1
P
1
1
X
P
P
P
D
1X West
NS: 0 EW: 0

Board 2

West
109543
J532
KQ53
North
A876
A74
108
KQ105
East
Q
KQ10
A764
J7432
South
KJ2
986
J92
A986
W
N
E
S
1
P
1
P
1NT
P
2
P
P
P
D
2 West
NS: 0 EW: 0

Board 3

West
KQJ105
74
986
K32
North
A73
1086
J4
AJ1065
East
86
AQ932
AK
Q984
South
942
KJ5
Q107532
7
W
N
E
S
P
P
P
1
2
2
P
2NT
P
P
P
D
2NT East
NS: 0 EW: 0

Board 4

West
KJ1093
Q9
KQ32
K8
North
872
J4
AJ654
A109
East
654
AK86
97
5432
South
AQ
107532
108
QJ76
W
N
E
S
1
P
1NT
P
2
P
2
P
P
P
D
2 West
NS: 0 EW: 0

Board 10

West
A9732
A10
KQ102
96
North
QJ105
63
A8
QJ1073
East
K64
J84
J965
AK8
South
8
KQ9752
743
542
W
N
E
S
1
P
1
P
1NT
2
X
P
2
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Board 14

West
862
10
10953
AK973
North
Q5
J732
AK8762
Q
East
AJ943
AKQ4
4
1042
South
K107
9865
QJ
J865
W
N
E
S
1
P
2
3
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 15

West
AJ865
Q
A3
AQ1062
North
1043
AJ76
KQ76
73
East
KQ2
K8532
104
J84
South
97
1094
J9852
K95
W
N
E
S
P
1
P
2
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Semi-finals segment 3

Board 4

West
109865
AKJ85
109
3
North
432
Q9762
Q
10975
East
A
43
AJ7643
K642
South
KQJ7
10
K852
AQJ8
W
N
E
S
P
P
1
P
1
P
2
X
2
P
P
X
P
P
P
D
2X East
NS: 0 EW: 0

Board 8

West
A863
KQ8
QJ2
1062
North
1074
A107532
96
74
East
K5
94
K8754
Q985
South
QJ92
J6
A103
AKJ3
W
N
E
S
1
P
1NT
P
P
P
D
1NT East
NS: 0 EW: 0

Board 9

West
AQ643
A102
95
AK2
North
85
KJ943
J6432
J
East
K972
Q865
10
10865
South
J10
7
AKQ87
Q9743
W
N
E
S
P
P
2NT
X
5
P
P
X
P
5
P
P
P
D
5 East
NS: 0 EW: 0

Board 11

West
KQ974
94
K76
KJ2
North
65
KJ1075
A83
Q64
East
832
AQ62
Q95
A75
South
AJ10
83
J1042
10983
W
N
E
S
P
1
2
X
P
2
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 13

West
Q732
K107
KQ2
AK10
North
A94
A96542
1095
5
East
KJ65
83
J63
J732
South
108
QJ
A874
Q9864
W
N
E
S
P
P
P
1NT
2
P
2
P
P
X
P
2
P
P
P
D
2 West
NS: 0 EW: 0

2: 1 major

Board 14

West
AK853
J103
J8
765
North
J7642
965
1052
KJ
East
10
K72
KQ964
9842
South
Q9
AQ84
A73
AQ103
W
N
E
S
 
P
1
1
P
P
X
P
P
XX
P
2
P
P
X
P
P
P
D
2X West
NS: 0 EW: 0

Board 16

West
K105
AK8
J104
AQJ3
North
AJ7
9754
6
K10984
East
Q963
103
A8532
65
South
842
QJ62
KQ97
72
W
N
E
S
1
P
1
P
2NT
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Semi-finals segment 2

Board 18

West
10642
Q52
AQ105
A6
North
K96
86432
87532
East
QJ985
A83
KJ7
Q10
South
AK73
J1074
9
KJ94
W
N
E
S
1
P
2NT
P
3NT
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 19

West
KJ10864
10954
3
KJ
North
3
AK72
A962
6532
East
972
8
KQJ854
A109
South
AQ5
QJ63
107
Q874
W
N
E
S
1NT
2
2
4
P
P
X
P
P
P
D
4X East
NS: 0 EW: 0

2: spades

Board 22

West
73
AK6
A64
AQJ65
North
A964
J72
10973
K8
East
K1085
Q98
J2
9432
South
QJ2
10543
KQ85
107
W
N
E
S
P
P
1
P
1
P
2NT
P
P
P
D
2NT West
NS: 0 EW: 0

Board 24

West
5
A92
10732
K10542
North
K10872
Q65
A8
976
East
AQJ63
J10
965
AQJ
South
94
K8743
KQJ4
83
W
N
E
S
P
P
1
P
1NT
P
2
2
3
P
P
3
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 25

West
A1042
Q9876
Q
AJ10
North
KQ75
K532
J3
KQ2
East
J86
A
A10765
9873
South
93
J104
K9842
654
W
N
E
S
1NT
P
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

2: majors

Board 29

West
Q752
A754
QJ
KJ9
North
K103
106
K10985
754
East
J96
K2
A7632
A106
South
A84
QJ983
4
Q832
W
N
E
S
P
1
P
1
P
1NT
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Board 30

West
K1087
AQ
Q106
10653
North
AQ
J743
A97
QJ74
East
J92
K965
K853
82
South
6543
1082
J42
AK9
W
N
E
S
P
P
1
P
1
P
1NT
P
P
P
D
1NT West
NS: 0 EW: 0

Board 32

West
K4
J964
K
AQJ1042
North
10972
Q107
8742
96
East
Q65
A32
AJ963
53
South
AJ83
K85
Q105
K87
W
N
E
S
1
P
1
P
1
P
1
P
3
P
3
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Quarter-finals segment 6

Board 19

West
KQJ86
Q65
K
AJ53
North
542
A8
Q10754
1042
East
10973
J103
AJ62
K7
South
A
K9742
983
Q986
W
N
E
S
P
1
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

3: Limit raise

Board 22

West
Q105
K76
8742
1032
North
AJ87
105
Q5
J9865
East
643
QJ94
KJ10
AK4
South
K92
A832
A963
Q7
W
N
E
S
1NT
P
P
P
D
1NT East
NS: 0 EW: 0

Board 23

West
K10954
K65
3
AKQ5
North
Q83
A9
AJ1072
643
East
A7
J842
K86
J1087
South
J62
Q1073
Q954
92
W
N
E
S
 
P
1
P
1N
P
2
P
2
P
3
P
3N
P
P
P
D
3NT East
NS: 0 EW: 0

Board 24

West
QJ1072
J5
A109
K93
North
8
K86
KQJ83
A842
East
K654
AQ942
7
1065
South
A93
1073
6542
QJ7
W
N
E
S
P
1
1
P
1
2
2
3
X
P
3
P
P
P
D
3 West
NS: 0 EW: 0

Board 25

West
AJ102
QJ1032
Q82
3
North
K96
A9
J10953
1052
East
54
K864
AK6
QJ96
South
Q873
75
74
AK874
W
N
E
S
P
1NT
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 26

West
KQ53
KJ3
Q975
104
North
9
AQ6
AK106
A7653
East
AJ762
5
J432
KJ9
South
1084
1098742
8
Q82
W
N
E
S
 
P
P
P
1
1
3
3
4
4
P
P
X
P
P
P
D
4X East
NS: 0 EW: 0

Board 27

West
1072
K108732
AKQ
3
North
K84
J64
J532
K107
East
A3
A9
876
AJ9842
South
QJ965
Q5
1094
Q65
W
N
E
S
 
P
1
P
2
P
2
P
3
P
3
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 28

West
A8
AJ8
AQ92
KQ52
North
Q102
K1042
J10
J1096
East
KJ7653
73
764
A7
South
94
Q965
K853
843
W
N
E
S
 
1
P
1
P
1N
P
2
P
2
P
2N
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

1: Strong

1: Spades

Board 29

West
K87543
10
108752
3
North
AQ
Q8762
QJ9
942
East
J10
AK3
K643
AKJ6
South
962
J954
A
Q10875
W
N
E
S
1
1NT
3
4
P
4NT
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Board 31

West
5
J985
K9865
K64
North
K10982
AK4
73
A75
East
AJ43
Q2
J1042
QJ10
South
Q76
10763
AQ
9832
W
N
E
S
P
P
1
P
2
X
XX
3
P
P
P
D
3 East
NS: 0 EW: 0

Board 32

West
K10
Q10843
K93
K85
North
85
652
A10652
432
East
Q9643
J7
QJ7
1076
South
AJ72
AK9
84
AQJ9
W
N
E
S
1
P
1
P
1NT
P
2
P
2
P
P
P
D
2 East
NS: 0 EW: 0

2: transfer to spades

Quarter-finals segment 5

Board 1

West
K8
9764
1063
10942
North
Q952
AQJ5
42
Q86
East
1076
K2
AKJ87
A75
South
AJ43
1083
Q95
KJ3
W
N
E
S
1NT
X
P
2
P
P
X
P
P
P
D
2X West
NS: 0 EW: 0

Board 2

West
Q84
7
98765
J1064
North
7
K93
AKQ3
87532
East
AKJ106532
AJ2
2
A
South
9
Q108654
J104
KQ9
W
N
E
S
1
2
P
4
6
P
P
P
D
6 East
NS: 0 EW: 0

1: Strong

Board 5

West
K96542
84
52
943
North
Q87
A106
10743
865
East
103
KJ532
KQJ96
A
South
AJ
Q97
A8
KQJ1072
W
N
E
S
P
1
2
P
P
X
P
2
P
3
P
3
P
P
P
D
3 East
NS: 0 EW: 0

Board 8

West
Q85
KQ10862
K92
8
North
764
A54
A1083
QJ2
East
AK93
9
J4
AK9754
South
J102
J73
Q765
1063
W
N
E
S
2
P
3
P
3
P
3
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Board 14

West
J
K1097
AQ653
AQ4
North
A865
2
K1084
J982
East
7432
AQJ8
7
K753
South
KQ109
6543
J92
106
W
N
E
S
P
P
1
P
1
P
3
P
4
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 15

West
AKQJ6
94
85
K763
North
52
K1087
KQJ63
AQ
East
1097
AQ653
A7
J102
South
843
J2
10942
9854
W
N
E
S
P
1
X
XX
2
P
3
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Quarter-finals segment 4

Board 18

West
AKJ6
Q10
AJ6
K1073
North
Q3
J9643
8754
95
East
10854
A2
K1092
AJ2
South
972
K875
Q3
Q864
W
N
E
S
1NT
P
2
P
2
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 20

West
AQ3
AQ10
J1082
A106
North
74
6
AKQ53
KQ983
East
J1085
KJ42
7
J742
South
K962
98753
964
5
W
N
E
S
1
P
1
P
1NT
P
2
P
2
X
P
P
P
D
2X West
NS: 0 EW: 0

Board 21

West
AQJ763
KJ1072
3
Q
North
K108
A964
A5
J732
East
92
85
KJ1092
K1094
South
54
Q3
Q8764
A865
W
N
E
S
1
P
1
1
P
P
2
3
P
P
P
D
3 West
NS: 0 EW: 0

Board 22

West
102
A10
AJ1073
AQ87
North
43
74
854
KJ5432
East
K865
KJ95
Q96
109
South
AQJ97
Q8632
K2
6
W
N
E
S
P
1
2
P
3
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Board 24

West
Q103
K932
AKJ7
98
North
AK87
J6
64
KJ1076
East
94
AQ7
Q9832
Q32
South
J652
10854
105
A54
W
N
E
S
1NT
P
P
P
D
1NT West
NS: 0 EW: 0

Board 25

West
10
KJ954
K107
Q1073
North
AQ10763
Q42
J864
East
AQJ765
AJ8653
5
South
K98432
82
9
AK92
W
N
E
S
2
2
P
2NT
P
3
P
P
P
D
3 East
NS: 0 EW: 0

Board 26

West
AK532
QJ32
A96
7
North
974
K104
Q542
AJ3
East
J8
8765
KJ
KQ1094
South
Q106
A9
10873
8652
W
N
E
S
P
P
1
P
1NT
P
2
P
3
P
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 27

West
K1065
107
AK7
K975
North
J942
AJ84
985
J2
East
A87
Q962
6
AQ1084
South
Q3
K53
QJ10432
63
W
N
E
S
P
1NT
P
2
P
2
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Board 31

West
75
AQJ98654
A6
J
North
Q43
7
Q843
96532
East
AK1098
2
KJ1072
87
South
J62
K103
95
AKQ104
W
N
E
S
1
4
P
P
P
D
4 West
NS: 0 EW: 0

Board 32

West
Q7
A10632
109
9874
North
J102
J9
AK2
KQJ105
East
AK643
K74
75
A32
South
985
Q85
QJ8643
6
W
N
E
S
P
1
1
P
2
X
3
P
P
P
D
3 East
NS: 0 EW: 0

Quarter-finals segment 3

Board 7

West
A52
AQ972
KJ5
Q5
North
Q43
84
AQ932
A83
East
J86
KJ3
108
KJ1094
South
K1097
1065
764
762
W
N
E
S
P
1NT
P
3NT
P
P
P
D
3NT West
NS: 0 EW: 0

Board 10

West
J983
AJ72
AQ4
A9
North
AK642
109
95
KQJ2
East
Q1075
K5
K10832
76
South
Q8643
J76
108543
W
N
E
S
 
P
P
1N
P
2
P
2N
P
3
P
3
P
4
P
P
X
P
P
P
D
4X West
NS: 0 EW: 0

Board 11

West
1098
AKQ75
5
AKJ7
North
A63
108
742
109863
East
Q
96432
QJ1093
Q5
South
KJ7542
J
AK86
42
W
N
E
S
 
2
X
3
P
P
4
P
4
P
5
P
5
P
P
P
D
5 West
NS: 0 EW: 0

Board 12

West
AJ9
1098653
AJ73
North
103
765
QJ42
9842
East
Q8
AKQJ102
7
KQ105
South
K76542
9843
AK
6
W
N
E
S
P
P
1
1
2
P
2
P
3
P
4
P
P
P
D
4 East
NS: 0 EW: 0

Board 14

West
AKJ10
42
K85
9742
North
Q986
AJ3
Q96
J65
East
753
97
AJ1032
A108
South
42
KQ10865
74
KQ3
W
N
E
S
P
P
1
P
1NT
P
P
P
D
1NT East
NS: 0 EW: 0

Board 15

West
A963
K95
KQ
K954