rumour and mathematics.pdf

Rumour and Mathematics By Krzysztof Jassem,

professor at Adam Mickiewicz University, Pozna, Faculty of Mathematics and Computer

Science,

author of books on Polish Club

This article concerns the case of withdrawing the invitation to Bermuda Bowl to the pair:

Cezary Balicki, Adam mudziski.

The article is designed as follows:

Section 1. states the main facts concerned with the invitation withdrawal and the

participation of team Poland in Bermuda Bowl.

Section 2. describes the method of analysis carried out in Section 3.

Section 3. analyses material sent unofficially by Mr. Brogeland to Mr. Kalita of the Polish

national team the day after the invitation withdrawal.

Section 4. concludes the article with the authors opinion on the case as well as a suggestion

for proceeding in similar cases.

Section 1. Facts concerned with the invitation withdrawal and

the participation of team Poland in Bermuda Bowl.

Saturday, 26th of November 2015, 6:50 p.m.

This communication aears on the WBF web-page:

The Credentials Commiee of the World Bridge Federation met earlier today. It

determined that the invitation extended to Cezary BALICKI and Adam ZMUDZINSKI be

withdrawn; consequently they will no longer be eligible to play in the Bermuda Bowl in

Chennai.

Saturday, 26th of November 2015, 7:00 p.m. 9:00 p.m.

Opening Ceremony

Saturday, 26th of November 2015, 9:00 p.m. 9:15 p.m.

A talk between the Chairman of the WBF Commiee, Yves Aubry and representatives of

the Polish team: Piotr Walczak, NPC, Krzysztof Jassem, player.

The Polish representatives want to know the rationale behind the decision. The Chairmans

answers that the Commiee is allowed to take a decision of not inviting players without

giving a reason. Mr. Aubry admits, however, that a material on Balicki-mudzikis

misbehaviour has reached WBF. The material has not yet been analysed.

Sunday, 27th of November, afternoon

Mr. Boye Brogeland and Mr. Jacek Kalita have a skype talk. Mr. Brogeland expresses his

opinion that the Polish team should withdraw from Bermuda Bowl. Mr. Brogeland sends Mr.

Kalita the file that proves the hypothesis on illegal communication between Balicki and

mudziski. Aording to the allegation the pairs code consists in the way they put the

bidding cards on the tray. Specifically, the distance between bids is proportional to the value

of the hand regarding the current bidding, in other words: the larger gap, the stronger hand.

The material sent to Mr. Kalita presents two matches played by the Polish team in European

Championship in Opatija: Poland-Israel and Poland Turkey. The material from the Poland

Turkey match is selected to six boards, and tagged with Mr. Brogelands commentary.

Section 2. Explanation of the analysis method As a mathematician by education and job, I will attempt to analyse the material with a simple

mathematical tool, the correlation coefficient.

Webster's Online Dictionary defines correlation as a reciprocal relation between two or

more things; a statistic representing how closely two variables co-vary; it can vary from 1

(perfect negative correlation) through 0 (no correlation) to +1 (perfect positive

correlation) (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3576830/).

I will try to determine the correlation coefficient between the messages coded by gaps in the

bidding as stated by Mr. Brogeland, and the actual values of the hands.

I will use the following translation between card value and integer numbers:

HAND VALUE NUMBER

VERY NEGATIVE -2

NEGATIVE -1

NEUTRAL 0

POSITIVE 1

VERY POSITIVE 2

Table 1. Maing between human hand evaluation and integer numbers

3. Analysis of the Boards from the Poland Turkey Match played

at European Championship, Opatija 2014, selected by Mr.

Brogeland

3.1. Analysis of each of 6 boards Board: 19. Dlr: South/EW

A J 4 2

Q 6 5 4 3

A 7

8 3

K Q 5 7 6

A J K 10 8 7 2

K 5 6 2

K Q 9 7 6 5 A J 10 2

10 9 8 3

9

Q J 10 9 8 4 3

4

Open Room

West North East South

ATABEY BALICKI KAYA ZMUDZINSKI

Pass

1 1 Pass 2

Dbl Pass 2 3

Pass Pass 4 All pass

Brogelands commentary:

Zmuds 2D bid is almost over Pass holding 1098x x QJ1098xx x

Comment: Super minimum response

Table 2. shows the range of hands that are consistent with the current bidding.

Hand value Example hand

-2 10732 3 KQ10865 J2 -1 10732 J6 KQJ865 2 0 10732 76 AQJ865 2 1 Q103 76 AQJ865 2 2 K107 76 AQ10865 32

Table 2. Board 19: Example hands consistent with the bidding

The actual hand does not fit to any row of the Table 2. The hand is non-standard, hard to

classify. Because of the scarcity of the material (6 boards) I will not remove this hand from

the analysis. For the favour of the hypothesis I am trying to verify, I will classify the hand to

the group indicated by the message code: very negative.

Message Code Hand Value

-2 -2 Table 3. Board 19: Message Code vs Hand Value

Board: 22. Dlr: East/EW

6 5

A 3 2

K J 9 4 3 2

J 8

7 2 A K Q 9 4 3

K 7 6 Q 10 9

Q 10 6 5

Q 10 9 7 3 K 6 5

J 10 8

J 8 5 4

A 8 7

A 4 2

Open Room



1 Pass

1NT 2 3 Pass

Mr. Brogelands commentary:

Zmuds second Pass is quite far from the first one holding J108 J8xx Axx Axx

Comment: Super strong for Pass

Technical commentary: The second pass is in the standard position (see Figure 1.).

Figure 1. The picture delivered by Mr. Brogeland commented as: The second pass is quite far from the first one.

Board: 25. Dlr: North/EW

A J 10 4 3

--

A J 10 5 3 2

K 6

K 8 5 2 9 7

Q 10 K 9 8 7 5 3

K 7 8

10 9 8 5 4 A J 7 3

Q 6

A J 6 4 2

Q 9 6 4

Q 2

Open Room



1 2 pass

Pass 3


Balickis 3D is quite far from 1S AJ10xx - AJ10xxx Kx

Comment: Very strong and extra diamond for 3D

Commentary on the technical part of the bidding:

In the Polish Club version used by Balicki mudziski 2 and 2 openings show 5-5

distribution in the range of 5-10 HCP. The lower boundary of 1 is 11 HCP. The upper

boundary of 1 opening is 17 HCP (stronger hands are opened with 11). A common

agreement is that the actual bidding shows 5-5 distribution with some extras in strength that

justify overriding the previously bid suit.


-2 AJ1043 AJ10532 J6 -1 AJ1043 AJ1053 K63 0 AJ1043 AJ10532 K6 1 AQ1043 AJ10532 K6 2 AQ1043 AQ10432 K6


Message Code Hand Value 2 0

Table 7. Board 25. Message Code vs Hand Value

Board: 26. Dlr: East/All

A 10 9 6

K 8 2

10 4 2

10 6 5

Q 8 7 K J 5 4 3

J 10 7 9 6 5 4

Q J 8 7 6 A 9 3

4 2 Q

2

A Q 3

K 5

A K J 9 8 7 3

Open Room



Pass 1

Pass 1 Pass 2

Pass 3


Balickis 3C is almost on his 1S A109x Kxx 10xx 10xx

Comment: Partners showing 16+ with clubs, he has subminimum for 3C after

his 1S bid (positive already).

Commentary on the bidding:

Balickis 3 rebid shows the range of 7-8 HCP. 2 would have been an artificial forcing bid

showing 9+ HCP.


-2 KJ54 QJ2 8432 65 -1 KJ54 QJ2 842 865 0 A654 K82 842 865 1 A1096 K82 1042 1065 2 A1096 K82 1042 J106

Table 5. Board 3: Example hands coherent with bidding

Message Code Hand Value -2 1


Board: 27. Dlr: South/None

K 10 6 5

A K 6

J

A K 8 3 2

J 4 3 A 9 8

2 7 5

Q 9 8 7 5 3 2 A K 6 4

Q 9 J 6 5 4

Q 7 2

Q J 10 9 8 4 3

10

10 7

Open Room



3

Pass 4NT Pass 5


Zmuds 5D is almost on 3H bid. Qxx QJ1098xx 10 10x

Comment: Very weak 3H opening, no useful values.


Mr mudziski opened 3 hearts non-vulnerable and showed no keycard.


-2 72 Q1098743 102 107 -1 72 QJ109843 102 107 0 Q72 Q1098743 10 107 1 Q72 QJ109843 10 107 2 K72 QJ109843 10 107


Message Code Hand Value -2 1


Board: 31. Dlr: South/NS

A 8 7 3

9 6 5 4

K 10 8 7

10

Q 10 5 2 K J 9 6 4

A 8 K Q 2

4 J 9 2

J 9 8 7 6 2 K 3

--

J 10 7 3

A Q 6 5 3

A Q 5 4

Open Room



Pass 1

Pass 1 1 3

3 dble

Mr Brogelands commentary:

Balickis double is almost on 1H bid Axxx xxxx K10xx 10.

Comment: Minimal values for Double.


I am not sure about Balickis intention for double. It looks to me like a kind of co-operative

double: partner should pass with flat distribution (given the bidding), e.g. 1444, and bid on

with better shape. Table 10. is consistent with such an interpretation. All examples take into

consideration that Balicki did not bid 4 instead.


-2 A873 9654 10 QJ73 -1 A873 9654 K1087 10 0 A873 9654 10 K1087 1 A873 9654 J2 KJ7 2 A873 9654 J2 KQ7


Message Code Hand Value -2 -1


Board: 32. Dlr: West/EW

A 9

A Q 5

4 3

A J 10 8 7 6

K J 7 6 3 2 Q 10 8 4

10 2 9 8 7

A 9 8 7 K 5

3 K Q 5 2

5

K J 6 4 3

Q J 10 6 2

9 4

Open Room



2D!! 2NT Pass 3(1)

Pass 4 4 Pass

Pass 5 Pass 5

Dbl All pass

The contract went two down, 4 spades would have been set one down.

Mr. Brogelands commentary on the bidding:

Zmuds pass is far from 3D bid x KJxxx QJxxx xx

Comment: Must be suggesting values given Balicki bids 5c by himself.

Commentary on the bidding: Balicki-mudziski treat this auction as a forcing pass situation (bidding

vulnerable game before non-vulnerable opponents). Table 11 is consistent with their point of view.


-2 KJ643 J1086 J943 -1 KJ643 J10862 J93 0 5 KJ643 QJ1062 94 1 KJ643 QJ1062 943 2 5 KJ643 K1062 Q94


Message Code Hand Value 1 0

Table 12. Board 32: Message Code vs Hand Value

3.2. The results of the analysis.

1) The analysis was carried out on a small sample of selected boards that are supposed to

support the thesis.

2) One of the boards (No. 19), hard to evaluate, was classified as very weak in order to

strengthen Mr. Brogelands hypothesis.

3) One of the boards (No. 22) was not taken into account because the picture is not consistent

with its tag (big gap between passes)

Board 19 Board 25 Board 26 Board 31 Board 32 Correlation Coefficient

Coded Message -2 2 -2 -2 1

0,314944889 Hand Value -2 0 1 -1 0

The coefficient shows very weak correlation between the code and the actual hand value.

4. Conclusions.

1) In my opinion this report should end The Balicki-Zmudzinski case.

2) I suggest the following objective method of examining similar cases:

1) Take a statistically significant sample of random boards.

a. Statistical significant the number of the sample should be determined by an expert

on statistics

b. Random - The selection of the boards should by no means be suggested by any

interested party

2) Evaluate the value of each hand by a panel of bridge experts of the same experience level.

Take an average of the marks

3) Automatically classify the position of the bids to one of the classes this can be done by a

computer program based on elementary machine learning technique

4) Calculate the correlation coefficient between human and automatic evaluation

5) Let an expert on statistics interpret the result.

rumour and mathematics.pdf

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