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Comments on the CAS Report
(Page of 14)

I am going to give some clarifications, corrections, and personal comments about the CAS ruling. There were a number of statements in the report that indicate that the CAS panel did not understand the statistical testing. I do not know how much the particular presentation caused the misunderstanding so I will not discuss that issue in detail. However, since this is the one thing many people have read about the statistical work on the case, I feel it is appropriate for me to respond. I am writing this to inform people about the case so that people can use this information for the future. I do not want to lay blame but rather let people use this to better understand the case.

This is a companion article to my other article describing the statistical modeling for this case and I recommend reading that first. I will try to restrict myself to comments made in the public CAS report, since inclusion in the report indicates that they were taken seriously by the panel. I use bold face for quotes from the report. A full copy of the report can be found at:

The paragraph numbers are from the CAS report. The first EBL accusation was made in September 2015 and there were several reports written by the defense in November 2015. The reports of Nic Hammond, Peter Buchen, and myself were written in December 2015. At least mine was written without seeing the September 2015 accusation or the November 2015 replies.

The opinions expressed in this article are my own and are my reactions to the CAS report. I have not been in contact with any representative of the European Bridge League since the CAS decision was released and they have nothing to do with this article. I am happy to open the comment section to clarifications by any party as well as reasonable debate and opposing views on these issues.

The report first lays out facts, then the Appellants (defense) argument, then the EBL response, and finally the CASopinions. I have chosen to make my comments in order of appearance in the CAS report, but this means that the comments about the CAS conclusions appear toward the end of this article.

The first comments that I quote come from the early reports made by the defense, in November 2015.

4. …physics clearly states that it is not possible to calculate the exact angle of an object through the 3D to 2D transformation of a video unless are known shooting distance, orientation angle, focal length and optical aberration of the lens.

This is an example in my mind (there will be many more) of scientific obfuscation. To some extent the fact as stated is true, but if one were to take this on complete face value one could never determine anything from a 2D picture. There are ways to determine horizontal (H) vs. vertical (V) precisely enough, even though it might be a little imprecise in edge cases. The fact that an occasional error could be made does not invalidate the statistical test (provided that the determination is made independently of viewing the hand). Nic Hammond did most of the work on this and I will not discuss these issues more.

5. a. If a real code exists it has be applicable to all cases, without discarding any of them according to marginal utility. An ambiguous card being neither clearly horizontal nor vertical clearly implies

i. Either the definition of a clear rule for ambiguous cards

ii. or the definition of the rule as a dichotomy…

This is clearly not correct. Also, and this is very important, even if there is an absolute code it is possible that only part of the code has been cracked. The statistical test is designed so that knowledge of the entire code is not necessary.

G) It has been pointed out to me that even opening leads in singleton suits have been discounted in order to increase the number of fits, when apparently this could have a high significance on the game if it is used to transmit unauthorized information at the same time.

Again, this was written before the statistical test was done explaining why only part of the code is being tested. It might have helped the case if the original accusation made in September 2015 included this information (this relates to my recommendation that committees include statistical expertise).

… cards defined as ambiguous must be included in the sample and their conclusion only leads to a reduction in the representatives and reliability of the sample.

This was written before the EBL Expert reports. These individuals did not appear in any hearing (in person or remotely) as far as I know. None of the statistical witnesses other than the latecomers (Regan and Viret who wrote reports after the EBL hearing) were part of the CAS hearing that I was involved in. Professor Canela did appear at the EBL hearing and as I mention below a statement that he retracted at that meeting is included in the report here. I am not sure that the Panel was informed about how bad some of the statistical reports were. I gave several informal reviews to the EBL committee and the lawyer, but I was never asked to prepare them formally and they were never presented as far as I know. (In fairness to the EBL, I was an unpaid consultant and they could have been worried about asking too much of me. I was not able to give unlimited time to this project.)

11. The first few pages of my report were about the general principle of statistical testing for cheating. Included in this was the fact that it was not necessary to determine the exact code in order to determine cheating. At no point does the panel state that I (as well as Peter Buchen) made this point even if they state the opinions of the other side on this issue. Peter Buchen has professional credentials in statistics. Nic Hammond has a good amateur knowledge of statistics and was in charge of most of the data collection (an important part of statistical analysis, of course).

One thing that I did was explain how to use the fact that we may be reusing the same data. I am later accused of evading the issue, yet they publish my (admittedly imprecise but the best I could do) recommendation on how to adjust the probability if none of the data were fresh. Later on we found out that some of the data actually was fresh since Maaijke Mevius had not viewed all the matches on the vugraph.

Peter Buchen and I used Kit Woolsey’s data (82 matches out of 85 signals) that were available on the web. Later matches were added to this. The other matches were not included by Kit only because he could not find them (it is my understanding they were slightly mislabeled and hence a little harder to find in a search).

Greg Lawler’s undated report … I will assume there were 85 signals given with 82 matches. There was a slight bias for horizontal leads … to be very conservative we will choose q=.6

The meaning of q is discussed in my other article. In my report to the EBL, I used the word “signal” for what I call “action” in my first article. While signal is probably the better informal term (and why I chose it), it can have technical confusion with the way signal is used more scientifically to represent what one is trying to send as opposed to what the person actually sees.

This is less than 10^{-14}

It becomes even smaller with the larger data set.

This is a straightforward mathematical computation, but it must be understood in context of the particular situation…I do not know how many matches were viewed by Ms. Mevius and the others in cracking the code. However, even if all of them were used, if we said that the number of possible codes viewed…is at most a million, the chance that any of these codes fit so well is less than 10^{-8}.

In the previous section of my report I had discussed how to handle data that was not fresh. I discuss this in my other article. Here I was trying to do a calculation assuming that all the data was not fresh (a fact that turned out not to be true but I did not know at the time).

14. Hammond chose to use a "balls in an urn" or ahypergeometric model (for those who know what that means) rather than a binomial model for calculating the probability of a very unlikely event. It really did not make much difference for computing a really small probability.

15. … Canela’s report dated 1 June 1016 … stated the following … Not only the data are changed, but also the hypothesis, which now associates the vertical position of the card to the unseen honors, dropping the singleton.

Professor Canela’s report was presented shortly before the EBL hearing on Fantoni-Nunes. Unlike some of the other reports, it was responding to the “EBL Experts” (Buchen, Hammond, and myself). This paragraph refers to the precisely formed hypothesis that differed from what was given in September 2015. I do not know the details of what happened before I was consulted, but I dare say that it might have helped here to have consulted with us earlier.

The first requisite is that the hypothesis has to be developed independently of the data used to test it, either from previous data or from a theory. Data always confirm hypotheses that have been extracted from the same data. In the academic jargon, we call this “fishing for a hypothesis”.

While I disagree with the absoluteness of the statement, there is some truth in it. One does need to worry about whether data is fresh, and I have discussed in my report and I will discuss more on the next page. Both the F-S and F-N defenses at various times proposed “alternative codes” that fit the data well.They were complicated, arbitrary codes that did not make sense from a bridge perspective; I discuss one below. At this time, it was still not known which matches could be considered “fresh data”. Professor Canela never discussed the fact that I had made an allowance for the fact that the data might not all be fresh.

Mr. Buchen’s report

… It may seem that p=.5 is an obvious choice, but it is not so. It would be if the players were always placing cards either horizontally or vertically, with equal probability. None of these is true…

Peter Buchen had done calculations with p=.5 as representative acknowledging that this was not the exact value. One needs some value of p to put in. My use of q=.6 with the explanation given, and the fact the probabilities were still astronomically small, should have satisfied this worry.

Mr. Hammond's report

Mr. Hammond suggests that…Because it turns out that the potential code is not a proper code, but an intermittent code. This, together with the fact that … some of the cards do not fit the presumed code, leaves us with a code such that

  • Sometimes one player cheats the other player
  • Sometimes includes ambiguous cards.

I do not see how such a code could work.

The term proper code is not a technical term that I know. There are several comments made here. One is obvious to me: one does not confuse a partner by not sending a message. It tells partner that one is not sending a message. A code does not require one to always send a message. Also, the fact that there are some placements of cards that we do not know the meaning of is not cheating or even necessarily ambiguous. It is possible that they have a meaning that we do not know, or perhaps they are telling partner that the player is choosing not to signal. Professor Canela is not a bridge player, so his comment, “I do not see how such a code could work” should be assessed with that in mind.

To evade the “testing on the same sample” question, Mr. Lawler says in the last page of his report that, even if other cards may be found, the probability of finding a code that fits as well as the proposed one is less than 1 in 100 million…the defense gave me the following code: the card is placed vertically when

  • The lead suit contains an ace and a 4 or
  • The led suit contains a king or
  • The lead suit is made of five cards in the suit without a jack or
  • Nunes leads with a singleton
  • And horizontally otherwise

There is a lot to criticize here. I did not evade the question, I addressed it. I discussed the use of non-fresh data earlier in my report in general and the comment on the last page to which Professor Canela refers is the quote from my report that is given above under paragraph 11: the quote starting “This is a straightforward…”. While it might be difficult for a lay person, any person trained in statistics should realize that I do NOT say what Canela claims that I say. Indeed, Professor Canela retracted the remark at the EBL hearing when this was pointed out. He was not at the CAS hearing, but the remark had been retracted but was still re-presented by the defense.

The code that the defense suggests is the kind of code that will fit well. It has a couple of properties:

  • It is relatively complicated.
  • It correlates fairly well with the simple code we are testing
  • The deviations from our conjecture that have been made are very arbitrary based on the actual data and make no sense as a code for bridge.

When I estimate maybe a million possible codes tested, I am trying to give an upper bound for the number of reasonable, simple codes that a code breaker might consider. It is not an estimate for the number of artificial codes one could create of the type mentioned above. The fact that Professor Canela knew no bridge might have something to do with his inability to see the inappropriateness of the defense alternative code.

The report of C. Colombo dealt with issues of determining “horizontal” vs. “vertical” and I was not the expert for this. (Nic Hammond was.)

42. 8. […] In particular, these expert reports analised the probability of observing the data assuming the hypothesis of randomness, but their conclusions express the probability that the players were cheating given the data observed. This represents a fallacy of the transposed conditional (also commonly known as the prosecutor’s fallacy). (…)

M. Viret is a lawyer with some specialty in doping cases. She decided to discuss the “Prosecutor’s Fallacy” and to spend a lot of time on it. There have been several cases when lawyers have made some ridiculous statements confusing “the probability of unusual behavior assuming innocence” with “the probability of innocence given unusual behavior.”I will not list the cases but the most famous ones were denounced by the statistical community and showed the need for statistical expertise as well as other scientific expertise when analyzing, for example, doping or medical malpractice cases. Dr. Viret was accusing the EBL disciplinary committee of making this kind of mistake.

Here she is at least misleading. It is true that the probability calculations were assuming randomness, and that we expressed the conclusion that the players were cheating beyond a reasonable doubt. However, at no point in the statistical analysis was the probability of data given randomness confused with the probability of cheating given the data nor was their any number given for the probability of cheating. I made a point of saying that this explicitly in the CAS hearing --- that this is not the kind of mistake that a statistician makes. There is no record in the CAS report about my refuting this statement nor the fact that Dr. Viret did not respond to my refutation. To me, to accuse a statistician of making a mistake like this is like saying that a WC bridge player could not have intentionally done a double squeeze since we all know that double squeezes are difficult for most players.

31.(…) Experts can only make statements with respect to evidence [E] they have been provided with. Only the legal panel is in a position to assess the probability of the hypothesis [H] at stake in the case. This is because only the panel has an overall view of the evidence on the record necessary to appropriately weigh that evidence.

It is important to realize that what Dr. Viret writes is mainly opinion although she does discuss some precedents from other cases. The first statement here is clearly wrong as stated literally. By definition, experts are bringing in more information than just the evidence; that is what makes them experts. In this case the statistical experts were also tournament bridge players who knew enough to give their assessment of guilt beyond a reasonable doubt. I certainly agree that the panel may have some more information than the experts have and hence they should use that information as well as the opinion of the experts in making their ruling.

34. (…) The panel cannot simply endorse the expert’s conclusions without assessing whether those conclusions are soundly rooted in the expert’s analysis.

I agree with the statement and it calls for sufficient competency on the panel to be able to do such an assessment.

Kenneth Regan’s report if read carefully first showed that he essentially found the statistical tests valid. His job (for which I assumed he was paid) was to try to find things that could be questioned. Some of his discussion used slightly different language but was essentially addressing the fresh data issue. He also wrote

The null-hypothesis modeling may need adjustments that entail a statistical test of lower sensitivity than the one described, requiring a calculation of Pr(R | H) that gives less extreme results.

Professor Regandiscussed among other things that it is very difficult to discuss “random” behavior. In my report, that was phrased at times a little informally for the sake of my audience, I described the null-hypothesis as being “plays at random” or something of the like. In fact, as I described mathematically in the report and I believe I expressed in the CAS hearing (with Peter Buchen agreeing) was that the statistical tests did not require defining the notion of random, and the only thing that was being used is the independence of the play by the player from the play that the conjecture would dictate. This is discussed in my other article.

51. The Disciplinary Committee concluded that the Appellants cheated by only trusting on the statistical analysis of the EBL Experts which has been seriously challenged by M. Colombo, Salvatierra, Canela, C. Columbo.

EBL Experts is being used in this document to mean the reports of myself, Buchen, and Hammond. These were done after the reports of M. Colombo and Salvatierra so this statement is clearly false. For Canela, while there were some perhaps legitimate issues for debate (fresh data), he showed that he did not understand my model nor could he understand the fact that the defense’s alternative code made no bridge sense. (It is unclear whether this was a question of competency, the amount of time that was spent on the reports, or possibly that he was particularly asked to find ways to criticize the report.) At the EBL hearing he retracted at least one of his incorrect statements. None of these four people were present (either live or remotely) at the CAS hearings.

I will go through some of things mentioned in paragraph 51. These are statements of the Appellants’ case (not statements of the CAS panel directly) but the fact that they are included imply that the panel used these facts in their decision making.

  • The cards are not always placed in a vertical or horizontal way, and the cards positioned diagonally were excluded from the statistical studies. Thus. The classification… is subjective, arbitrary, and unfair.

This was explained in the model but the model itself was not directly referenced or criticized.

  • Canela and Salvatierra have established that the method used by the EBL is incorrect since it is based on the probability of causality far below 100%; the evidence supporting an accusation of culpability shall be based on a probability as close to certainty …

I do not recall what they are referring to in these statements. The Salvatierra report was written before the EBL Experts reports.

  • Lawler stated that we cannot talk about randomness when the Appellant’s natural position for placing their cards and further kind of behavior has not been previously analyzed.

As I stated and you can read in the probability calculations, that the upper bounds did not depend on knowing the natural “random” placement of cards of F-N. I admitted that this is something we could not determine, but at the same time pointed out that it was not important. This would be noted by someone with moderate statistical expertise.

  • Furthermore, Regan stated that the EBL classified the cards in a biased way, the statistical tests were construed with key elements determined after the facts…

This is another way of discussing the “fresh data” issue. Probabilities were modified in my report when discussing not fresh data. This comment does not have any validity when looking at fresh data.

  • Canela rejected the subjective classification of the cards as horizontal and vertical because the Players also placed…

Again my report and the reason for the statistical test were not described in the CAS report. This same issue is brought up many times (as you have seen) and the issue seems only valid in the context of not fresh data. For studying the future, the fact that one is looking at a subset of hands does not reduce the validity of the test. (It might reduce the power of the test, that is, the probability of detecting signaling if it is happening; but it does not invalidate the test if communication has been detected on those hands.) As far as not fresh data, my report discussed this.

  • Viret has argued that the experts should normally assess the “probability to observe the evidence assuming a hypothesis” and the deciding bodies should look for the “probability that a hypothesis is true, based on the overall evidence”.

I agree with both of these statements to some extent, but they do not preclude the experts, especially if they are statistical experts with knowledge of tournament bridge, to express their opinion of the “probability” that the hypothesis is true, based on the overall evidence. This probability was not calculated exactly (it never is because it is too imprecise an idea and depends too strongly on a priori probabilities of cheating that cannot be given exactly) but the usual notion of confidence “beyond a reasonable doubt” was expressed by the experts.

  • According to Viret, the Disciplinary Committee has concluded from the statistical evidence what is known in criminal law as the prosecutor’s fallacy i.e., “the fallacy of equating (1) the probability of the presence of the evidence, assuming innocence, to (2) the probability of innocence, assuming presence of the evidence….

This was not done by the statistical experts and the Disciplinary Committee relied on the recommendations of the statisticians. Viret’s comments were about the statistical reports and they do not confuse these.

  • Viret stated that the EBL experts included in their conclusions that the Appellants “cheated beyond reasonable doubt”. However the Panel members --- and not the experts --- are those who shall give value to the evidence taking into account the entire file.

The first statement is true and certainly the Panel should reassess any such recommendation from experts using material in the entire file that the experts did not have. However, there is nothing that prevents qualified experts who know the difference between P(H | E) and P(E | H) (which expert statisticians do) from expressing their opinion given the information that they have.

103. In the Panel’s view, the main issues to be resolved were…

B. Was there Inappropriate Communication between the Appellants…

There were three possible issues in the report mentioned in paragraph 103. One was a technical issue about the members of the Disciplinary Committee that the CAS Panel found in favor of the EBL posiiton. A third was the severity of sanctions if the parties were found guilty which the CAS panel did not deal with. The second and the most important, to which the above quote applies, was the one was determining in inappropriate communication occurred. Here the panel has it correct --- it is the existence of inappropriate communication that is the issue and not the precise nature of it.

112. … the Panel has to be convinced of the existence of the “prearranged method of communication" (i.e. the alleged Code).

Most of paragraph 112 is fine until one gets to this last sentence. In my opinion, the word “the” before prearranged should have been “a”. As I pointed out, and is pointed out in paragraph 103, the key thing is to establish that they have a method of which we may know a part; the issue is not the entire Code. As I have stated before, I stated this in my report explicitly, but it is so logical maybe I did not emphasize it enough. If every time a person says “Bagga” they are referring to a dog and every time they say “Magga” they are referring to a cat, I can conclude that they are communicating with each other even if I have yet to figure out what they mean when they say “Tagga”.

115. Taking into account the elements of the Code, and given the evidence brought to these proceedings, the majority of the Panel finds that there are several inconsistencies in the alleged pre-arranged method of communication identified by the Respondent…

Most of these are not inconsistencies for the test that I described. I cannot say how much the presentation by the EBL affected the view of the Panel here (as I have stated, I believe it is very important for the statistical modelers to be part of the committee investigating and making charges against players based on statistical evidence).

The positioning of the cards: It has been proved that the Players did not place the cards solely in a horizontal or vertical way but also in a diagonal way… The majority of the Panel considers that this is problematic for the function of the Code because the Player placing the diagonal leads would only mislead his partner about the information intended to give.

As far as I know, the Panel were not bridge players. This paragraph also casts doubts, frankly, on their reasoning abilities. If H means one thing, and V means another thing, and one plays D there are at least two reasonable interpretations: there is no meaning for D and hence the player is choosing not to signal or there is a meaning for D that we do not know it at the moment. (There is also a possibility of player mistake.) It will not mislead partner; at most it is telling partner that the leader is choosing for whatever reason not to give information.

(ii) “False positives”: A second inconsistency in the EBL’s accusation is that there are several cards that are “false positives” meaning that when the leads are vertical the suit does not contain a high honour and when… The Respondent itself has stated that in 112 lead cards there were 8 “false positive” cards. Again,… this is a problems for the proper functioning of the Code since the Player on lead would be giving the wrong information to his partner.

A “false positive” in this case is a play that does not match the play that would be predicted by the conjecture. The exact number of false positives recorded depends a little on some details of data collection. I will not discuss this. Rather, there is no discussion here that the statistical model allows for “false positives”. There are a number of possible reasons for a false positive: the code is not known precisely, a player chooses to lie for some reason, a player choosing to stop signaling for some other reason such as state of the match, or player error. Even using these numbers, anyone with any basic statistical knowledge would realize that for an event of probability between .4 and .6 of happening (matching the conjecture), the probability of 104 matches out of 112 is incredibly small. The Panel forgot again what it was testing (see paragraph 103 above).

(iii) The Value of the Code…

I was not present for the bridge expert testimony in the hearing and so I will not comment on the accuracy of the description here. (My knowledge of the statistical part of the hearings does not give me confidence that the Panel gave a fair description of the events so I would prefer other verification before deciding what is written is fair.) I will say that the reason to have the testimony is to demonstrate the value of the code. This is the kind of explanation that is very hard to give in front of people who do not play bridge. I would just warn people that any discussion of cheating at bridge that goes to a hearing or trial outside the bridge community could be subject to decisions made by people who do not understand the game.

116. Given the aforementioned inconsistencies, the majority of the Panel cannot be convinced…of the existence of the Code (or at least of the one asserted by the Respondent) because …

The Panel’s job was to determine if illegal communication was occurring; it was not to determine if exactly this Code was correct.

117. Furthermore, the Panel has also noted that Prof. Lawler stated at the hearing (and in his report) that “it is possible that we do not know the entire Code, we are only considering part of the Code”. This was seconded by Prof. Buchen who stated also at the hearing that “we do not have the whole story because the original observations even went down to second hand leads and…” The majority of the Panel follows from these statements that the (EBL) experts themselves find the analysis of the Code to be incomplete and considers that it cannot take the risk of sanctioning the Players based on an alleged partial code (with inconsistencies) because there is a significant risk that the Code does not exist at all or that the subsequent hypothesis, if any, would be completely different than the one at stake.

There is much to say here. First, I have talked about the model. We were not testing if the Code was exactly correct. That was not the intent of the analysis. (Let me emphasize again it is important for disciplinary committees to understand this and to make this clear, This is why there should be statistical representation on these committees.) The statistical model would not find such a strong correlation if the “actual” codes of the Players did not correlate very strongly with our conjecture on the hands that were are observiting. We just cannot tell if it exactly correct. Again, the Panel has to go back to paragraph 103 to determine what its goal was. The further comments of the Panel are, frankly, question even more their competence. The EBL tests were on opening leads. There have also been analysis of other leads and the possible meanings for them. The fact that the EBL did not test for these is saying nothing about the existence of them. Whether or not they exist has no bearing on whether the part that the EBL was looking at is illegal communication. The final sentence above shows that the Panel did not understand the statistics --- the chance that the “entire Code” (whatever that means) would be significantly different than the conjecture Code, when viewed on opening leads from non-singletons with H or V, is miniscule --- the chance of so many matches is so small.

118. How can the Panel be comfortably satisfied in condemning the Players if the Code is contradictory? It should be recalled, that the Respondent took the responsibility…of proving the “prearranged method of communication” which, in the eyes of the majority of the Panel, has not been done

This is all explained in the statistical model. As far as I can tell, the Panel never understood the statistical model that I made (and was backed up by Buchen and Hammond). Understanding the model is the first step to answering the question above. Again, the word “the” before prearranged should be “a”. Again, look at Paragraph 103.

For paragraph 120, I will not consider the issues that have already been discussed and just point out one big issue.

➢ The inconsistencies on the “fresh data”. There is a common understanding between the parties that the hypothesis could not be tested with the same information used to discover it. In this regard, the Panel notes that the Respondent took into account as “fresh data” the 7 matches of the Competition not studied by Ms. Mevius and the cards played in the Bermuda Bowl (i.e. 20 cards). As a first remark, the Panel has reviewed the videos of the Bermuda Bowl, and, given the low quality of the videos, it is very difficult to state in first place which cards were placed in a horizontal or vertical way. As a second remark, it should be said that it is unknown how many of these cards could be considered diagonal, … how many could be false positive (including the Slavinky “Jacks”), or how many plays could be considered non-sense for the game. Therefore, the major of the Panel considers that the calculations based on “fresh data” are not reliable either.

This is almost unbelievable. Let us start with the second sentence. If they read my report they would have known that I DID discuss how to test data that was not fresh. I certainly agree that the tests are much more powerful with fresh data and that is why we pressed to find out which data was fresh. There was one Bermuda Bowl match where the video was not as good. One can debate if one can tell the orientations well enough (Nic Hammond says yes although it takes careful looking) but perhaps this could be debated. However, if one were to remove those hands from the analysis, one would still have the data from the 7 unwatchedsets/matches in the Competition. There is no reason to throw them out. The discussion about Slavinsky “Jacks” is obfuscation and should have been noticed as such. The statistical tests were about a particular conjectured code and has nothing to do with this issue.

121. With regard to the other elements brought forward by the EBL to prove the existence of the cheating allegations, the majority of the Panel finds that they are not effective either. In particular, the sanction imposed on the Appellants by the American Contract Bridge League was not based on the Code (as stated by the EBL) but on a more complex code that combined “noises” made by the Players and “spacing bidding cards”… This only confirms that the cheating hypotheses against the Appellants vary considerably.

This paragraph is even more incredible. The fact that the EBL might have not found all the codes and the ACBL found others does not in the least bit invalidate analysis of a particular aspect of a code. The only thing that it does is increase the a priori probability that the pair was cheating. While I do not know the details of the ACBL allegations, I believe they dealt with another aspect of communication, the bidding. The fact that the EBL did not discover, or did not have sufficient evidence to press charges on, irregularities that occur during the bidding (or maybe in later opening leads) does not in any way invalidate tests on irregularities on opening leads. If anything, it INCREASES the probability of cheating since it increases the a priori probability that players might be willing to have illegal codes. Even if some of the alternative code referred to the opening leads, that would only mean that the code we were testing was not complete, and this is something we allowed in our testing.

If another group has proposed a more complex code that deals with other aspects, thisdoes not imply that the hypotheses "vary considerably" on the aspects studied by the EBL.

To me the reasoning of the Panel sounds analogous to this. Suppose a man is accused of robbing a bank. Evidence is given about the bank robbery. However, it is found out later that someone else has accused him of robbing another bank the day before. Since theevidence of robbing the bank is incomplete (does not discuss the other robbery), it cannot be used to find the man guilty.

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