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Judy, Given the record of US citizens in generally imperfect knowledge of other countries customs/history etc., why do you assume that a likely non-American is obliged to know anything about Gettysburg Address?

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JoAnna, I think it appropriate to remind Karl Popper's opinion on rational discussion, i.e. that the adjective ‘rational’ applies whenever the parties involved have some doubt in the certainty of their statements

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Nick, That's sets the point: it is really difficult to state cheating in legal terms unless the diamond king lead type of fact was established. If the evidence is statistical, one expert witness may argue that p-value is 0.15 (not significant) and the other it's 1e-100. Of course, the legal costs may cause a given pair to give up yet it may be still an innocent pair. That's scary both ways: innocent pairs may be dragged to courts; guilty pairs may invent cheating methods too difficult to be clearly unveiled.

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I have ‘legalese’ question to Nick. A convincing proof of bridge cheating can be constructed only on statistical basis. Here I note an exception: we observe something blatant and successful, like leading diamond king from KQJT9,xxx,Kx,xxx against 1N-3N with partner holding AQJxx in diamonds. Apparently this exception doesn't apply to BZ; therefore, in such a proof, a null hypothesis of not cheating has to be rejected with some low p-value. What kind of p-value (if any) provides a proof ‘beyond reasonable doubt’ in legal terms? 0.05, 0.01, 1e-20?

At a different post I critiqued Jassem's piece, which finds no evidence for BZ cheating based on 6 hands and faulty methodology (similar critique applies to those who find BZ proven guilty on the basis of six hands, unless the exception similar to the above applies). For somebody able to collect enough data and with some knowledge of statistics, I repeat this critique with the link describing proper methodology:

I read Jassem's report. Unfortunately, plain correlation he used doesn't work with categorical data. One needs to build a contingency table; apparently, much more hands are needed for any statistical conclusions. Here's a vary plain description of the methodology for those willing to work on it: http://www.pitt.edu/~nancyp/stat-1000-s07/week5.pdf Chi-square test is in any statistical package and in excel (chitest function).

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Actually, if Poland wins BB, it will be the worst penalty for BZ. They've never won any worlds (transnational teams don't really count as such). Should BZ be proven guilty, will the results of BB be adjusted?

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Having read the Josh piece I find it unfortunate that the present atmosphere surrounding bridge provides an opportunity for promotion of personal views filtered with little critical thought

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I read Jassem's report. Unfortunately, plain correlation doesn't work with categorical data. One needs to build a contingency table; apparently, much more hands are needed for any statistical conclusions. Here's a vary plain description of the methodology for those willing to work on it: http://www.pitt.edu/~nancyp/stat-1000-s07/week5.pdf Chi-square test is in any statistical package and in excel (chitest function).

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Michael, I don't have time to be in the crowd looking for patterns busy with my finance papers, so my only contribution could be methodological. I'd like to address one more issue, called overfitting. For every data set, there exist a worthless model perfectly fitting each piece of data (worthless, since it will not work on any other data set). This may correspond to finding a very complex pattern of cheating. Apparently, such complex pattern may still exist. The only way to show it is in addition to showing strange gains for a given pair, is to verify that a similar pattern exists for a different set of hands.

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Michael, I believe that it is not difficult to find spurious patterns in any data, also as a researcher by profession. For example, the number of sheep grown in Australia would predict well the stock market in the US for many years. So the key issue is showing the link between the alleged pattern and successful actions which are difficult to justify on the information available to players lege artis. I'm not trying to say it is wrong to look for complicated patterns. I'm trying to say that the proof for such patterns must be stringent and that such patterns must survive the test ‘Will it be possible to accuse everybody of cheating based on such pattern?’.

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Richard, First, many thanks for the striking clarity of your response. Second, please explain how a pair may defend itself against an accusation of cheating via the pattern of signals complicated enough so that breaking it down is hardly possible?

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Richard, According you your approach, every single pair can be shown to cheat. Hypotheses to which every single possible fact conforms are worthless since they don't allow discriminating between the facts

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Olivier, The logic behind your question is similar to the logic of a question “Why do you steal, rape, torture and murder every Friday?” so don't expect too many answers

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Max, Yes and No. ‘Yes’ in this sense that statistical analysis of decisions of a particular pair compared to the decisions made by their peers on the same hands may help identifying potential cheaters. ‘No’ in this sense that very rarely there are two (or more) plays with exactly the same expected value (alternatively, two plays with exactly the same probability of success), which is a necessary condition for your method to produce alone a proof of cheating. Such proof will demand finding making plays with lower probability of success which succeeded nevertheless. An apparent extreme example of such play is leading diamond king from KQJT9, xxx, Kx, xxx against 1N-3N.

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

At a different post I critiqued Jassem's piece, which finds no evidence for BZ cheating based on 6 hands and faulty methodology (similar critique applies to those who find BZ proven guilty on the basis of six hands, unless the exception similar to the above applies). For somebody able to collect enough data and with some knowledge of statistics, I repeat this critique with the link describing proper methodology:

I read Jassem's report. Unfortunately, plain correlation he used doesn't work with categorical data. One needs to build a contingency table; apparently, much more hands are needed for any statistical conclusions. Here's a vary plain description of the methodology for those willing to work on it: http://www.pitt.edu/~nancyp/stat-1000-s07/week5.pdf

Chi-square test is in any statistical package and in excel (chitest function).

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Chi-square test is in any statistical package and in excel (chitest function).

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

I believe that it is not difficult to find spurious patterns in any data, also as a researcher by profession. For example, the number of sheep grown in Australia would predict well the stock market in the US for many years. So the key issue is showing the link between the alleged pattern and successful actions which are difficult to justify on the information available to players lege artis. I'm not trying to say it is wrong to look for complicated patterns. I'm trying to say that the proof for such patterns must be stringent and that such patterns must survive the test ‘Will it be possible to accuse everybody of cheating based on such pattern?’.

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko

Michal Czerwonko