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Applying Law 12C2 with many Possible Results

by Steve Willner, Boston, USA & Jesper Dybdal, Naerum, Denmark

in reply to a suggestion by David Stevenson


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In a discussion of a particular ruling on the Bridge-Laws mailing list it was decided that a particular 3C bid was an infraction. So it was necessary to decide on an assigned adjusted score in a jurisdiction where Law 12C3 does not apply.



David Stevenson

OK. Let's have a little table of likely outcomes for N/S without the UI, and disallowing the 3C bid....

ContractResultN/S score LikelihoodResultN/S scoreLikelihood
2S -330030%-440015%
2S* -380010%-411005%
3S -440013%-55007%
3S* -411007%-514003%
4S* -514007%-617003%

Which of these count as likely? Law 12C2 says that the non-offenders get assigned "the most favourable result that was likely had the irregularity not occurred". Forget the flawed ACBL definition of likely: it works for limited numbers of possibilities. Be honest: what do you think is a likely outcome of a case when there are several options? Would you not say that if one occurs better than one time in six it is likely? That would mean that the likely outcomes are 300 [30%] and 400 [28%]: nothing else is more than 12% [one time in eight].

So we adjust the non-offenders' score to +400.

Similarly the offenders' score should occur more than one time in twenty, which is 5%: 1700 does not apply [only 3%] but 1400 does [10%].



Steve Willner

Nonsense. The ACBL definition, properly applied, works for any number of possibilities once you have constructed a probability table as above. Just arrange the results in order with their percentages:

N/S scoreLikelihoodNotes
30030%(least favorable to non-offenders)
80010%"likely" = 1/3 is in here
11007%"at all probable" = 1/6 is in here
17003%(most favorable to non-offenders)

+800 for the non-offenders, -1100 for the offenders would be correct in the ACBL, given the above percentages. Other jurisdictions may adopt different definitions. For example, if "likely" means 1/2, the non-offenders would get +400.



Jesper Dybdal

Is this really the right way to determine "likely" when there are many possibilities?

Note that 35% of the time, the non-offenders score 800 or more. So it is "likely" that they will score at least 800, though each single possible outcome only has a small chance of occurring. Is is then reasonable (or the intention of Law 12C2) to award only 400?

I think the reasonable way of estimating the "likely" non-offenders' score in such cases is to choose the most favorable result that has the property that the non-offenders are likely to get at least that good a result. I.e., if we set the limit for "likely" to 1 in 6 (16%) as David does above, we should award the non-offenders here 1100, since the probability of at least 1100 is 25% and the probability of at least 1400 is only 13%.

I've made up an artificial and extreme example where it is even more obvious that we must do it this way in order to get a reasonable result:

N/S scoreLikelihood

If you require 1 in 6 in order to call a result "likely" and only look at single results, then the only "likely" result is -50. It would make no sense at all to award -50 to non-offenders with an 80% chance of scoring at least +400.

I've used the word "reasonable" above - but is it also legal to interpret the words "the most favourable result that was likely" in this way?

A very literal interpretation of the word "result" would lead to the answer "no", but there are many places in the laws where the accepted interpretation is not that literal. The laws do not specify all details, and when they do not, we must interpret.

I suspect that Law 12C2 were written primarily with a simpler case in mind (two or three possibilities), and I believe it is legal to consider "at least 1100" as a "result" whose likelihood is to be determined, and thus award 1100 to the non-offenders instead of David's 400.


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