Silly question about randomizing

[campboy]

That sounds illegal to me. Law 40C3a.

Unless permitted by the Regulating Authority a player is not entitled

during the auction and play periods to any aids to his memory,

calculation or technique.

What he is doing definitely doesn't aid "memory" or "calculation". I don't think it aids "technique" either though you could argue that one (to me that sounds more like having a book on your lap explaining compound squeezes). I think it just aids "strategy", which is not mentioned.

"Strategy" would be whether or not to randomise; it doesn't aid that. It does aid his randomising technique, though, I would say.

[eyhung]

Anything in your external environment can aid your randomization technique if you look hard enough -- such as the last digit of the round timer, the number of objects on the table, or even the color of a random person's shirt. This is in contrast to a bridge book, system notes, or a calculator. The law is directed at specific aids, not general ones.

[Jlall]

You should often be giving suit preference rather than making a random play fwiw.

[Cascade]

Anything in your external environment can aid your randomization technique if you look hard enough -- such as the last digit of the round timer, the number of objects on the table, or even the color of a random person's shirt.  This is in contrast to a bridge book, system notes, or a calculator.  The law is directed at specific aids, not general ones.

Then there is improper use of the word "any" which gives the law a general meaning.

[jdonn]

Anything in your external environment can aid your randomization technique if you look hard enough -- such as the last digit of the round timer, the number of objects on the table, or even the color of a random person's shirt.  This is in contrast to a bridge book, system notes, or a calculator.  The law is directed at specific aids, not general ones.

Then there is improper use of the word "any" which gives the law a general meaning.

True, but a totally literal interpretation of "any" is not feasible. For example, vitamins I took that morning aid my memory (I am still digesting them during the auction and play period). A book I read 8 years ago aids my technique (it is still aiding my technique during the auction and play period). Etc.

[Echognome]

I think we just need to apply some sensibility here. If I use my watch or have a private rule* about how to use external information on the board, whether it be vulnerability or board number modulus N or whatever, I feel that is within the spirit of the laws. If I bring an electronic random number generator to the table, then I feel that is an aid to technique. I understand that I'm saying I think it's ok to use a watch as a randomization device, but not a separate standalone randomization device. I view the difference mainly from the point of view of enforceability perspective. It seems highly impractical to ban people from wearing watches or looking at their watches. Are we going to also ban people from looking at the board number or vulnerability or who is dealer? Any laws that are completely unenforceable are pointless. However, banning someone bringing a device to the table for the specific purpose of producing random numbers would seem against the spirit of the "aid to technique" part of the laws.

 

* I stress private rule, because I think it should be (is?) illegal to have an agreement with partner on your randomization rule, particularly if undisclosed and even if disclosed. For example, suppose partner and I both have a rule that if we have QJ tight, we play high on odd number boards and low on even number boards. My problem with having this rule, even if disclosed, is when would you disclose it? Would it require a pre-alert? You obvious cannot alert it while defending.

[Jlall]

You can randomize based on your cards also (like if I have the beer...)

[helene_t]

I ran the study using this rule, which I took to mean "consider instances where a defender held QJ in a suit, and the first of those cards was played following suit to declarer or dummy's lead", and I also eliminated cases where the defender was GIB.

 

Among my sample of BBO hands, there were more J plays than Q plays: 59.1% of the time the J was played (out of 74703 instances).  I also grouped the instances by BBO username.  For instance, among the 339 people who faced the problem exactly 6 times, there were

 

     23 people who played the J 0 times (always the Q),

     27 people who played the J 1 time,

     51 people who played the J 2 times,

     51 people who played the J 3 times,

     49 people who played the J 4 times,

     65 people who played the J 5 times,

     74 people who played the J 6 times.

Waiting for Helene to tell us how often we have to see someone play the Q from QJ until it is worth trying exploit his tendency.

Hmmm ... suppose he plays the queen from QJ with probability p. If we miss two spots and he would play the queen only from Q sec and QJ tight the the a priori the probability of QJ is 12/23 so the posterior is p*(12/23) / (p*(12/23)+11/23) which breaks even for p=11/12.

 

Suppose we model p as beta (1,1), then the posterior mean of p after having observed him playing the queen n times from QJ tight and never the jack from QJ tight is (n+1)/(n+2), so we have

 

(n+1)/(n+2) = 11/12

 

i.e.

 

n=10.

 

Here I have not made any attempt to model the data. beta(1.4,0.9) fits the data reasonably. That would give us, in 33900 players:

0 1 2 3 4 5 6

2301 3381 4213 4701 5650 6218 7436

 

For beta(1.4,0.9) the equation becomes

(n+1.4)/(n+2.3) = 11/12

 

so 9 is enough.

 

This is not quite correct since our decision depends on the posterior mean of p*(12/23) / (p*(12/23)+11/23) rather than the posterior mean of p but I don't think it makes much difference.

 

BTW last friday I gave a talk at a symposium on Bayesian methods in medical research. I talked about safety monotoring in drug combination studies. Suppose a patient takes both booze and coke so when he collapses due to a booze intoxication it is a slight indication that he is hypersensitive to booze only since otherwise he might have collapsed due to coke intoxication first. Now suppose we have, for a particular group of patients, evidence that if they afterwards appear to actually be hypersensitive to both drugs they will always collapse due to the booze intoxication and therefore being taken off study before they get to the point of being coke intoxicated, then the restricted choice argument weakens. Same thing.

[gwnn]

this is very interesting, I would have thought the graph would be a bit like a U, with a possible smaller peak at the middle! weird weird weird. but then again matmat says about BBO experts that they truly play their cards randomly.

 

Helene's reply was also interesting but only after extensive research on Bayesian statistics on wikipedia.