[lucky81]

A method is correct if and only if it always gives a correct answer. What is your definition of a correct method?

Let me state a more general proposition: the method will work for all types of fits (not just 6-3). I leave the (easy) proof as an exercise.

[Trumpace]

lucky81, on Sep 20 2007, 04:53 PM, said:

A method is correct if and only if it always gives a correct answer. What is your definition of a correct method?

Let me state a more general proposition: the method will work for all types of fits (not just 6-3). I leave the proof as an exercise.

A correct method is one which can be justified by the proper axioms at each step.

Just because you got the right answer does not mean there is no hole in your steps.

If you are a bridge player you should know this. Just because you make a contract does not mean you took the best play... does it? Not exactly a perfect analogy, but hope you see the point.

[lucky81]

Justified to do what? To give the correct answer. The method used can be justified to give the correct answer, as I have said. Please think about it for a while so that I do not have to explain more. You will probably see WHY the method is correct. Or else you will see a counterexample for the method (you won't), proving the method incorrect. If you really do not see it AFTER you have really thought about the method (which I think you have not done at all) - then I will be more than happy to justify the method in detail.

[Trumpace]

I won't waste anymore of your time. Sorry.
Please don't bother trying to explain it to me.

[Stephen Tu]

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I believe in his latest simulation he was trying to count the following: assuming that given two hands (not necessarily a partnership) have a 6-3 spade fit, what is the distribution of the other two hands. He correctly assumed this would be the same distribution as for NS having a 6-3 fit.

No, he *incorrectly* assumed this. That is why his numbers came out wrong for the original question. His numbers are accurate if you phrase a different question. The question "if you have a 6-3 fit, how often will the opponent's cards divide 2-2?", is a different question, with a different answer, than "if you have a 6 cd suit, and someone else at the table has 3 of the suit, how often will the remaining cards be split 2-2 between the remaining hands?".

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His method just gives more samples using the same set of deals than your method.

It doesn't "just give more samples", it gives samples that don't apply to the original question, samples where there are 6-2, 6-0, 6-1, 6-4 fits, not 6-3 fits. He overcounts all the splits, it so happens that his method of counting gets 3x the 2-2s and 1.5x the 3-1s.

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He is not counting anything 3 times - the numbers are not even divisible by 3. He is trying to count something else than you think he was trying to count.

This is nonsense. I am not saying his script was counting the same deal 3 times. He is counting bogus deals, in such a way that his statistics (for the 2-2 & 4-0 split cases) will in the long run approach 3x the theoretically expected number. Since this is a statistical sample, of course the numbers do not have to be divisible by 3, that would only happen by pure chance. Only if one programmed the computer to exhaustively generate every possible bridge deal would you be able to guarantee divisibility by 3.

[helene_t]

Trumpace, on Sep 20 2007, 11:47 PM, said:

Sorry, but in mathematics, ends don't justify the means.

Getting the right answer does not automatically imply the correctness of the method.

Lol. I was recently asked about my opinion about a machine learning method that had been proposed for some bioinformathics problem. I said that it seemed completely ad-hoc and I could see no reason why it would work. A colleague replied that I should not reject such methods solely on theoretical grounds, if they work fine in practice it is good enough. I replied that I'm a mathematician so it's my blody job to reject stuff solely on theoretical grounds.

As a mathematician I take the word "correct" as refering to its absolute, mathematical meaning. If that is not what is meant, a word like "useful" may be better.