[hrothgar]

cherdano, on Nov 24 2006, 11:21 AM, said:

Richard, you are doing the same mistake as whereagles, just in a more fancy version.

Lets forget about opening requirements, passes etc., just focus on the fact that we know LHO has >= 5 spades. There are two problems:
1. Deal me my cards, then deal LHO 5 spades, then deal the remaining cards randomly.
2. Deal me my cards, then deal the remaining 39 cards, and throw out all deals where LHO doesn't have at least 5 spades.

Only no. 2 will give the correct answer, but you and whereagles are computing the answer for problem 1. It is pretty easy to convince yourself that in model 2, LHO will have exactly 5 spades a lot more often.

Incidentally, I had an e-mail exchange with Richard Pavlicek about this, as his random dealer suffers from the same problem (he agrees). It seems quite a tricky problem to generate random deals with constraints without brute force (= deal completely randomly and throw out all deals that don't match the constraints).

Thanks for the clarification

Makes much more sense on an empty stomache.

[Blofeld]

cherdano, on Nov 24 2006, 03:21 AM, said:

Richard, you are doing the same mistake as whereagles, just in a more fancy version.

Lets forget about opening requirements, passes etc., just focus on the fact that we know LHO has >= 5 spades. There are two problems:
1. Deal me my cards, then deal LHO 5 spades, then deal the remaining cards randomly.
2. Deal me my cards, then deal the remaining 39 cards, and throw out all deals where LHO doesn't have at least 5 spades.

Only no. 2 will give the correct answer, but you and whereagles are computing the answer for problem 1. It is pretty easy to convince yourself that in model 2, LHO will have exactly 5 spades a lot more often.

Incidentally, I had an e-mail exchange with Richard Pavlicek about this, as his random dealer suffers from the same problem (he agrees). It seems quite a tricky problem to generate random deals with constraints without brute force (= deal completely randomly and throw out all deals that don't match the constraints).

For shape constraints, can't you do something like:

Pick all the acceptable shapes (relatively small finite number). You know all the absolute probabilities of these, so can work out the probability of any of them given that it's one of them easily enough. Do this, then deal cards according to these constraints, and finally throw out any that don't match your other constraints.

?

Or does that also fail?

Obviously it's still a bit of a hassle, but it's better than the pure brute force approach.

[Fluffy]

Well, if you are insane enough to calculate this accuratelly, I'll tell you there is still a missing argument, The ♠ expectancy for West is also modified by wich ♠s you have, since he has opening strenght

I tried to calculate a different problem, that was finding ♠Q at trick one when you know one player has 5♠ and 5-6 HCP, and the other has 2♠ and 18-19 HCP. The answer was that you needed to know wich HCP exactly were missing.

[cherdano]

Blofeld, on Dec 5 2006, 03:39 PM, said:

cherdano, on Nov 24 2006, 03:21 AM, said:

It seems quite a tricky problem to generate random deals with constraints without brute force (= deal completely randomly and throw out all deals that don't match the constraints).

For shape constraints, can't you do something like:

Pick all the acceptable shapes (relatively small finite number). You know all the absolute probabilities of these, so can work out the probability of any of them given that it's one of them easily enough. Do this, then deal cards according to these constraints, and finally throw out any that don't match your other constraints.

Yes, that works when you have only shape constraints. I can count it as brute force to save my statement above, though

It gets a little more tricky when you also have hcp constraints, as they do influence the likelyhood of different shapes. (If you have xxx xxx AKQJ AKQ and partner opens 2N (20-21), it is quite unlikely that he has 5 clubs...) Maybe the best approach is to deal the shapes as you suggest, then deal the cards randomly, and throw everything out if it doesn't match the hcp constraints.

Arend

[Blofeld]

cherdano, on Dec 5 2006, 11:16 AM, said:

Maybe the best approach is to deal the shapes as you suggest, then deal the cards randomly, and throw everything out if it doesn't match the hcp constraints.

Sorry, yes, this is what I was trying to get at. I didn't phrase it very well.

I agree that it's still basically a brute force method, but it should be a good bit faster than the naïve brute force method.