Declarer play problem

[HighLow21]

Suppose that the hands were 4432-5152 LHO has to discard three spades. if 3442 then he gets two spades and one diamonds, and if 2452 then two diamonds and one spade. So if LHO is any of the 5152 6142 or 7132, then on the third he must discard three spades, if the middle or the first I have some choices.

 

However, I need to use my mixed strategy not only to give equal probability to 5152 and 2452, but also to balance 4432 and 6142 and it is not clear to me that these aims are simultaneously acheivable. For example, 4432 could be enough more common than any other layout that the best you can for your overall strategy is to always try to look like 4432 whenever you do not have four hearts. In that case the best strategy overall would never involve discarding two diamonds from 5152.

 

Gnashers argument of treating them all like one suit would be true if all the distributions were close to equally likely, because in that case you can definitely achieve an optimal mixed strategy. I have no idea if a perfect mixed strategy is acheivable here. If it is then the odds are for RHO because lho was not squeezed, because you will be able to balance the relative likelyhood of diamonds being 5-3 in discards on other hands, so its irrelevant. If you cannot acheive a mixed strategy, or if your best mixed strategy involves mostly trying to look like diamonds are 4-4 then it would almost never involve discarding two diamonds, and so I should include that information.

 

I see you slept well thinking about this. ;-)

 

Hey Fred --> who had the J♥ guarded so we can all stop dreaming about making this grand?

[benlessard]

but also to balance 4432 and 6142 and it is not clear to me that these aims are simultaneously acheivable

The side that has 4H his discard are forced. The other side should discard S and D at random to give the illusion that hes the one with 4H. Its really a mixed strategies case.