An interesting play problem from rec.games.bridge

 

I read an interesting problem on rec.games.bridge yesterday and I am still thinking about it. 

You have to play this holding for no losers and 5 tricks (it’s the trump suit).  You are sitting South holding the K87

AQ932

K87

The first question is should you play the Ace or King first.

Two people commented that you should play the king first. I don’t see why. Let’s say that the suit splits 5-0. You can’t pick the suit up anyway. LHO can just cover the 8 and the 7 and his little spot will hold up. There is no situation where it is better to start with the king.

You play the ace and RHO drops the 5 and LHO plays the Jack.  Should you finesse the 8 playing LHO for a stiff Jack?

One answer which I like by Dave Flower is:

If LHO is Mrs Guggenheim, finesse the H8

If LHO is Papa. play for the drop

If LHO is the Hideous Hog, you will always guess wrong

There is a lot of truth in that answer.  In general with most opponents they probably are NOT false carding with J10X so you are in a restricted choice situation and should finesse.  Wait though RHO played the 5 (we are not told what he played at trick two but let’s say it is the 6.)  If this isn’t some sort of signal than someone has the 4 so I guess you need to rethink whether LHO is good enough to false card.

What if your opponent would routinely drop the Jack or 10 from J10x?  It is right to play for the drop then. 

But what are the odds? I believe that there is some restricted choice implications still in that with J10x he could drop the J or the 10. 

Many cases have been eliminated.

We know that there is no 5-0 split and RHO has the XX.  We can also assume that LHO would not throw the Jack from Jxx or Jx so we can eliminate these cases too.  If LHO has a singleton it is the Jack so we can eliminate a lot of 4-1 cases.  

Here is what I came up with but I am looking for help from the mathematicians out there.  There are now only three relevant cases since only one spot is still missing.

1) J 10abc

2) J10  abc

3) J10c ab

Simplistically it is only right to finesse in one of them and I believe that 2 and 3 are more likely anyway than 1.  But with both 2 and 3 LHO could toss either the 10 or the jack but with one he has to throw the jack.  So it seems to me that the odds may be quite close in terms of finesse or drop.