Confusing the defense

It is match-points and I was playing against three robots.  The bidding went:

W

West

N

Pard

E

East

S

Me

—

—

1♦

1♥

1♠

3♥

All Pass

Dummy comes down with 4 hearts and a diamond void. Plan the play on the lead of the 4 of diamonds.

N

North

♠

AJ83

♥

9842

♦

—

♣

Q9432

Lead: ♦4

S

South

♠

952

♥

AKJ10

♦

K10652

♣

6

Yes, I over-called my chunky 4-card suit; wouldn't you? Anyway, assume you did and partner raised to the "law" level. How do you play this?

It is a little hard to count tricks in this situation. With the lead, I have two top tricks: Ace of spades and king of diamonds. And three hearts if I give up the queen. That is 5 tricks. Where are four more tricks? One way is to use all 4 of dummy's trumps to ruff.  In order to enter back to my hand, though, I have to give up a club. And the opponents will lead trump at that point. So, it is only 3 dummy ruffs, 3 hand ruffs and two top tricks. Only 8 tricks. What am I missing?

What I was missing was that the opponents had not led trump yet. I needed to plan the hand assuming that the defense will not find a trump switch. The defense thinks I have five trumps and so, I need to act like a guy who has a spade honor and is missing heart honors.  If I had Q10 of spades and only AJTxx of hearts, I would be throwing a club, so that is what I need to throw from the dummy.

The second thing that I was missing was that even if the opponents led a trump, I may need only 3 ruffs in dummy if I can finesse the queen of trumps.  So, 3H has a a couple of chances. I need to maximize both.

One advantage of playing robot tournaments is that I can look over the other boards and see what would have happened if I had thrown a club on the first trick. Then, East cashes his King of clubs (to show where his entry lies) and leads a diamond, hoping his partner has a singleton heart honor and can ruff in front of dummy.  Instead, if one throws away a spade (as I did), East simply continues diamonds (go figure) and then once a club is led, they find the trump switch. At that point, if I take the finesse, I scamper home with 9 tricks (if the finesse loses, I get only 7 tricks: which is why throwing a club on the first trick is so important).

The complete deal:

p.s. The double-dummy line to make 3H without resorting to subterfuge is very interesting. Essentially, it involves ruffing the first trick (!), cutting defender's communications in diamonds and then finessing the spades. Highly unlikely that I would find it at the table!