Which is More Likely?

Playing in the fourth quarter of a tight Spingold match, I hold
 S:K63 H:1097 D:KQ108 C:432
LHO deals and bids 1C:. The bidding proceeds with our side silent.
Upon request, we are informed that 2S: was forcing and 3C: was not. It's obvious to lead the D:K, and I do. This dummy hits
S: A4
H: AQ53
D: 3
C: AQ10865
S: K63
H: 1097
D: KQ108
C: 432
Partner encourages and my D:K holds.

Obviously, I'm going to continue diamonds, but which one? In order to beat this, partner needs either the D:A or D:J and five of them. In addition, he'll probably need to have the C:K. It looks promising, but if he has the D:A, I need to continue with the D:8, and if he has jack-fifth, I need to play any diamond except the D:8! Argh!

Which holding for declarer is more likely, D:Jxxx or D:Axx? Would he be more likely to try 3D: with either of those, maybe getting to a 5-2 spade fit instead of 3NT if partner has no diamond help? I think just maybe he's more likely to try 3D: with the weaker holding. Hmmm...plus, I need partner to have the C:K; it's far more likely he has that if declarer has the D:A, since partner rates only to have one useful card. He could have two, but if he has both, declarer has at most a soft 8-count, including three jacks. No one is red, so maybe he'd either pass 3C: or soft-pedal to 3NT without a sure entry or a club card.

OK, I've convinced myself that declarer probably has the D:A, so I continue with the D:Q. It holds. I continue with the D:10; maybe declarer has only Jxx and we can take the first five tricks, but partner stares at this card as if it were an adder. He scowls, and after a minute's reflection, wins his D:A and continues with the D:9 to declarer's jack. The club finesse loses, but declarer has nine tricks.

How could I tell which case to play for? A few hands later, declarer (a great player), says, "did you have the D:9 on that 3NT?" I answer that I didn't, but I did have the eight. He says, "how about playing the ten at trick two? You win if partner has the jack or if he has the ace and the nine." That's a clear improvement, so the D:Q is clearly an error, since the D:10 is 50% better. More importantly, it would have worked this time.

Maybe there's a better solution. If partner has both the C:K and the D:A, what's his rush to cash diamonds? If he discourages, I can shift to a heart, and when he's in with the C:K, he can run diamonds himself. On the other hand, what if my diamonds are KQJ tight or declarer has five spades tricks, three heart tricks, and the C:A, and I had five diamonds that were cashing? Of course, that'd give declarer a very strange 3NT bid with  S:KQxxx H:Kx D:Jxx C:Jxx. We've all seen worse before.

Is there a better way?

Copyright © 2009 Jeff Goldsmith