[gartinmale]

Last round of a 7x7 Swiss teams. Your team is doing pretty well but is not in contention for first (you are currently 5-1, but with only 75 VPs). Your opponents are strong and play Precision. On the second to last board you have the following auction. Many spots (but not the relevant trump spots) approximate.

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Trick 1: ♠T, ♠2, ♠A, ♠J
Trick 2: ♠3, ♠K, ♠7, ♠5
Trick 3: ♥K, ♥5, ♥6, ♥2

1. How do you play the heart suit?

[spoiler below, with second question]

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2. I thought for quite some time (well, for me, anyway) and eventually decided I would run the ♥T. I had two reasons, both of which are probably not very good. First, I was missing 14 HCP. Lefty and righty were both in and neither cashed a high club, so there's a mild inference that the club honors are split. If they are, righty is pretty close to a minimum opener, and he only has AQ fifth of spades. I doubt the heart J would have made much of a difference when he evaluated his hand and opened it, but a stiff heart might have. Second, it somehow felt right, because there was tension at the table even though both opponents knew I was looking at a ton of tricks. In any case: lefty covered with the ♥J, so I didn't have to follow through, but the hearts were indeed 4-1. I drew trump and conceded two clubs, making 4. I thought we might pick up some IMPs on the board, but we did not, which brings me to my second question:

At the other table, my counterpart sitting S reached the same contract after a different auction (starting with 2NT - our teammates did not bid). He got a diamond lead around to his A, cashed the heart king, and ran the ten correctly without appearing to pause for thought. He is a much better declarer than I am, so this makes me think that there is some reason to play the suit that way, but I haven't been able to figure out what it is, even though I had more information available to me. What's going on? Or maybe our teammates gave something away?

[Mbodell]

I'd play ♥T to the ♥Q and then a heart back (taking the marked finesse if they were 1=4). Compared to the finesse of the ♥T:

We lose to 4=1 hearts with the J in W which happens about 20.3% of the time.
We win on 3=2 hearts with the J in E which happens about 17.7% of the time.
We win on 2=3 hearts with the J in E which happens about 17.7% of the time.
We win on 1=4 hearts with the J in the W which happens about 5.9% of the time.

We do the same on 3=2 hearts with the J in W (about 26.6%) and 2=3 hearts with the J in W (about 11.9%) which will make on both lines.

So play a heart to the Q (may as well be the T to induce a cover occasionally from 4=1 to improve the odds even more) we win 79.8% of the time from here. If we were to finesse the T then we would win 58.8% of the time.

This is all based on the knowledge that E was 5 spades and W 2.

If E/W haven't bid, then the finesse is even more odds against, so team mates must have hitched, or flashed a card, or somehow given away the situation.

I wouldn't have been able to calculate this exactly at the table. But given that in a vacuum with a 7 card suit you'd play for the T to drop, it seems like the 3 card vacant space differential shouldn't be enough to over weight the correct play with an 8 card suit.

I don't think the inference on club honors is very strong, E may well be hoping partner's spade is stiff and then hoping that the club honors are the entries to give W spade ruffs.

[han]

Whatever you decide to do, make sure you lead the 10 of hearts to give LHO a chance to blunder as they did here. Weak opponents will cover the 10 more often than you might think.

Instead of thinking for a very long time and then playing the 10, you can play the 10 and when it is not covered think about how you are going to play.