Weekly Free Instant Tournament - Apr 8, 2022 - Board 3

Board 3
Opponents vulnerable

♠ A 10  ♥ A 9 7 5 3  ♦ A Q 8 7  ♣ 8 2

I open with one heart and partner raises to two hearts. I have six losers. By loser count, this hand is worth invitation, but point count says otherwise. 14 HCP with "5422" shape is a bit shy of an invitation. Which evaluation method is correct?

Sometimes it's easier to think in terms of what cover cards you need rather than what losers you have. When partner has made a single raise, ask yourself whether two cover cards (either two kings or an ace and a queen) plus the right doubleton gives you a game on normal breaks without any finesses. A major-suit king and king doubleton of diamonds still leaves me with four losers, so this hand is not worth a game try. In short, "six losers" overstates the value of the hand, because no doubleton in partner's hand covers a loser. You can make a game try in the hope of finding partner with three cover cards, but you can't count on all of those cover cards' being high cards.

I pass. LHO passes also and leads the club king.

	NORTH Robot ♠ 6 3 ♥ J 8 6 ♦ K 10 3 ♣ A 7 6 5 3
	SOUTH Phillip ♠ A 10 ♥ A 9 7 5 3 ♦ A Q 8 7 ♣ 8 2

West	North	East	South
Robot	Robot	Robot	Phillip
			1 ♥
Pass	2 ♥	(All pass)

Partner has a maximum raise and game is quite poor, so it appears I was right not to invite. 

I have two losers in the black suits, probably two trump losers, and potentially a fourth-round diamond loser. If trumps are three-two, I can gain a trick by ducking a trump, then cashing the ace. If diamonds don't come home, I can ruff the fourth round in dummy. If they do, I can pitch a spade from dummy and ruff a spade instead. Ducking a trump could work out badly, however, if someone has a stiff heart honor. In that case, if I play ace and another heart, I'll lose only two trump tricks. If I duck a heart then cash the ace, I'll lose three. 

It's possible I don't need to duck a trump. There are quite a few layouts where the hearts are blocked plus a few more where the defense could unblock them but might not work out to do so. In such a scenario, ace and a heart might not hurt.

If I intend to play ace and a heart, perhaps I should duck trick one, since a blockage in hearts won't help if I leave the opponents with communication in clubs. Ducking does risk having the club ace ruffed at trick two. But if the ruff is with a natural trump trick, that won't matter. In fact, it might help. If East ruffs with three trumps, it solves my problem.

What worries me about ducking isn't so much the possibility that the club ace will be ruffed. It's the possibility that the defense may switch to a spade. Now I lose my chance to avoid a spade loser if diamonds come home. For that reason, I'm gong to win the first club trick. I'm still undecided about whether to duck the first heart. But I don't have to decide that until I see what card East plays.

I take the club ace; East follows with the jack. That could be a singleton, in which case the opponents don't have communication in clubs after all. It might also be from jack-ten--either doubleton, third, or fourth.

I play the heart six from dummy, and East plays the ten. If that's a singleton, I must win this. If I duck, I lose three trump tricks instead of two. But if it's from king-queen-ten, I must duck, since if I play ace and another, I lose my ruff. If those were the only two possibilities, winning would be clear. East could play any one of his three cards with king-queen-ten, so, by restricted choice, a singleton ten is three times as likely.

What are the other possibilities? It could be from ten doubleton, but I'll assume it isn't, since that would be a strange play. It could also be from king-ten or queen-ten doubleton. If so, I would prefer to duck. But ace and another heart won't cost if the club jack was a singleton. In fact, ace and another might gain, since West may hop, crashing his partner's honor. A human West should work out not to do that, but that's just the kind of mistake a robot might make, since he draws no inference from how I choose to play. He is especially likely to hop with queen third, for fear I have the king, and might hop even with king third to ensure he can draw dummy's last trump.

All in all, taking the ace looks like the better choice. I play the ace, and West follows with the deuce. I play the heart three, and West pitches the diamond four. East split with king-queen-ten-four of hearts? I didn't even consider that possibility, since I wouldn't expect him to split. Splitting costs if West has a stiff nine, and it seems unlikely to gain in any event.

West's diamond pitch might mean the suit is running. If it's not, perhaps I can manage a club-diamond squeeze.

East wins with the heart queen and cashes the king, drawing dummy's last trump, as West pitches the club four. East now switches the to deuce of diamonds, solving my problem in that suit. I win in dummy, play a spade to my ace, draw the last trump, and cash my tricks, losing a club and a spade at the end. Making three.

	NORTH Robot ♠ 6 3 ♥ J 8 6 ♦ K 10 3 ♣ A 7 6 5 3
WEST Robot ♠ Q 9 8 5 ♥ 2 ♦ J 5 4 ♣ K Q 10 9 4		EAST Robot ♠ K J 7 4 2 ♥ K Q 10 4 ♦ 9 6 2 ♣ J
	SOUTH Phillip ♠ A 10 ♥ A 9 7 5 3 ♦ A Q 8 7 ♣ 8 2

Some declarers made only two, and some Souths reached four hearts after making the aggressive game try. So plus 140 was worth 79%. I'm still in first place, with 85%. 

Incidentally, look at that hand West sold out to two hearts with. I would double on the first round at a different vulnerability. West should certainly balance with a double after the raise. East would then bid two spades, and we would have a tough decision. We could double and collect 200, but that's hard to do when we each have a doubleton spade. If we choose to defend undoubled, we get a terrible board. And if we compete to three hearts, we might go down and get an even worse board. It was very kind of West to let us play two hearts.