Free Weekly Instant Tournament - July 25 - Board 5

Board 5
Our side vulnerable

♠ A 9 6 4 3  ♥ J 10 4  ♦ A K J  ♣ 10 6

Two passes to me. I open with one spade, LHO bids three clubs, and partner bids four spades. Everyone passes, and LHO leads the king of clubs.

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

West	North	East	South
Robot	Robot	Robot	Phillip
	Pass	Pass	1 ♠
3 ♣	4 ♠	(All pass)

I have a potential loser in each suit. I can hold that to three losers by pitching a diamond on a heart. The key will be the spade suit. Since West has seven clubs to East's three, I'll probably end up finessing East for the spade queen to make an overtrick. The fact that West led a club makes finessing East even more attractive. If West had a red-suit singleton, he probably would have led it. So, unless he is specifically 2-2-2-7, he probably has a stiff spade.

This inference would be stronger if I knew what his club honors were. The robots lead king from ace-king, so I don't know whether West has ace-king or king-queen. If he has ace-king of clubs, the presumption that he doesn't have a red-suit singleton is considerably weaker.

East plays the nine of clubs. Assuming East is playing high, he denies the club ten. That means the ten is the card I'm known to hold, so I play it. West shifts to the queen of diamonds. What's he up to? He could be going for a diamond ruff. Or he could just be trying to set up diamond tricks before dummy's hearts are established. Give me something like 

♠ A Q x x x x  ♥ J x  ♦ A x x  ♣ 10 x,

for example, and West must shift to a diamond to beat me.

East plays the six of diamonds and I win with the ace. If East intends the six as count, then West shifted from queen doubleton. But the robots don't always signal on partner's leads. The six could just be a random card.

I play the three of spades to dummy's king. West plays the seven; East, the deuce. I play the jack of spades from dummy. East follows with the eight.

Do I finesse or not? Here are West's possible hands with their relative frequencies:

Holding	Freq
(A) ♠ Q x  ♥ x x  ♦ Q x  ♣ ? ? x x x x x	10
(B) ♠ x  ♥ x x x  ♦ Q x  ♣ ? ? x x x x x	10
(C) ♠ Q x  ♥ x x x  ♦ Q  ♣ ? ? x x x x x	2
(D) ♠ x  ♥ x x x x  ♦ Q  ♣ ? ? x x x x x	1

(The relative frequencies were calculated as follows: There are three ways for West to hold queen doubleton of spades and three ways to hold a small singleton. And West is just as likely to hold two out of five small hearts as to hold three. So (A) and (B) are equally likely. Since there are five ways to hold queen doubleton of diamonds and only one way to hold a stiff queen, (A) and (B) are each five times as likely as (C). Finally, since there are ten ways to hold three small hearts and five ways to hold four, (C) is twice as likely as (D).)

If we assume East gave count with the six of diamonds, then only (A) and (B) matter. So it's a tossup whether or not to finesse. If we assume East's diamond six was random, then playing for the drop is 12 to 11, a slight favorite. A bit less if we factor in that West might have led a stiff diamond.

But that's only the a priori odds. Since it's close, any inference from the play or bidding will likely sway the odds. What clues do we have from the play?

I have heard one person argue that West wouldn't look for a diamond ruff unless he had a doubleton trump. That may be true. But who says West was looking for a ruff? As we pointed out above, there are layouts where a diamond shift is necessary simply to set up diamond tricks before the heart ace is knocked out. So this reasoning is faulty. There is nothing to infer from that fact that West chose to shift to a diamond.

What about West's bidding? (B) is a more attractive pre-empt than (A). 7-2-2-2 with two doubleton queens is an ugly three-club call. But East is a passed hand. So that matters less. If I had opened in first seat, I would be disinclinded to play West for (A). But pre-empts can be quite flaky opposite a passed hand. So, while there is some inference West doesn't hold (A), it's not especially strong.

What about East's bidding? If West holds (A), then East holds

♠ x x  ♥ A x x x  ♦ x x x x  ♣ ? x x

If West holds (B), then East holds

♠ Q x x  ♥ A x x  ♦ x x x x  ♣ ? x x

In the former case, West, with three trumps and a ruffing value, might have sacrificed in five clubs at favorable vulnerability. In the latter case, with a 4333 pattern and a potential trump trick in spades, a sacrifice is less appealing. We've finally found an inference I can buy. I doubt East would sacrifice in case (B). But he might well sacrifice in case (A). In essence, it's a restricted choice argument. Better to play East for a hand where passing four spades is arguably his only option rather than play him to have a choice.

I play low. West takes the queen, and I claim ten tricks.

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

Plus 620 is worth a mere 14%. Most of the field played for the drop.

I don't regret my decision. I think the finesse was percentage for the reasons I gave. If you take the percentage action and fail, you have to be philosophical about it, knowing you'll do well in the long run. Note, by the way, the opponents do have a good save in five clubs. It is a little surprising East didn't bid it.