Event 3 - Match 4 - Board 8

Board 8
Neither vulnerable

♠ Q 10 5 4 ♥ Q 10 ♦ K J 10 5 2 ♣ 6 2

The match is a tie going into the last board. Partner opens one club in second seat; RHO passes. I bid one spade, and partner bids two clubs. That seems high enough to me, and LHO agrees. RHO leads the six of hearts.

	NORTH Phillip ♠ Q 10 5 4 ♥ Q 10 ♦ K J 10 5 2 ♣ 6 2
	SOUTH Jack ♠ K 2 ♥ A K 5 2 ♦ 9 6 ♣ K 10 8 4 3

West	North	East	South
William	Phillip	Harry	Jack
		Pass	1 ♣
Pass	1 ♠	Pass	2 ♣
(All pass)

One notrump looks like a better spot than two clubs. This board demonstrates one of the downsides of weak notrumps: Partner can't rebid one notrump over one spade, since that shows 15-17 high-card points, so he has to rebid clubs with a bad five-card suit. Of course, if you strengthen partner's hand a bit, it is the strong notrumpers who have the rebid problem--and a considerably more difficult rebid problem at that.

What do I know about the opponents' hands? They have 19 high-card points between them. East passed in first seat, so he is limited to 11, giving West at least eight. West passed over one club non-vulnerable, so he is unlikely to have a five-card spade suit. (Personally, I would be unlikely to have a four-card spade suit.)

If I play the heart ten and it holds, I won't have the fourth-round heart loser to worry about. But if gets covered, I'm poorly placed. If I win and play a heart back to the queen, I've helped the opponents in two ways: I've given the opponents a tempo by releasing two of my heart stoppers. And, if hearts are five-two, I've set up a defensive ruff. If I try to get to dummy by playing a diamond instead, I open up the possibility of a defensive diamond ruff. The heart jack is a slight favorite to be on my right (since jack third or fourth would be an unattractive lead), so I choose not to risk the ten. I rise with the queen; East plays the three.

East would presumably encourage with the jack. So, unless East has jack-three doubleton, it appears I did the wrong thing. I'd just as soon West not continue hearts when he gains the lead, so I "discourage" by playing the deuce.

I play the deuce of clubs from dummy; East plays the seven. That's a nice card to see, since it brings dummy's six into play. I play the eight. West wins with the nine and shifts to the four of hearts--ten--jack--ace. I guess I did the right thing at trick one after all. It appears East has jack-three doubleton and West has five small. The opponents lead fourth best, so six, four is consistent with a five-card suit.

It's possible hearts are two-five instead of five-two, but there are two reasons that is less likely: One, as I've already mentioned, is East's failure to encourage at trick one. The other reason involves a principle of probability that is often overlooked. Sometimes when West has a doubleton heart, his higher heart will be too high to be a plausible fourth best. So his lead from a doubleton will be ambiguous only part of the time. His lead from a five-card suit will always be ambiguous. It will always be possible for his fourth best card to be top of a doubleton. Thus the very fact that there is an ambiguity means that he is more likely to have five hearts than to have two. This is the bridge version of the anthropic principle.

I need to get to dummy to play another club, so I lead the six of diamonds. West plays the four. Finding the ace onside is not as useful as finding the queen onside. I'm going to need to do something with my fourth heart. If the diamond queen is onside, I may be able to pitch the heart on the third round of diamonds. Accordingly, I play the jack. East wins with the ace. That's a bit unexpected. If East knew I had a doubleton diamond, he would probably duck, making it harder for me to score a second diamond trick. Perhaps he couldn't read his partner's card. That would be true only if West has a doubleton. In that case, East would be unable to tell whether West has queen-four or queen-nine-four.

East shifts to the nine of hearts. So I was wrong about the heart split. Anthropic principle notwithstanding, West did have six-four doubleton, and East, for some reason, did not encourage with jack-nine-eight fifth.

That means West is 5-2-2-4. But that's impossible. Why didn't he overcall one spade? Perhaps I'm wrong about the doubleton diamond. Maybe East chose to win the diamond despite knowing I have a doubleton in order to give his partner a heart ruff. Assuming West would give honest count with queen fourth of diamonds, he must be either 5-2-3-3 or 4-2-3-4. (He might have overcalled one spade with 5-2-3-3. But that's not nearly so attractive a pattern as 5-2-2-4, so I'm not as confident in ruling that pattern out.)

Should I play the deuce or the king on this trick? In order to make this, I must dispose of my heart loser and I must avoid losing more than two trump tricks. Playing the deuce aids in the first goal but makes it harder to achieve the second. West can pitch a diamond, forcing me to ruff with dummy's club six. I will now need considerable luck to avoid losing three trump tricks. Playing the king aids in the second goal, since it forces West to ruff, but makes it harder to avoid a heart loser. If East has an entry, the opponents can now draw dummy's trump and cash a heart trick.

To decide which play works more often, general principles will not help. I must examine specific cases. I'll start by assuming West is 4-2-3-4. In that case, if East has either black ace, I must lose three trump tricks. West can ruff this trick with the queen or jack. If East has the club ace, West leads a trump to East and gets a second ruff. If East has the spade ace, West cashes the club ace and leads a spade to East for a second heart ruff.

So if West is 4-2-3-4, I must hope he has both black aces. Is there any way to make it if he does? If I play low on this trick, West can pitch a diamond, letting me ruff in dummy with the club six. He will now have three natural trump tricks. So a low heart does not work. What happens if I play the king? (1) If West ruffs low, I overruff in dummy and lose only two trump tricks. (2) If West ruffs with the queen or jack, I can lead the club king to smother East's honor and lose only two trump tricks. (3) If West pitches, I lead the spade king. Say West wins and plays the diamond queen, putting me in dummy. I can now cash the spade queen and ruff a spade to reach this position (West's side card could be either a spade or a diamond, depending on what he discarded on the heart king):

	NORTH Phillip ♠ 10 ♥ -- ♦ 10 5 ♣ 6
WEST William ♠ x ♥ -- ♦ -- ♣ A J 5		EAST Harry ♠ -- ♥ 8 7 ♦ x ♣ Q
	SOUTH Jack ♠ -- ♥ 2 ♦ -- ♣ K 10 4

When I lead the heart deuce, West is dead. If he ruffs (with the jack or low), I lose only two trump tricks. If he pitches his side card, I can ruff in dummy, then ruff a diamond to my hand. If West overruffs, he is endplayed. So, if West is 4-2-3-4, I must play the heart king and must hope West has both black aces.

What if West is 5-2-3-3? If West has the club ace, I can always hold my trump losses to two tricks. I may have some guessing to do later on, but it makes no difference which heart I play to this trick. What if East has the club ace? If I play a low heart, West can pitch a diamond. I ruff in dummy and must lose two trump tricks and a ruff. And if I play the king? West ruffs with the queen or jack and plays a club to his partner's ace. East can now cash a heart. So it makes no difference which heart I play. I'm down either way.

The king, then, allows me to make the contract whenever it can be made. Although, later on, I may have to guess whether to duck out the club ace on my left or play East to have a singleton honor. I play the heart king, and West ruffs with the jack of clubs. I pitch a diamond from dummy. West cashes the spade ace. East plays the six. It might be nice to have a second dummy entry just in case I'm wrong about three-three diamonds, so I unblock the king. West plays the nine of spades. I win in dummy with the queen as East plays the seven. As the opponents have defended, no club guess is necessary. I play dummy's six of clubs--queen--king--ace. West exits with the eight of spades; East plays the jack. I ruff and draw the last trump. I don't need to repeat the diamond finesse. Dummy's spade ten provides a pitch for the heart.

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

Not a very good defense. East could beat me by ducking the diamond ace, which seems pretty routine. Since he has no second entry and can't give West two heart ruffs, what's the hurry? In fact, it must be better to wait until dummy's club is gone before playing hearts. So ducking seems like a good idea all around. After East did win the diamond ace and play a heart, West should have pitched a diamond rather than ruff. As we saw, that doesn't beat me by force, but it makes things much harder for me. That play, too, should be fairly routine. Ruffing with a natural trump trick is seldom a good idea.

Our counterparts at the other table reached the easier contract of two diamonds and made two. So the match ends in a tie. We score 15 victory points. We are still in the lead, but by a mere three victory points.


Table 1: +90
Table 2: -90

Result on Board 8: 0 imps

Result on Match 4: 0 imps (15 VP)
Current Total: 73 VP