ACBL Daylong 1 - Jul 29, 2021 - Board 12

Board 12
Our side vulnerable

Last chance to beat the other couples.

♠ A 9 6  ♥ 7 4  ♦ K J 6 3  ♣ K 9 7 2

LHO passes, partner passes, and RHO opens one spade in third seat. I pass, LHO bids two clubs, Drury, and RHO bids two diamonds, showing a minimum but full opening bid. LHO probes with three diamonds. RHO probes right back at him with three hearts. LHO, out of probes, bids three spades, ending the auction.

The opponents have lots of high cards, but their hands apparently don't fit will. So this doesn't sound like an auction to lead aggressively against. I lead the seven of hearts.

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

West	North	East	South
Phillip	Robot	Robot	Robot
	Pass	Pass	1 ♠
Pass	2 ♣	Pass	2 ♦
Pass	3 ♦	Pass	3 ♥
Pass	3 ♠	(All pass)

Declarer plays low from dummy, partner wins with the king, and declarer plays the five. We might have heard from partner if he had six hearts, and declarer might have gone on to game at some point with ten major-suit cards. So I am provisionally crediting declarer with five-four in the majors.

Partner shifts to the eight of clubs, declarer plays the six, and I win with the king. I don't think partner would be shifting from the club queen with the jack in dummy. Declarer probably has ace queen and partner is leading low from a doubleton, as robots are wont to do. If so, I can give him a ruff when I'm in with the trump ace. I play the deuce of clubs--five--ten--ace. Declarer for some reason concedes the ruff himself. He cashes the club queen and partner ruffs with the seven.

By the conditions of contest, declarer can't have more HCP than I do, so he has at most 11. He has so far shown up with the queen of hearts and ace-queen of clubs for a total of 8 HCP. If he has the spade king, he can't have any other high cards. Is it possible he has both major-suit jacks instead of the spade king? It seems unlikely. For one thing, that would that give him a questionable two-diamond bid. And, more importantly, he wouldn't be playing the hand this way. If he had queen-jack of hearts, he would just draw trumps. His failure to do so suggests he has a heart loser to worry about. So I'm inclined to play him for

♠ K x x x x  ♥ Q x x x  ♦ x  ♣ A Q x

Declarer can dispose of his heart loser either by ruffing it or or by pitching it on the club jack. So our only chance for a setting trick is to score a second spade trick somehow. 

Partner shifts to the seven of diamonds--eight--jack--ace. Declarer ruffs a diamond with the spade deuce as partner contributes the diamond queen. He plays a heart to the ace, partner playing the nine, and ruffs another diamond with the spade five. This is the current position. Declarer presumably has king third of spades and queen doubleton of hearts remaining.

	NORTH Robot ♠ Q 10 3 ♥ -- ♦ 4 ♣ J
WEST Phillip ♠ A 9 6 ♥ -- ♦ K ♣ 9

Declarer leads the heart queen. It can't help to ruff this. Shortening my trumps just makes it easier for declarer to pick up partner's jack of spades. I pitch my diamond king. Declarer pitches dummy's good club. Declarer plays the heart ten. Again, my best shot at scoring partner's spade jack is to hold all my trumps, so I pitch the club nine. Declarer ruffs in dummy with the three. 

Obviously declarer will play a diamond from dummy now. When partner follows, declarer will have a complete count. He will know I have three spades left and partner has one spade and one heart. He will not know the location of the high cards, however. Partner could have the spade ace and still not have an opening bid. And the possession of the spade jack is immaterial to either of us.

So declarer will ruff the diamond with the king, leaving me with two choices: (A) I can underruff. Now declarer has to guess whether to play a spade to the ten, playing partner for a stiff ace, or a spade to the queen, playing partner for a stiff jack. (B) I can overruff with the ace and play a trump myself. Declarer then has to decide whether to finesse, playing me for AJx or to hop with the queen, playing me for Axx. 

Because I'm playing against robots, I can think about this position as long as I want. At the table, against humans, I wouldn't be able to do that without giving away that I have the ace. Fortunately, I don't need to think about it. This is a well-known position. It has been analyzed before by others, and I know what to do. 

Declarer plays dummy's diamond and ruffs with the king. I overruff with the ace and return the six. Declarer, to my surprise, rises with the queen, dropping partner's jack. Making three.

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

74%. No one beat three spades. Quite a few allowed declarer to make four (via an initial club lead for example). 

Why did I choose to overruff with the ace in the three-card end position? The first thing to note is that, if declarer plays correctly, it makes no difference what I do. Let's examine this problem from declarer's perspective to see why. He knows partner began with Ax, Jx, or xx of spades. (AJ doubleton is possible but irrelevant, so we can ignore it.) Each case is equally likely (since there are three possible spot-card combinations for each case). The way to decide what to do in such situations as this is to decide ahead of time which cases you want to pick up, then play accordingly, refusing to be deflected by anything the opponents do.

In this layout, declarer can guarantee winning in two of the three possible cases by finessing the ten at trick twelve regardless of how West defends. This works if East began with Ax or xx and fails if he began with Jx. No other strategy can do better. 

To make sure this is true, let's examine the three possible alternative strategies. Note that if East has xx or Ax, West has no choice in how to defend. He must overruff in the first case (else his jack will appear on the next round), and he must underruff perforce in the second. The only time he has a choice is when he has Axx.

Strategy A: Finesse the ten if West overruffs; play low to the queen if West underruffs. This picks up East's xx and loses to his Ax. How it fares against Jx depends on how West defends. It can't do any better than two wins out of three, and it might do worse.

Strategy B: Do the opposite. Play the queen if West overruffs; finesse the ten if West underruffs. This loses to xx and picks up Ax. Again, how it fares against Jx depends on how West defends. So, again, it can't do any better than two wins out of three, and it might do worse.

Strategy C: Always play the queen at trick twelve, regardless of what West does. This is clearly wrong, since it loses to both xx and Ax. It does pick up Jx no matter how West defends, so it wins in one case out of three.

In short, strategies A and B might tie the recommended strategy, provided you are 100% correct in your assumption of what West will do with Axx, but it can't do better and will do worse if your assumption is wrong. So it is right for declarer to finesse the ten at trick twelve regardless of how West defends.

What should I do as West? Since my play doesn't matter if declarer plays correctly, I must assume declarer will play incorrectly. I must assume there is some scenario where he will play the queen at trick twelve and must avoid that scenario. What might that scenario be? What mistake might declarer be tempted to make?

In my judgment, declarer is unlikely to play the queen if I overruff. Some declarers might reason incorrectly, "West has three spades to East's two; therefore, he is three to two to have the jack." So even if declarer doesn't know the correct play, he is still apt to make the correct play, even if it is for the wrong reason. 

If I underruff, declarer's possible faulty reasoning depends on his level. If he is naive enough not even to consider that I might underruff with ace third, he will of course lead low to the ten and be surprised when it loses to the jack. The danger comes when declarer is good enough to know that I might underruff  but not good enough to know the correct odds. Such a declarer might reason this way: "East has Jx or Ax. Each is equally likely; therefore, I have a 50-50 guess what to do on the next trick." I'll leave it to you to work out why this reasoning is wrong. In any event, if you are playing against such a declarer, underruffing runs the risk he will, by sheer chance, guess to play the queen on the next round. Therefore, I believe it is right to overruff.

Why did the robot misplay this position? I can't say. It's an error, so he must have had some kind of "blind spot." Robots appear to have different blind spots than humans.

My final score was 79.77%, which lands me in second place out of 1206, 0.3% behind first place. I would have won easily had I not misplayed board nine.