Free Weekly Instant Tournament - December 13 - Board 2

Board 2
Our side vulnerable

♠ A 7 3  ♥ Q 8  ♦ K J 10 5 3  ♣ A Q 9

RHO passes. I open with one notrump, and partner bids two diamonds, a transfer to hearts. I bid two hearts, and partner bids three diamonds. I have quite a good hand in support of diamonds: five-card support, the queen of partner's primary suit, and aces in the side suits. If partner is interested in slam, I have what he needs.

Of course he isn't necessarily interested in slam. He could be probing for the right game, and my first responsibility is to aid in that probe. If he has a minimum game force, he should have a singleton in one black suit or the other, else he should simply bid three notrump. If his singleton is in spades, three notrump could easily be the wrong game. How do I suggest that?

Three spades shows strength in spades and implies clubs may be a weak spot. Unfortunately, without special agreements there is no way to suggest spades may be a weak spot. This is a flaw in standard methods.

The problem springs from the fact that three hearts is natural. There is no reason it should be. It's foolish to waste a three-level bid to show heart support when you know you are bidding past three notrump. All four-level bids should show heart support, and all three-level bids below three notrump should show diamond support. Since three spades shows good spades, three hearts, by elimination, should show good clubs and concern about spades.

Without that agreement, however, I have a problem. Neither three spades nor a standard three hearts conveys the meaning I want, and I'm not about to sign off in three notrump with such a slam-positive hand. So I decide to bid four diamonds. 

It's dangerous to bid past three notrump at matchpoints with a minor-suit fit. But if partner isn't interested in slam, perhaps five diamonds will be a reasonable spot. It might make when three notrump doesn't. Or it might make when we have only nine tricks in notrump. Also, partner might bid four hearts to show hearts playable in a five-two fit, in which case I can pass.

I bid four diamonds. Partner passes. That was unexpected. I would have thought we were in a game force. RHO leads the ace of hearts.

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

West	North	East	South
Robot	Phillip	Robot	Robot
Pass	1 NT	Pass	2 ♦
Pass	2 ♥	Pass	3 ♦
Pass	4 ♦	(All pass)

I see. Partner didn't have a game force. I would have just transferred to hearts and passed with partner's hand. One of the reasons I pre-accept on almost any hand with four trumps is so partner needn't stretch with a marginal invitation like this one.

I have two heart losers and a potential diamond loser. I can ruff both dummy's clubs in my hand, so I need to dispose of dummy's spade loser. West is making that easy for me by leading my suit.

East plays the heart deuce; I play the three. West shifts to the six of clubs. I rise with the ace, ruff a club, and play ace and king of diamonds. Trumps are two-two. I ruff the last club and concede a heart. Making five.

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

+150 is worth 18%. Almost everyone is bidding a timid three notrump over three diamonds. That doesn't have to make, but East leads a club, presenting declarer with his ninth trick.

A few are taking ten tricks. Should you? For some reason, West doesn't play the club ten at trick one, so declarer wins the trick with his nine. If declarer now runs diamonds, he comes down to the following position (flipping the board to make North dummy):

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

To score ten tricks, declarer must hope that the defense can't score two club tricks before he can take a heart trick.

To prevent this, East must hold three clubs. (If he holds only a doubleton, declarer can drive a heart honor, duck the club shift, then drive the other heart honor.) Since East must hold two hearts and three clubs, he must come down to a doubleton spade. That means West must hold all his spades. He must also hold three clubs, so the defense can take two clubs. And he must hold a heart as an exit card, so declarer can't endplay him in spades. If the defense does all this, declarer can't score a tenth trick.

In practice, West pitched a spade at his first opportunity. Most declarers, however, did not exploit this error and made only three. So we would have been only slightly below average if partner had not chickened out on his game force and had raised four diamonds to five.

I believe the agreements I outlined after Jacoby and a minor-suit rebid make sense. I glossed over opener's four-level bids, simply stating that they should all show heart support, so let me expand on that idea now. 

Four hearts should be a minimum with heart support, and four clubs should be better than a minimum. (It needn't be much better, since you are limited by the fact that you didn't pre-accept.)

Four diamonds should show support for both suits: three-card heart support and four- or five-card diamond support. The bid suggests diamonds as the strain for slam (using hearts to provide discards) but hearts as the strain for game if partner isn't interested in slam. This is a very useful agreement. Without it, you have to support hearts with support for both suits. If partner turns out to be interested in slam, it can then be hard to steer the hand back to diamonds.  

Free Weekly Instant Tournament - December 13 - Board 1

Board 1
Neither side vulnerable

♠ A J 7 6 3  ♥ K Q 7  ♦ K  ♣ 10 8 7 5

Two passes to me. I open with one spade, LHO passes, and partner bids two diamonds. This bid isn't forcing by a passed hand, and it seems high enough to me. But before I can pass, RHO chimes in with three clubs.

Really? He wasn't willing to open three clubs, but he's willing to come into the middle of a potential misfit auction when both of us have shown decent hands? Ten fourth of trumps, a singleton in partner's suit, and an ace in my suit, which could easily be facing a singleton in partner's hand, make this a clear double.

I double, everyone passes, and I lead the king of diamonds.

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

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

Declarer echoes with dummy's eight, partner plays the five, and declarer follows with the three.

What do I know about the layout? Partner has at least six diamonds and at most two spades. He probably has a singleton club, since RHO would have opened three clubs with ace-queen-jack seventh. That means partner is probably 2-4-6-1. The four-card heart suit is probably why he chose not to open two diamonds. 

Could partner be 2-3-7-1? That would mean we have a heart trick coming. But I doubt it. Chiming in at the three level between two bidding opponents is bad enough as it is. I can't see South's doing that without a singleton somewhere. And "somewhere" has to be hearts.

Could partner have a singleton spade, in which case I can give him spade ruffs? That would make partner either 1-5-6-1 or 1-4-7-1. Partner might pull with those patterns, but that's not clear. He is right to pull if I have this hand, but for all he knows I'm 6-5 in the black suits.

What about high cards? Partner should have 9 or 10 HCP for his two-diamond bid. If he has ace-queen of diamonds, he still needs a queen and a jack or two queens. 

What does declarer have for tricks? If he has ace-queen-jack sixth of clubs, he has six club tricks, one heart, and one spade. If he scores a diamond ruff in dummy, that's nine tricks. So perhaps I should switch to a trump at trick two. If declarer wins and plays another diamond, partner can win and put me in with the spade ace for a second trump play, stopping the ruff. But is that good enough? Perhaps declarer doesn't need the ruff. Perhaps he can make use of the heart suit instead. 

Say I switch to a trump. Declarer wins in his hand. Heart to the ace, ruff a heart, club to dummy, ruff a heart. Dummy now has two good hearts. He draws my trump and leads a spade toward the king. I have no entry to partner's hand to cash diamonds, so he makes an overtrick. In fact, even if partner has a stiff queen or jack of clubs to hold declarer to five club tricks, declarer can still come to nine tricks if I let him set up hearts. 

Forget the trump shift. I need to shift to a spade to kill the late dummy entry. That allows declarer to ruff a diamond, but if partner has a club honor, we can afford that. So long as we kill the heart suit, declarer takes one spade, one heart, five clubs, and a ruff for eight tricks. 

Switching to spades has the additional advantage that I might catch partner with a singleton. I play the ace of spade--four--nine--deuce. Now three of spades--king--queen--ten.

Declarer plays a spade off dummy, and partner ruffs with the queen of clubs as declarer pitches the nine of hearts. The club queen is a good card to see, but I'm surprised declarer is pitching a heart. Could he be 2-2-3-6 after all? 

Partner cashes the diamond ace. Declarer follows with the seven and I pitch a spade. Partner continues with the nine of diamonds and declarer follows with the jack. We've reached this position, with me to play to the current trick:

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

This doesn't add up. If declarer is 2-2-3-6, then partner just underled his queen of diamonds to declarer's stiff jack. Did declarer make a truly bizarre three-club bid with

♠ 10 2  ♥ x x  ♦ J 10 x x  ♣ A J x x x ?

I ruff with the club five, forcing dummy's king. Declarer cashes the ace of hearts and pitches the ten of diamonds. OK. 2-1-4-6 after all. I eventually score the club ten for the setting trick.

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

Plus 100 is worth 93%. Only one other player doubled three clubs. This field is a bunch of ninnies. The other doubler managed to beat it two tricks. At trick two, he shifted to the king of hearts. With the spade entry intact, declarer could now make this. But he took the heart ace, ruffed a heart to his hand, and led the club jack for a backward finesse, finishing down two.

The heart shift makes no sense. If declarer has a stiff heart, it accomplishes nothing. If he has doubleton, he simply ducks, and the defense can't take more than four tricks. The heart suit is a source of tricks for declarer, not for the defense. So you need to attack dummy's side entry.

But, while the spade shift was correct, ace and a spade isn't good enough. Declarer can win the spade, play ace and ruff a heart, play a club to the king, and ruff another heart, stripping me of my last red card. After he cashes his top clubs, we will reach this position:

	NORTH Robot ♠ 8 5 ♥ J 6 ♦ -- ♣ --
WEST Phillip ♠ J 7 6 ♥ -- ♦ -- ♣ 10		EAST Robot ♠ -- ♥ 10 ♦ A Q 9 ♣ --
	SOUTH Robot ♠ -- ♥ -- ♦ J 10 7 ♣ 9

Now he exits with a club, pitching dummy's small heart. I get the spade jack, but I must concede the last two tricks to dummy. I think declarer knew enough about the layout to find this line. A good declarer would have made the hand after my defense.

To beat the contract, I must shift to low spade at trick two. That both kills the heart suit and builds an entry to partner with the spade queen. Now if declarer goes for the end play, I can reach partner to cash his diamonds.

A low spade isn't 100%. If declarer has

♠ Q x x  ♥ 9  ♦ x x x  ♣ A J 9 x x x

ace and a spade gives us the first four tricks, and I still have a club trick coming. A low spade is not a success. So at least my defense wasn't hopeless. 

But I didn't see the endplay coming. If I had seen it, noticed a low spade shift would prevent it, and then chosen to play for ruffs anyway, that would be one thing. As it is, I have to count my defense as an error.

Free Weekly Instant Tournament - October 25 - Board 7

Board 7
Both sides vulnerable

♠ 8 7 5  ♥ A Q 10 6 2  ♦ 9 8 5  ♣ K Q

I'm in first seat. Under normal circumstance, I wouldn't open a "5332" with 11 HCP. But this is a "best-hand" tournament, which means if I don't open, there is a good chance the hand will be passed out. If so, do I mind? Was I likely to go plus had I opened?

If I open with one heart and partner bids one notrump, I can pass. It's forcing, but partner doesn't have a cup of coffee to throw at me. If that happens, we will probably go plus in one notrump. 

If partner bids one spade, however, I have a problem. If I pass, we could easily miss a spade game. But if I rebid one notrump and partner raises to two, I suspect I'm a favorite to go down. All in all, I don't think opening rates to be a winning decision. 

With a balanced ten-count, I would be more tempted to open. I would be less worried about passing a one-spade response. And knowing everyone has exactly 10 HCP is a huge advantage in the play.

I pass. As does everyone else.

Passing the board out is worth 64%. Those who opened typically rebid one notrump over their partner's one spade response and played it there. Let's pretend I did the same and try to predict what would have happened.

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

West	North	East	South
Robot	Robot	Robot	Phillip in an Alternate Universe
			1 ♥
Pass	1 ♠	Pass	1 NT
(All Pass)

West leads the five of clubs. East takes the ace, dropping my queen, and returns the four of clubs to my king, West following with the eight.

Partner has 9 HCP, so the outstanding high cards must be distributed 10-11.

How should I continue? It looks natural to attack the diamond suit. I can lead the nine and let it ride. If it loses to the king or queen, I can lead the eight next, picking up the suit for three tricks if East holds king-seven or queen-seven doubleton. But that's still only six tricks. I'll need to find the heart king onside to come to seven.

If I need the heart finesse anyway, perhaps I'm better off forgetting about the diamond suit and trying for four heart tricks. I can start with a low heart from my hand, giving West a chance to make a mistake and hop with king doubleton. If that doesn't happen, I get to dummy and lead a heart to the queen, hoping for three-three hearts. 

This offers a better chance to make my contract than playing on diamonds. The problem is, I go down more if it doesn't work. I won't even score the heart ace, because I'll have no entry to my hand. I don't think that's a serious consideration, however. The board will be passed out at most tables, so I need to go plus to get a decent score.

I lead the five of hearts from my hand. West hops with the jack and leads the six of clubs to his partner's jack. I pitch the five of diamonds.

East cashes two more clubs. I pitch a diamond and a spade from each hand. West pitches the three of diamonds and the six of spades. We've reached this position:

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

East shifts to the spade queen, and West overtakes with the king. I see nothing to gain by winning this trick, so I duck on principle.

West continues with the spade jack. I take dummy's ace, and East follows with the four. East has shown up with the spade queen and ace-jack of clubs. There is room in his hand for the heart king. I lead the heart eight from dummy--five--queen--king. I score only the diamond ace after that. Down four.

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

The pairs who played one notrump all floated the diamond nine at trick three. So I would have gotten a zero for down four. I'm happy I didn't open.

Free Weekly Instant Tournament - October 25 - Board 6

Board 6
Opponents vulnerable

♠ 5 4  ♥ K 9  ♦ K Q J 5 4 3 2  ♣ K 4

RHO opens with one spade, and I overcall with two diamonds. LHO bids three diamonds, showing a limit raise or better in spades, and partner bids four diamonds. RHO bids four spades.

I have five losers. Can partner cover three of them? No doubleton is useful, so partner needs three working high cards. That's a limit raise. With a limit raise, partner would have bid three spades rather than gently raising to four diamonds. So five diamonds does not rate to make.

Next question. Can we beat four spades? I have one trick on defense (no tricks in diamonds and half a trick for each side-suit king). Partner needs three tricks to beat this, and I've already expressed my doubt that he has them. So four spades rates to make, and five diamonds should be a good save.

I bid five diamonds. LHO and partner pass, and RHO doubles, ending the auction. LHO leads the seven of spades.

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

West	North	East	South
Robot	Robot	Robot	Phillip
		1 ♠	2 ♦
3 ♦	4 ♦	4 ♠	5 ♦
Pass	Pass	Double	(All pass)

I can't avoid losing the two red aces. Is there any way I can pitch my spade loser? Spades are three-five, but West doesn't know that. From his point of view, East might have six spades, giving the defense no spade tricks. Further, West doesn't know his partner has no small trumps. So perhaps if I give him a chance to give his partner a heart ruff, he will take it rather than try to cash a spade.

This shouldn't work. Why would I play hearts before drawing trump if East might be ruffing hearts? But it's my only chance. I rise with the ace of spades. RHO plays the six; I play the four. Now deuce of hearts--six--king--ace.

West doesn't fall for it. He lays down the queen of spades, then shifts to the jack of hearts. I win in dummy and claim down one.

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

Minus 100 is worth 57%.

We have a shot at beating four spades. Declarer must pick up the jack of spades. Will he do so? Say I lead the diamond king. Declarer wins in his hand and plays a spade to the queen and ace. Partner returns a spade. What's the right play?

If North has ace doubleton of spades, it makes no difference, so let's assume he has ace third. (Yes, he might have ace fourth. Let's ignore that possibility for now.) Some might think this makes the odds three to two that North has the spade jack. Actually whether that's true or not depends on what we knew about the ace.

There are three ways for North to hold ace-jack third, and there are three ways for South to hold jack doubleton. So if North was known to hold the ace (from the auction perhaps), then it's a toss-up whether to finesse or not. Once you factor back in the possibility that North holds ace-jack fourth, finessing becomes the percentage play, but only by a small margin. If North can't have four spades or if you can't handle the hand if he does, then your play is indeed a toss-up. It's worth remembering this combination, since a lot of players don't realize that. 

In this case, however, North was not known to hold the spade ace until he played it. That makes a difference. Holding ace-empty third, he might duck the queen, but with ace-jack third, he can't afford to duck, since his jack will pop up next. In other words, with ace-jack third, his choice is restricted; with ace-empty third, it isn't. So, when he wins the ace, ace-jack third is more likely by restricted choice. Finessing is now a favorite even without factoring in the four-one break. So if we sell to four spades, declarer should finesse and make his contract.

One player almost managed a top. He bid an imaginative four diamonds over one spade. West bid four spades, and North bid five diamonds. After two passes, West decided to take the push to five spades, making this South the only player who found a way to get a plus score. But then he turned his top into a near zero. After two passes, he saved in six diamonds. There are two good reasons not to bid six diamonds:

1. It violates captaincy. A pre-empt describes your hand, so it's partner's job to make any further decisions. In this case, overruling partner is especially bizarre, since South has more defense than he has promised.
2. If you don't care about theoretical matters like captaincy, there is a practical reason not to save: Not everyone will take the push to five spades. Five diamonds doubled will be the contract at some tables--perhaps many tables. If you compete to six diamonds, you are automatically losing the board to everyone who bought it in five diamonds. So even if you are right, your gain is small. The odds favor defending even if you think five spades is a moderate favorite to make.

Free Weekly Instant Tournament - October 25 - Board 5

Board 5
Our side vulnerable

♠ K 10 4  ♥ 10 7 3  ♦ A 6 5  ♣ A K 5 4

Two passes to me. I have only 14 HCP, but I have three and a half honor tricks and two tens, so I open with one notrump. (No. I'm not "upgrading." I'm evaluating. I'm judging that this hand rightly belongs in the strong notrump category. I find the term "upgrading" annoying, because it implies there is something canonical about the Work point count. There isn't. It's just one method of evaluation.)

LHO bids two clubs, showing a one-suiter but declining to identify the suit. Partner bids two hearts, a transfer to spades. I bid two spades and everyone passes. LHO leads the king of hearts.

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

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

It appears West's suit is hearts. I have three hearts losers, a diamond loser, and probably two losers in spades. Unless I can avoid one of those losers, I'm going down.

East plays the deuce of hearts, and I follow with the three. At trick two, West shifts to the three of clubs. That's a strange play. I'm guessing that's a singleton club. But he knows at least one more heart is cashing. What does it cost to cash it? Is he hoping his partner can ruff hearts twice and give him two ruffs? That's awfully greedy. Is he really going to lead a low heart next, risking his partner has a doubleton? Robots don't signal at trick one, so there is no reason his partner couldn't have a doubleton heart.

I might as well win this trick in dummy and try a spade to the ten. I play the club queen, and East follows with the deuce. When I play a spade from dummy, East hops up with the ace. I play the four; West, the three.

East shifts to the jack of clubs. I play the ace, and West ruffs with the nine of spades.

West will presumably cash a heart. When his partner shows out, he will lead a low heart for his partner to ruff, then get a second club ruff, reaching this position:

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

At least West will be endplayed at that point if he has the diamond king. So I'll get out for down one.

West cashes the ace of hearts. To my surprise, East follows with the nine. Oh? Here I was assuming West's suit was hearts. Apparently it was diamonds. West presumably has three hearts. With a doubleton ace-king, he would have led the ace, and with four, he might have overcalled two hearts, showing hearts and a minor. So he's either 3-3-6-1 or 2-3-7-1.

I follow with the heart seven. West continues with the five of hearts to East's queen, and East plays another club, which West ruffs with the spade queen, reaching the above position in a different way than I anticipated.

At least I'm right that West is endplayed after taking his ruffs. He has only diamonds left. He leads the king of diamonds, and I claim down one.

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

This result is worth 93%! The opponents can make three diamonds and most of the field played it there. A typical auction was

West	North	East	South
	Pass	Pass	1 ♣
1 ♦	1 ♠	Pass	1 NT
2 ♦	Pass	Pass	2 ♠
3 ♦	(All pass)

I'm not sure I would have found that three-diamond bid. One diamond, then two diamonds seems like enough bidding to me, especially when the opponents are probably in a four-three fit. (North will usually bid two spades himself with five.) But West was right to bid on, so who am I to complain?

Our auction gave the West at our table a different problem. The way it timed out, West didn't know my two-spade bid was getting passed out, and he didn't want to bid at the three-level in a live auction. My one-notrump opening gained, as it sometimes does, by making the auction harder for the opponents. Although, interestingly, it wasn't my opening per se that gave West the problem. It was partner's transfer, which kept West in the dark about partner's intentions.

Free Weekly Instant Tournament - October 25 - Board 4

Board 4
Both sides vulnerable

♠ K J 10 9 7 6  ♥ A 7  ♦ K  ♣ A K Q 5

Partner opens with one heart in second seat. I have twenty high-card points and a good six-card suit. We're bidding some slam. It's just a question of finding the right one. The robots play two spades as a strong jump shift, but this isn't the hand for it. Strong jump shifts are for slam invitations, not slam drives. It's a way to let partner know you have about an ace more than a minimum game force, which can be hard to do in Eastern Science Fiction. And it surrenders captaincy. If you know you want to be in slam, you shouldn't jump shift, because you want to maintain captaincy yourself.

I bid one spade, and partner bids two hearts. After a one spade response, two hearts guarantees six, since there are no awkward patterns that might require a rebid in a five-card suit. In my style, it also denies three spades. Unfortunately, the robots don't play that way.

I bid three clubs, and partner bids three diamonds. In my methods, I would know I was facing a singleton or void in spades. The two-heart bid denies three spades, and the failure to take a preference denies a doubleton. This is one of the advantages of my approach. Discovering partner is short in your suit can be useful.

Perhaps I should just ask about partner's keycards. If he has king-queen sixth of hearts and two aces, we have thirteen top tricks if hearts break. And if hearts don't break, we have the spade suit in reserve. 

Actually, we don't necessarily need the heart queen. The spade queen is just as good. And grand slam is worth bidding at matchpoints even if partner has ace doubleton of spades and ace-jack of hearts. Opposite that hand, I can try to drop the heart queen first, then try to run spades if that fails. The combined chances are better than 50%. But I don't know how to find out about either of those hands. So I'll settle for six notrump if we're missing a key card or the heart queen.

Four notrump now would agree the last bid suit, diamonds. So I bid three hearts to set the trump suit. Partner bids three spades, a cue-bid, showing the spade ace. I bid four notrump, and partner bids five clubs, showing three keycards. I bid five diamonds to ask about the heart queen. Partner bids five notrump, showing the heart queen but no kings. I bid seven notrump. Everyone passes, and West leads the deuce of spades.

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

West	North	East	South
Robot	Robot	Robot	Phillip
Pass	1 ♥	Pass	1 ♠
Pass	2 ♥	Pass	3 ♣
Pass	3 ♦	Pass	3 ♥
Pass	3 ♠	Pass	4 NT
Pass	5 ♣	Pass	5 ♦
Pass	5 NT	Pass	7 NT
(All pass)

If either major suit runs, I have all the tricks. If neither major runs, I have eleven tricks: three spades, three hearts, two diamonds, and three clubs. If I had twelve tricks, I might have a squeeze. But with only eleven tricks, a simple squeeze isn't going to work. So I need to run one of the majors to make this.

I suspect spades are running. A spade lead from a singleton or from queen fourth would be strange on this auction. The lead is probably from three small.

I play low from dummy; East plays the four, and I win with the six. If the lead is from three small, why didn't East play the queen? I can't believe West would lead a spade from queen third, so I suspect he actually did lead a singleton, and East withheld the queen from queen forth.

I don't see how it hurts to cash the spade ace to see if I'm right. I lead a spade to the ace. West plays the five, and East discards the club deuce. West led from queen fourth. That's a strange choice.

We've reached this position, with the lead in dummy.

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

Now I need hearts to run. East's discard of the club deuce is probably from a five-card suit, since robots like to discard count cards. Could East be 1-4-3-5? If so, then I'm going down, since I'm not about to finesse him for the heart jack. But I need to make sure I'm down only one if that's the case. This was not a tough hand to bid, so most of the field should be in seven no trump. If this makes, it will be a little above average. My best chance for a good board is that it doesn't make and I go down fewer than the rest of the field.

I have only eleven tricks if hearts don't break, and I can't set up hearts and get back to dummy without burning a diamond trick. So I'll need an endplay to take twelve. If East is 1-4-3-5, can I arrange that? I can play a diamond to my king and cash the spade king, pitching a diamond from dummy. East can't afford a heart or a club, so he must pitch a diamond, coming down to a singleton. Now I start hearts. If West shows out on the second heart, we'll be down to this position:

	NORTH Robot ♠ -- ♥ Q 10 9 8 ♦ A 6 ♣ 10
		EAST Robot ♠  ♥ J x ♦ x ♣ J x x x
	SOUTH Phillip ♠ J 10 9 ♥ -- ♦ -- ♣ A K Q 5

I can cash the ace of diamonds, stripping East of his last diamond, then play four rounds of clubs to endplay him.

Wait a minute. None of this is necessary. I get two extra tricks if I set up hearts, so I can afford to overtake the diamond king to get back to dummy. Is that right? Five hearts, three spades, and three clubs makes 11 tricks. So yes, I need only one diamond trick to make twelve. I had a blind spot for a moment. Good thing I caught it before leading a diamond to my king.

I play the three of hearts from dummy. East plays the jack. I win with the ace and claim. Making seven.

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

A little above average? Shows what I know. This result is worth 100%. Most of the field is in six heart or six notrump. Those who could count to thirteen bid seven hearts instead of seven notrump. That's not a good choice. Not only does seven notrump score higher; it is also more likely to make.

Does Restricted Choice Work Against Robots?

[Below is an excerpt from a series of Substack articles I'm working on. It wasn't until I started writing this article that the conclusions I draw concerning playing against robots occurred to me.]

In the April 1954 issue of Contract Bridge Journal, Alan Truscott concluded a discussion of a bridge deal with the words "This line of thought, allowing for the defenders having had a choice of plays, crops up in many disguises."

The line of thought Alan was referring to had been introduced to the bridge world three years earlier in an article in Bridge Magazine by the mathematician A. O. L. Atkin. But it did not become widely known until Terrence Reese discussed it in his book The Expert Game, in 1958. There he devoted an entire chapter to the concept and gave it the name The Principle of Restricted Choice.

The applications of Restricted Choice go well beyond the game of bridge. It can provide intuition for understanding a number of apparent probability paradoxes. But its proper application can be tricky at times. In this series of articles, I shall examine some of these "paradoxes" and show how Restricted Choice can shed light on them.

[At this point, I introduce Restricted Choice, using Atkin's original example:

	NORTH ♠ K 10 7 6 2
	SOUTH ♠ A 9 6 3

After explaining enough of the rules of play to allow the non-bridge player to follow the argument, I show how, when East drops the jack under ace and West follows low at trick two, Restricted Choice shows that finessing is better than rising by a factor of 2 to 1.]

There is an issue one might raise with applying Restricted Choice to this problem. Let’s consider what happens on trick two. You lead the three and West plays the eight. If West has both the queen and the eight, he has a choice of cards to play. Thus, when he plays the eight, you might reason that he is only half as likely to have queen-eight as to have just the eight. We already decided that Case QJ is half as likely as it was before play began. Now the same is true of Case J. So it’s even money whether to finesse or rise.

What’s wrong with this argument? It doesn’t hold because of two constraints that were not explicitly stated but that a bridge player would assume: 

Constraint 1: The defenders (East and West) have a goal of preventing declarer from taking five tricks. 

Constraint 2: The defenders assume that declarer cannot see their cards.

When declarer leads toward dummy’s ace-ten and West holds queen-eight, West’s only hope of scoring a trick is to play the eight and hope declarer plays the ace. He has no way to win by playing the queen. Because of Constraint 1, his choice is just as restricted as East’s but for a different reason. So there is no adjustment to the likelihood of Case J.

Constraint 2 is also important. If West thinks declarer can see his cards, he will think it makes no difference which card he plays. So if we remove Constraint 2, West has no reason to prefer one card over the other, and his choice is no longer restricted.

We took these constraints into account when we specified the rules for the defenders’ play in the proposed simulation. It’s worth noting, however, that Constraint 2 does not necessarily hold any more. We now have robots that play bridge. While robots are programmed to try to thwart declarer in his goal (satisfying Constraint 1), they make an assumption humans do not: that declarer can see their cards.

Why? Because programming computers to play bridge is hard, and no one has yet found a suitable algorithm that does not require this assumption. The code for robot play is not open source, so I can’t say for sure that a robot West would randomize his play with queen-eight. But I have seen them rise with the honor in this situation, so I believe they do. If so, then the odds for rising and finessing are approximately the same. 

I say approximately because, as we said earlier, Case QJ is slightly more likely than Case J. The difference didn’t matter when the odds were 2 to 1, but now it does. So rising is actually the percentage play by a small margin.

It's worthwhile emphasizing the reason Restricted Choice applies differently to robots and to humans. Some assume, before hearing my analysis, that I am going to claim they don't randomize properly. As we saw in the Prior Strategy discussion [part of the redacted section above] whether an opponent in fact randomizes his play doesn't matter. What matters is that he might. 

The critical factor in deciding whether to apply Restricted Choice is whether an opponent has a choice of plays or whether his play is restricted. This restriction could be because he has no other card to play, or it could be because his alternative is proscribed by the logic of the situation. The latter consideration is what matters here. Because of a glitch in the way robots "think" about bridge, they have a choice of plays in situations where a human does not. That's where the difference lies.

Free Weekly Instant Tournament - October 25 - Board 3

Board 3
Opponents vulnerable

♠ J 5 4  ♥ K 10 9  ♦ A Q 8 6 3  ♣ A Q

I open with one notrump. LHO bids two hearts, showing hearts and a minor. Partner bids two notrump, lebensohl (a puppet to three clubs). I dutifully bid three clubs and partner passes.

RHO now comes to life with three hearts. I can't imagine why he let me find out what partner's suit was before bidding three hearts. Bidding three hearts immediately must be better.

I pass, LHO passes, and partner balances with three spades. See? If RHO had bid three hearts the first time, partner wouldn't be able to bid three spades. The delayed raise gave partner a chance to show both his suits.

RHO doubles three spades. Partner should have four spades and longer clubs. The four-three spade fit doesn't look appetizing, so I'll correct to four clubs. But, with ace-queen of clubs to fill out partner's suit, I might as well bid three notrump on the way. If partner doesn't fancy three notrump, he can always pull to four clubs.

I bid three notrump and partner pulls to five clubs. Partner had no game interest originally but now, after his LHO showed a stack in his second suit and I've shown wastage in hearts, he's suddenly willing to try for eleven tricks?

For some reason, the opponents don't double. Everyone passes and West leads the three of spades.

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

West	North	East	South
Robot	Robot	Robot	Phillip
			1 NT
2 ♥	2 NT	Pass	3 ♣
Pass	Pass	3 ♥	Pass
Pass	3 ♠	Double	3 NT
Pass	5 ♣	(All pass)

Pulling to five clubs was an unfortunate decision. We have nine tricks off the top in three notrump. Ten if they lead a heart. This contract I'm not making.

The spade lead is either a singleton or three-deuce doubleton. If it's a singleton, I can hop with the ace and draw trump, reaching this position with the lead in dummy:

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

Now I lead a heart to the nine. If West has the heart ace, as seems likely, he is endplayed. He must give me a tenth trick in one red suit or the other for down one. If the lead was a doubleton, however, the endplay won't work. He will win the heart and exit with a spade for down two.

What happens if I duck the spade at trick one?  If it's a singleton, East can win and give his partner a spade ruff. But that's OK, since he's ruffing a loser. After ruffing, West will exit with a trump. I will win, draw trump, and execute the same endplay. I still get ten tricks.

What if I duck the spade and East wins and returns a heart to get his partner off the endplay? I play the nine, and West wins with the queen or jack. We've now reached this position with West on lead:

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

If West plays another spade, I can win in dummy and play a third spade, eventually ruffing a spade to my hand for my tenth trick. And if, instead of a spade, he shifts to a trump, then I can draw trump and lead a spade toward my jack for my tenth trick.

In short, hopping with the ace works if West has a stiff spade, but ducking works whether he has a stiff or a doubleton. (Assuming you define "works" as getting out for down one, which seems like the best I can hope for.)

I play a low spade from dummy. East wins with the queen and returns the deuce. I hop with the jack and West ruffs with the four of clubs. He doesn't give me the satisfaction of endplaying him, however. He cashes the heart ace, then shifts to a club. I claim the rest. Down one.

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

Minus 50 is worth 64%. That's pretty generous for going minus when we're cold for a game. Five clubs was played at a few tables. Most declarers rose with the spade ace at trick one. While not best, that works as the cards lie. Or it should work. After that start, they failed to find the endplay and went down two. 

Some sat for three spades doubled, which seems like an odd decision. Two of them made it after a poor defense. But most were down several.

Free Weekly Instant Tournament - October 25 - Board 2

Board 2
Our side vulnerable

♠ K J 10 2  ♥ A Q 5  ♦ Q 9 6 3  ♣ A Q

RHO passes. I open with one diamond and partner bids one spade. 19 support points is worth a four-spade bid. But the ace-queen in my short suit isn't pulling full weight, nor is the unsupported queen of diamonds. And I have six losers. This hand doesn't merit driving to game. I bid three spades.

Partner bids four notrump. I bid five clubs, showing my three keycards. Partner bids five diamonds to ask about the queen of trumps.

If I bid five spades and partner passes, then we are off an ace and the queen of spades. Am I unhappy if that happens? Should I lie and say I have the queen to make sure we get to slam?

One doesn't normally lie about holding the trump queen unless you are known to have a ten-card fit. But holding the jack and ten of spades may make this hand an exception. If partner holds five spades and passes, we've missed a 52% slam. If he has four spades and passes, we've missed a 50% slam. 

Actually both of those percentages are slightly overstated. The opponents might start the defense with ace and a ruff. Or, if partner has four trumps, we might run into a five-zero break. So slam is good, but only marginally so, if partner has five spades and against the odds if he has four. 

He is more likely to have five spades than four, since, with four, he needs a better hand in high cards to bid Blackwood. In other words, the set of hands where he will bid Blackwood is larger when he five spades. So if small slam were the only consideration, it's probably right to lie. But I can't be sure we're off an ace. If we aren't, partner is intending to bid seven if I show the spade queen. I certainly don't want to get to a marginal grand slam. It's close, but I think the odds favor telling the truth.

I bid five spades, and partner passes. RHO leads the three of hearts.

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

West	North	East	South
Robot	Phillip	Robot	Robot
Pass	1 ♦	Pass	1 ♠
Pass	3 ♠	Pass	4 NT
Pass	5 ♣	Pass	5 ♦
Pass	5 ♠	(All pass)

Partner has five spades, so slam is a favorite. Nothing I can do about that now. All I can do is take as many tricks as I can in this contract.

Some players think that, in a situation like this, you should take an anti-percentage play in spades, taking a finesse rather than playing for the drop, in the hope that six spades is going down. That's faulty reasoning. You aren't competing against the pairs in six spades. You are either going to beat them or lose to them, and nothing you do at your table will change that. You are competing only against the other pairs who didn't reach slam, and your best chance to beat those pairs is to take your percentage play. So I'm winning the heart and cashing two top spades.

What do I do after that? What I would like to do is sneak a diamond through. If I can, then I can pitch my last diamond on dummy's hearts and avoid a diamond loser. I don't want to play a side suit to get to the right hand for the diamond lead. That would give the defense unnecessary information. So I need to decide now which hand I want to be in after I cash the spades.

Which hand is more likely to have the diamond ace? West might have led the diamond ace if he had it. He might be afraid to lose it, or, if he has diamond length, he might hope his partner has a singleton. That's not a lot a go on, but it's all I've got. So I want to end up in dummy to lead toward my hand after cashing the spades.

I play low from dummy on the heart lead. East plays the nine, and I win with the king. I cash the spade ace--six--deuce--five. Now a low spade--three--king--queen. Unfortunately, six spades is making. I lead a low diamond from dummy as planned--four--king--five. I claim the rest. Making seven.

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

A few players did reach slam by lying about the trump queen. And perhaps they were right to do so. It's close.

The overtrick was important. Plus 710 is worth 46%. Plus 680 would have been worth 29%. Only one player decided to finesse the spade because he missed a slam. He scored 650 for a zero.

Free Weekly Instant Tournament - October 25 - Board 1

Board 1
Neither vulnerable

♠ K 5  ♥ A 9  ♦ K 7 6 4 2  ♣ A 9 4 2

Two passes to me. I open with one diamond, and partner bids one spade.

We had a similar deal a few weeks ago where I chose to rebid one notrump instead of my lower-ranking four-card suit, and I received a number of objections. (Not well-articulated objections. Simply comments like "One notrump is wrong.") On that deal one could argue for either rebid. This time I think one notrump is clear. Half my high cards are in my short suits. And I have decent secondary support for spades. If we belong in two spades in a five-two fit, we won't get there if I bid two clubs.

I bid one notrump, and partner bids two hearts, non-forcing. I correct to two spades. I'm glad I rebid one notrump. If partner is 5-4-1-3, he would pass two clubs, and if he's 5-4-2-2, he would correct to two diamonds. I suspect in either case I would rather play in two spades.

But partner doesn't pass two spades. He bids three hearts, invitational with a fifth heart. I have a maximum in high cards and two fitting honors in partner's suits. But having no third card in either suit is a liability. We are probably high enough at the three level. I correct to three spades and partner passes. RHO leads the five of hearts.

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

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

It looks as if I'm going to lose two hearts, the diamond ace, a club, and possibly a spade. I could conceivably set up the diamond king for a club pitch. But I'm in danger of losing control. It's not clear I can afford the tempo of playing a diamond to the king.

I don't think East is leading a low heart from honor doubleton or from both honors. So there isn't much point in finessing the nine. I rise with the heart ace. East drops the queen, and I play the deuce.

The four of hearts is still out, so it appears the lead was from a five-card suit and the queen was a singleton. If I pick up the trump suit and drive the king of hearts, I can take five spades, three hearts, and the club ace for nine tricks. If West has five hearts, it's likely East has spade length, so my best play in spades is to cash the king and finesse the ten. That is, assuming I can handle four-two spades. Can I?

After four rounds of spades, say I lead a heart to the nine and West ducks. I need to get to my hand twice--once to drive the heart king and a second time to cash my heart. I have only one trump left, so I'll need to find the club king on my right and use the club queen as one of my entries. If spades are three-three, I don't need the club king onside.

Even though the finesse is the right play in the spade suit, the fact that it works only half the time even when it's right makes playing for the drop better. Playing for the drop works any time the suit is three-three or when West has jack doubleton and the club king is onside.

I cash the king of spades--eight--three--nine. Why are they playing their high spades? I lead the five of spades from dummy, and East plays the six. Would East play 86 from J864 or J862? What if his partner had Q9? I would win the second trick with the ace and could now drive East's jack with my 107x. If East had saved the eight, he would have a second trick.

East can't afford the eight from jack fourth, so even if I were intending to finesse the ten, I would now change my mind. 

I play the ace; West plays the four. I cash the queen--jack--diamond from dummy--deuce. This deal is a good illustration of the folly of blindly falsecarding. You must decide whether you want to feign shortness or length. If you want to feign length, as here, you must play low cards, since you often can't afford high cards from length.

While East's play of the eight was an error, he might have gotten away with it if his partner hadn't outed him. East could afford the eight from J98x, but West's play of the nine told me that wasn't the case. While it turns out I wasn't going to finesse, the defense didn't know that. The two errors combined might have talked me into the winning play.

I'm up to nine tricks. Can I afford to try a diamond to the king? Say I lead a diamond to the king and ace. East taps me with another diamond. I lead a heart to the nine and it holds. Nope. I'm in trouble. I can't afford to play a diamond. I have to lead a heart to the nine.

I play a heart. Dummy's nine wins and East discards the three of diamonds. That looks like a five-card diamond suit, making West 3-5-2-3. Here is the current position, with the lead in dummy:

	NORTH Phillip ♠ -- ♥ -- ♦ K 7 6 4 ♣ A 9 4 2
	SOUTH Robot ♠ 10 7 ♥ J 10 6 ♦ 8 ♣ Q 7

West presumably has K87 of hearts, two diamonds, and three clubs remaining. If he has the club king, can I endplay him? I can't let East in to put a club through, so I must hope West has the diamond ace as well. Say I lead the diamond king off dummy to West's ace. If he exits with his diamond, I can endplay him. So he must exit with a low heart instead. I win and cash a spade, and West pitches a club. We've now reached this position:

	NORTH Phillip ♠ -- ♥ -- ♦ 7 6 ♣ A 9 4
WEST Robot ♠ -- ♥ K 8 ♦ x ♣ K x
	SOUTH Robot ♠ 7 ♥ J 6 ♦ -- ♣ Q 7

When I cash my last spade, West simply pitches a heart, giving me a heart trick I can't make use of. There is no way I can extract that last diamond, so I can't endplay him.

Perhaps I'm better off hoping East has ace-queen or ace-queen-jack of diamonds and the club king. If I play a low diamond from dummy, he may hop with an honor for fear I'll score my singleton, then exit with a club, playing his partner for the queen.

That seems like my best option. I play the four of diamonds from dummy. East plays the five. That didn't work.

West wins with the jack and continues with the queen of diamonds. I doubt if he would do that with the club king, but it's my only chance. I ruff in my hand and lead the jack of hearts. West wins and plays a club. I duck, and East wins with the king. Making three.

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

Plus 140 is worth 79%.

If you rebid two clubs instead of one notrump, partner bids three hearts, natural and invitational. So three spades would appear to be the normal spot. Strangely, only one other declarer played it, and he went down three. Half the field was in three notrump, which three declarers managed to make. The other half was in three or four hearts, down several.