Free Weekly Instant Tournament - December 23 - Board 2

Board 2
Our side vulnerable

♠ A 9 4 3 2  ♥ Q 3  ♦ 10 3  ♣ A J 5 3

RHO opens with two hearts. One generally needs at least an opening bid to overcall a weak two-bid. While some would consider this hand an opening bid, it certainly doesn't qualify once you devalue the heart queen. It could be right to overcall anyway. I have the spade suit and heart shortness, both of which argue for being aggressive. But it still feels too thin for me, especially at this vulnerability. At matchpoints, the vulnerable game bonus doesn't compensate for the danger of going minus 200.

I pass, LHO passes, and partner balances with two spades.

Despite my five-card support, this hand, with eight losers, is worth only a strong invitation. In a competitive auction, it's OK to overbid with a ten-card fit, since, if you go down, it is likely the opponents could make something. But on this deal the opponents have shown no interest in bidding past the two-level, so going down at the four level is unlikely to be a good result. I'll simply show my limit raise by bidding three hearts.

Over three hearts, partner bids four spades and buys it. RHO leads the diamond ace.

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

West	North	East	South
Robot	Phillip	Robot	Robot
2 ♥	Pass	Pass	2 ♠
Pass	3 ♥	Pass	4 ♠
(All pass)

If partner accepts an invitation with that hand, I was right only to invite. The five-card heart suit is a serious liability, since it gives him a lot of losers to dispose of. If I had only three-card spade support, he would need me to have quite a good hand to have any chance of making this. Even with four spades, I would need good trump spots to avoid overruffs. I would have settled for three spades with partner's hand.

I'm off three fast tricks and a heart ruff, so I can't make this against best defense. But the fact that East is void in hearts may prove fortunate. If West continues diamonds at trick two, East loses his ruff, since he doesn't have a stiff heart to shift to.

East foolishly encourages with the diamond nine. Which card is more likely to induce West to continue diamonds? The five or the queen? If I play the queen, West may worry I have a singleton. If I play the five, he can be fairly sure I have another diamond, since his partner, with king-queen-jack, would play the king rather than the nine if he wished to encourage. In addition, I need to make sure East wins the next diamond trick. If I play the queen, East may be able to underplay West's spot at trick two.

Accordingly, I play the five. West, sadly, ignores his partner's signal and shifts to the heart ace. East pitches the club four, gets his heart ruff, and cashes the diamond king. I take the rest for down one.

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

An eight-one diamond split! West had no diamond to continue, so I had no chance to make this. Obviously East should have discouraged at trick one, since, if his partner had the thirteenth diamond, East certainly didn't want him to play it. East signaled with blinders on, looking only at his diamond holding rather than at the entire hand. He was lucky not to be punished. 

Some might play the diamond jack at trick one as an alarm-clock signal to suggest a void somewhere. I don't think that's the right use of the alarm-clock signal. The alarm-clock doesn't necessarily suggest a void. It says, "I don't want a continuation. But if I discourage, you will shift to the wrong suit. Please lead the other one." In this case, the natural shift is to a heart, not to dummy's source of tricks. So "the other one" is clubs. Perhaps you have the king-queen of clubs and can see an endplay coming if you don't get a club shift.

Minus 100 is worth only 25%. Plus 140 would not have been much better, scoring 43%. To get a good board, I have to overcall with two spades. We make game from my side unless East leads a diamond, and the club king is his normal lead. Over half the field did overcall. It's possible my judgment is wrong and overcalling is the percentage action. But if so, this deal is not evidence of that fact. The reason the overcall worked was rather random, having nothing to do with the merits of the bid.

Free Weekly Instant Tournament - December 16 (Beethoven's Birthday) - Board 1

Board 1
Neither vulnerable

♠ A K 10 8 7 2  ♥ K 7  ♦ A J  ♣ K J 5

Partner opens with two hearts. The robots tend to have good suits for their weak two-bids, so it's likely partner has ace-queen sixth. We could have a slam if we have a spade fit, so I'll start with two spades to find out. If partner raises, I'll bid Blackwood. If he bids three hearts, I'll settle for four hearts or three notrump. I'm not sure which, but there's no reason to worry about that yet.

Over two spades, partner bids two notrump. Since we don't have a spade fit, I'll give up on slam. As far as which game to play, I was contemplating three notrump even before partner suggested it. So I'll accept his suggestion.

I bid three notrump. Everyone passes and RHO leads the three of diamonds.

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

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

That looks more like a one-heart opening to me. But it wasn't my decision to make.

Assuming hearts come home, I have eleven tricks after this lead. If I can take a club trick, I have twelve. Some pairs will be in four hearts, and it's not clear how many tricks they will take. If they can set up spades, they might make seven. But I can't beat that result, so it's not a concern. There may, however, be some plus 480s, which I can beat if I guess the clubs.

I play the diamond jack from dummy. East covers with the queen and I win with the king. The diamond deuce is still out.

I can't run hearts before guessing clubs, since I would have to cash my diamonds as well, setting up diamonds tricks for them. And it's not clear that would give me any useful information anyway. I might as well play clubs now. Perhaps I can exploit the robots' tendency to cover an honor with an honor anytime it might gain. If I lead the club ten, will West cover with the queen? If he knew I had the diamond ten, he might not, since he would know a second club trick is of no use to me. But with the information he has, not covering may cost a trick. So I'm fairly sure he will cover.

I lead the club ten. West plays the six, so I go up with the king. No luck. East takes the ace. I assume it didn't matter. East presumably has the queen as well.

East shifts to the six of diamonds. West plays the five and I win in dummy. I still haven't seen the deuce.

Is there any chance to make six? I might have a black-suit squeeze against East. Unfortunately both the club jack and spade ten are in front of him. The only possible threat behind him is the club eight, so I would need to find East with the only spade guard and with queen-nine of clubs. If I hadn't led the ten, it would work as a threat, so I wouldn't need East to hold the nine. Too late now.

I cash the heart king, and East discards the spade four. Whoa! I'm down to four heart tricks. I have two spades and three diamonds, so I'm still making this. Is it possible to make an overtrick?

I have four hearts and three diamonds to cash and I've lost a club trick. So I'll be down to five cards in the end position. Dummy will have three spades and a doubleton club. Here's what the position will look like:

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

If East has the only spade guard, he is in trouble. If he holds three spades and two clubs, I can endplay him in spades. If he stiffs the queen of clubs, I can duck it out. He may have a diamond to cash, but then I'll take the last three tricks. If he has a small diamond to lead to his partner, the endplay won't work. So I need to hope that's not the case. 

I need to guess his shape so I know if he stiffs the club queen. The robots give count on their first discard, so the spade four is either lowest from three or five or third best from four. It's hard to believe he doesn't have a more attractive discard than a spade from a four-card suit, so it's probably three or five. Given his heart void, it's more likely five. I still don't know how diamonds split. West could have three or four--conceivably even five, since the deuce is still missing.

On the next heart, East discards the diamond deuce. So I now know West began with three or four diamonds. On the next two hearts, East discards the club three, then the deuce. The robots don't always give accurate count after the first play in a suit, so I can't read too much into the echo. But I doubt he would stiff the club queen without knowing I have a third diamond winner. So my best guess is East is 5-0-3-5, which is good news, since that means he won't have a diamond exit in the end position. If my construction is correct, East has four spades and queen doubleton of clubs remaining.

I cash the diamond ten. West plays the nine; East, the seven. So my construction is wrong. East started with at least four diamonds. I can still endplay him if he's 4-0-4-5. But is that possible? I said earlier I didn't think he would pitch a spade from four, and I see no reason to change my mind. Most likely he's 3-0-5-5, probably with three small spades, since I doubt he would have pitched from honor third.

If that's the layout, I can't endplay East. Can I endplay West? West should be down to

♠ Q J 3  ♥10  ♦ --  ♣ x

When I lead a spade, he will split, and I will take the ace. Now I can lead a low club from dummy. If West's club spot is the nine, I have him. If East hops with the queen, he gives me the club jack. If he ducks, West wins with the nine. He can cash the ten of hearts but must then lead a spade into dummy's king ten.

That seems like my best chance at this point. I play a spade. Will I have the courage of my convictions and play the ten if West plays low? West doesn't put me to the test. He inserts the jack. I take the ace and lead a low club. Unfortunately, it is East who wins with the nine. He has a club and a diamond to cash. I take the spade king at the end. Making three.

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

Almost the entire field is in four hearts, which I find surprising. I expected some pairs to play four hearts, but this seemed like a pretty routine auction. (At least from my side of the table. And we are all playing with the same partner.) 

Four hearts made four, so plus 400 is worth 11%. Had I led a small club at trick two instead of the ten, I would have scored 430 for 100%. Little did I know I had won the whole board in the auction.

Did I make a mistake? I don't think so. Against these opponents, the club ten gives me a 75% chance to take a club trick instead of a 50% chance. The only time it costs is when both club honors are offside and hearts are five-zero offside. It's wrong to forgo the vig in leading the club ten for fear of a layout as unlikely as this one.

Free Weekly Instant Tournament - December 9 - Board 8

Board 8
Neither vulnerable

I started this week's tournament with a zero, going down in a marginal slam that no one else reached. But I've managed to pull my score up to 74% going into the final board:

♠ A K J 7  ♥ Q 9 7 5  ♦ A 3  ♣ A 6 3

Three passes to me. With 18 HCP and a balanced hand, I have a routine two-notrump rebid. I start with one club. Partner responds with one heart. My heart queen has gone up in value, so I can re-evaluate this hand as a game force. I bid four hearts and partner passes. RHO leads the diamond five.

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

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

The diamond five isn't very informative. It could be from shortness or length. Since the four and deuce are missing, it could even be from a six-card suit. 

While the lead isn't informative, it at least picks up the diamond queen for me. I have ten tricks after knocking out the top hearts. If trumps are three-two, I can score an eleventh trick via a ruff. A ruff may be problematic if trumps are four-one.

Sometimes one can cater to a bad trump break by taking a ruff early. Does that work here? Let's say I play ace, king, and ruff a spade now. Already there are problems with this line. Someone may ruff the second spade, or someone may pitch a club on the third spade, setting up an eventual club ruff.

And those aren't my only problems. After I ruff a spade, say I lead a heart and it holds. Now what? I've exposed a spade loser. So if I play another trump, the defense may be able to draw dummy's trumps and cash a spade. To prevent that, I have to ruff my last spade, giving the opponents another chance to pitch a club and set up a club ruff.

It might be worth taking the risk of an early spade ruff if not for the fact that I have other chances for an eleventh trick. The clubs may come home, I may have a black-suit squeeze, or I may take a spade finesse. Given I have those other chances in reserve, I'll forgo the early ruff.

I play a low diamond from dummy. East plays the queen, and I win with the king. I want to keep all high trumps in dummy in case I do decide to ruff a spade and draw trumps. So I lead the heart jack--three--five--king. East shifts to the club deuce. I could insert the ten, which would be my eleventh trick if it held. But a shift from the jack into dummy's ace third is unattractive. It's more likely West has jack doubleton and inserting the ten would give up my chance to drop it. I can always finesse East for the jack later if I change my mind. So I go up with the king, retaining a club entry to each hand.

I play the heart deuce and West discards the three of spades. I play the seven, and East underplays with the six. So the four-one trump break I was worried about transpired. Should I ruff a spade now? Say I play ace and king of spades (hoping they both cash) and ruff a spade. If East shows out on the third spade, I'm home. I just lead the ten of hearts to the queen. Whether East wins or ducks, nothing bad can happen.

What if East follows to the third spade? Then I'm down to this position:

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

If the spade jack isn't high, I have to ruff it. Can I do that safely? Diamond to the ace. Club ace (hoping it cashes), to guard against East's pitching his last club as I ruff the spade. Now I take my ruff. East is down to two trumps and one minor-suit card. I have to guess which minor suit and cash the right winner. Then my only loser is the trump ace.

There are too many ways that line can fail. It seems better just to drive the trump ace now and hope I can score an eleventh trick in the black suits. We're back to this position:

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

I lead the heart nine. East takes the ace as West discards the seven of diamonds. I haven't seen the four or deuce, so I'm still not sure how diamonds are splitting.

East plays his last trump, and West discards the club nine. Unless West began with five clubs, my clubs are now good. If he did, I have to hope the spade queen drops or West is squeezed.

I win with the heart queen and cash the club ace. East follows, so I claim.

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

Plus 450 is worth 61%. The only person to do better opened with one notrump then refused to show a four-card major over Stayman. He reached three notrump, making five.

I don't know why people think you have to do bizarre things to win. I averaged 72% doing nothing more than trying to take the percentage action at every turn. And if I had actually succeeded in taking the percentage action at every turn, I would have done better. Surely that's a more promising approach--and more rewarding even if you don't end up winning.

Free Weekly Instant Tournament - December 2 - Board 7

Board 7
Both vulnerable

♠ K 10 9 6 4 3  ♥ A Q 5  ♦ A 5  ♣ 8 5

I open with one spade, and partner bids one notrump. I bid two spades, and partner raises to four. Partner probably has a three-card limit raise. Once I've shown a sixth spade, a three-card limit raise becomes a game drive.

Everyone passes, and West leads the diamond three.

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

West	North	East	South
Robot	Robot	Robot	Phillip
			1 ♠
Pass	1 NT	Pass	2 ♠
Pass	4 ♠	(All pass)

Hmm. Partner upgraded his two notrump rebid to a game drive. I think that's a mistake. The sixth spade doesn't significantly improve your hand when you have only two trumps. Fortunately, this is a decent game, but that's because I have a clear acceptance over three spades.

I play the diamond ten from dummy. If East has the queen, he should duck this. I get three diamond tricks whether he covers or not, but it must be better to tangle up the suit and give me communication problems. East doesn't see it that way. He covers with the queen, and I take the ace.

It's tempting to cash my diamonds and pitch a club. But that could work out badly. For one thing, West may have a doubleton diamond and score a ruff with the club ace onside all along. For another, after I take my pitch, I'm in the wrong hand to start trumps. I'd like to play the first trump from my hand to guard against ace-jack tight on my left. But if I cross to my hand with a heart, I expose myself to a possible heart ruff. 

Even if no one has a singleton heart, I could run into problems. Say I lead a heart to my hand, then a spade to the queen and ace. East plays a second heart. I win in dummy and finesse against the spade jack. It loses, and West gives his partner a heart ruff--or crosses to the club ace and gets one himself.

Perhaps I'm better off postponing the pitch. I could lead a spade to the queen at trick two. Playing a spade now could work out badly also. If West has the spade ace and East has the club ace, West could hop and lead a club, making me wish I'd taken my pitch. But there is only a 25% chance both aces are wrong. And even if they are, why should West find the winning defense? If he had some club holding where shifting to a club is safe (queen-jack-ten, for example), he would have led a club at trick one. So hopping and shifting to clubs has to entail some risk.

Whenever declarer might take an early pitch but doesn't, it suggests either that he can't (on this deal, for example, that I have ace third of diamonds) or that the pitch is unnecessary (on this deal, that I have the club ace). So West might reason that hopping with the spade ace and shifting to clubs is unlikely to be the right defense.

It's a common mistake to forget that the opponents can't see your hand. Worrying that they will find some double-dummy defense is fine if you can cater to that possibility with virtually no risk. But that's not the case here. The risk in taking the pitch may be small, but it's not insignificant. The risk that the opponents will find the killing defense probably is insignificant.

I play the spade three--deuce--queen--ace. East plays the diamond eight. I win in dummy as West follows with the seven. At this point, I have to take the pitch. At least I now know that West didn't start with a doubleton diamond.

Could I set myself up for an uppercut by taking the pitch? Suppose West has three diamonds and jack-eight fourth of spades. I take my pitch and lead a spade. East shows out. I take the king and concede a trick to the jack. If East has the club ace, West can now lead a club to him for a fourth diamond, scoring his spade eight. But If East has the club ace, there was never anything I could do. I could stop the uppercut, but then I would have to lose two club tricks. So there is no reason not to take the pitch.

I cash the last diamond, pitching a club. East follows with the six; West, with the nine. I lead a spade from dummy and East follow with the eight.  I finesse the nine, and West pitches the heart eight. So I have another spade loser plus a club loser unless East started with three hearts. If he did, he can't ruff in until I pitch my last club. Unfortunately, West's heart eight, assuming it's a count card, makes that unlikely.

I cash the spade king as West pitches the club deuce. I've reached this position:

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

I cash the ace of hearts--seven--three--deuce. West echoed, so it appears he began with four hearts. On the other hand, why would West pitch a heart from four? He doesn't know I don't have the spade jack. If I had it, pitching from four hearts allows me to make six.

I cash the heart queen--four--six--ten, then play another heart. West follows with the jack. So he did have four hearts. I see. He must have the club ace as well. He knew he was getting squeezed if my spades were good, so pitching a heart couldn't hurt.

I play the king. East ruffs and plays a club to his partner's ace. Making four.

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

Plus 620 is worth 64%. One declarer made five. After reaching the end position above, he conceded a trump trick rather than attempting to run the hearts. East won with the jack and failed to return a club, so declarer got his discard.

After West's heart pitch, perhaps that was a better line. Since the robots almost always give count on their first discard, the only way hearts could be three-three was if West had jack-ten-eight of hearts. And if he did, he might have led one. Conceding the trump trick was my best shot. 

I forgot that East couldn't see my hand.

Free Weekly Instant Tournament - November 25 - Board 6

Board 6
Opponents vulnerable

♠ Q 7 6  ♥ K Q 9 3  ♦ A Q 3  ♣ Q 5 4

RHO passes. In the early days of bridge, this hand would not qualify for a strong notrump opening, since it contains only three honor tricks. A one-notrump opening was expected to contain three and a half or four. Possibly this judgment is correct. Queens are overvalued relative to aces in the Work point count. So with four queens and only one ace, 15 HCP overstates the value of the hand. 

Still, such considerations are less important--possibly even wrong--for notrump bidding. So I'm opening with one notrump anyway. If partner steers toward a suit contract, I'll consider this a sub-minimum.

Over one notrump, LHO bids two spades, showing spades and a minor. Partner bids two notrump, a puppet to three clubs. I bid three clubs and LHO doubles. The tooltip says this shows "rebiddable clubs," so I assume LHO has at least five clubs. He might have only four spades.

Partner bids three diamonds, to play, ending the auction. RHO leads the club deuce.

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

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

Partner had quite a problem over two spades. A negative double, intending to correct three clubs to three diamonds, might work out. But if opener passes the double, as he usually will with four spades, you won't be happy. I don't believe the robots play negative doubles here anyway, so pass and two notrump were partner's only options. While I don't like passing with spade shortness, I don't like playing five-two fits at the three level either, so I would have simply passed.

I play a low club from dummy. East wins with the king and I play the three. Presumably West has jack third of clubs and East has ace-king-ten fifth.

East shifts to the heart five. This is probably a singleton. I must conceal the four so West won't be sure about that. I play the heart seven, and West takes the ace.

West cashes the spade ace. East plays the three and I drop the four. I haven't seen the deuce. The robots don't signal. But if they did, East's card should be attitude--low to say his heart shift was a singleton and high to say it wasn't.

On this particular layout, most players would probably agree on that. But some would play East's card as suit preference if dummy had the spade king instead of the queen. They would play high to ask for hearts and low to ask for clubs. I think that is a serious error. Playing low to ask for hearts sometimes and high to ask for hearts at other times is begging to have an accident. This is an attitude situation. Was your heart shift a singleton or not? It makes no difference whether the likely alternative to giving you a heart ruff is continuing spades or shifting to clubs. Sometimes the alternative won't be obvious, so the defenders should have to worry about that in order to determine to what kind of signal East should give. Switching signaling methods based on some irrelevant criterion provides no benefit, so why bother? If you always play attitude here, you can't have an accident.

West continues with the jack of spades. I don't want to give him another chance to find the heart ruff, so I cover with the queen. East wins with the king and cashes the club ace. West plays the eight. That's the fifth trick for the opponents, so I'm already down one.

East now plays the spade five. I can ruff high or low. When does it matter?

Ruffing low costs if West is out of spades, since West can overruff and give his partner a heart ruff. In other words, it costs when East is 6-1-1-5. If that's the case and I ruff high, I promote a trump trick for West and go down two. But if I ruff low, I lose two more tricks and go down three.

Is that construction possible? Personally, with a six-card major I would just treat the hand as a one-suiter and forget the club suit. Taking an auction where you might have only four spades but actually have six is an easy way to miss a game. But the robots may not agree, so that is at best a mild inference.

When does it cost to ruff high? It costs if West has four diamonds but is following to the spade. If I ruff high in that case, I promote a trump trick for West for no reason. So ruffing high costs if East is 5-2-1-5.

Is that construction possible? I was assuming East's heart shift was from a singleton. But perhaps it wasn't. East didn't know his partner had the spade ace, so neither black suit was attractive at trick two. Maybe East shifted to heart simply to be passive. In fact, that seems quite likely, since it would explain West's failure to give him a ruff. West can be pretty sure I don't have five hearts, so if he has ace third of hearts, he knows East's heart wasn't a singleton.

5-2-1-5 is more likely a priori than 6-1-1-5, and it is suggested by both the auction and the play. So I ruff with the eight. East overruffs with the nine and gives his partner a heart ruff. Down three.

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

Minus 150 is worth 57%. It's above average because the opponents are cold for a spade game and get there if you don't open with one notrump. If I ruff high and go minus 100, I get 86%.

One thing that didn't occur to me at the time is that West might have assumed I had six diamonds. Perhaps he didn't give his partner a heart ruff because he didn't think his partner had any trumps. Perhaps he thought East was 6-2-0-5. But even if I had thought of that, I doubt I would have changed my mind. East's holding 5-2-1-5 seemed like a pretty likely construction.

Free Weekly Instant Tournament - November 18 - Board 5

Board 5
Our side vulnerable

♠ A Q J 10 2  ♥ A 2  ♦ A 10 9 3  ♣ 10 8

Two passes to me. I open with one spade. Partner responds with two clubs (Drury), showing 10 to 12 support points and at least three spades. RHO doubles, showing a good club suit.

I don't need much for game. King fourth of spades and king doubleton of diamonds is enough, and that's not even close to a two-club bid. What do I need for a slam? King fourth of spades, king-queen of hearts, the club ace, and a doubleton diamond? That's not possible, since that's an opening bid. And even if it were possible, it would be too aggressive to make a slam move. You don't want to invite a slam unless it's virtually laydown opposite a perfect minimum.

I bid four spades, which ends the auction. West leads the club queen.

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

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

I have two club losers. If I can find the diamond queen, I can take the rest. Perhaps I can exploit the robots' tendency to assume I'm double-dummy and to cover an honor with an honor any time it might gain a trick.

If I lead the diamond ten out of my hand, can I assume West will cover? No, I can't. Whether he covers or not, I can take three diamond tricks, then ruff the fourth one. There is no reason for West to cover.

How about East? If I lead the jack from the dummy, will he cover? With queen doubleton or third he will, since it might promote his partner's ten. The fact that I'm unlikely to lead the diamond jack unless I hold the ten myself won't occur to him. With queen fourth, however, he might not cover. If he works out I have four diamonds, then covering with queen fourth can't gain unless he has the eight. Still, it appears my best chance at finding the diamond queen is to lead the jack from dummy. If it isn't covered, I'll take the ace and finesse against West.

East plays the club five on his partner's queen, and I drop the eight. West continues with the nine of clubs to his partner's king. There is no reason for East to break a red suit. He will probably shift to a trump. He does. He plays the spade six. I play the ten, and West discards the heart three.

The robots' first discard is usually honest count, so it appears West has five hearts. I know from East's double of two clubs that West has at most four clubs, so West is probably either 0-5-4-4 or 0-5-5-3. East might have shifted to a stiff diamond at trick three, since for all he knows his partner has the ace, so that eliminates the latter possibility. My working assumption is that West is 0-5-4-4.

The fact that I have to draw four rounds of trump changes things. Since I can no longer ruff the fourth diamond in dummy, I can't afford to start the suit by leading the jack. If West has queen fourth, I'll need to take a first-round finesse to pick up the suit. No. I'm wrong. Three diamond tricks are enough, since West gets squeezed in the red suits. This will be the position after I win the third round of diamonds in dummy:

	NORTH Robot ♠ -- ♥ K 10 5 4 ♦ -- ♣ --
WEST Robot ♠ -- ♥ ? ? x ♦ Q ♣ --		EAST Robot ♠ -- ♥ ? x ♦ -- ♣ A x
	SOUTH Phillip ♠ 2 ♥ A 2 ♦ 8 ♣ --

I now lead a heart to the ace, cash the last trump, and West is squeezed. This means I can still afford the fishing play of leading the diamond jack.

But first I have to draw trump. Standard technique is to play your cards so that the defender making discards must play first. It's better to force him to play before he sees his partner's card. So I play the spade three from dummy on this trick, then lead the spade jack. West discards the diamond six. This looks like a count card from four, confirming my suspicion that West is 0-5-4-4. It also suggests the diamond queen is on my right, since West might be reluctant to pitch from queen fourth. Although perhaps he sees the squeeze coming and knows it doesn't matter.

I follow to this trick with the spade five from dummy, then lead the spade queen from my hand. West discards the diamond deuce. If my construction is correct, the remaining diamonds are two-two. I play the spade seven from dummy, continuing to leave the lead in my hand. I now lead the spade deuce, West discards the diamond five, and I win in dummy with the king.

There are only three diamonds left. They are probably one-two. But I might as well assume my construction is wrong. Sometimes the hardest problems occur when you are 98% sure you know what is going on and it makes no difference what you do. You should always assume it makes a difference. Even if there is only a 2% chance it matters, it's important to work out how to cater to that 2%.

Leading the diamond jack from dummy isn't going to work anymore, since East no longer has any reason to cover. So if someone has three diamonds, I must decide who it is and cash the right honor first.

Who might it be? If it's East, then West is either 0-7-3-3 or 0-6-3-4. The latter is inconsistent with West's low heart discard. In addition, East would have shifted to a stiff heart at trick three.

Could West be 0-7-3-3? With that, he might have bid something at favorable vulnerability. And holding seven hearts, he might have worked out to give his partner a heart ruff at trick two--or at least have led the club jack to retain the lead.

If West has all the diamonds, then he is 0-5-6-2. Again, he might have bid with that hand. But I see nothing in the defense or carding inconsistent with this layout. It's the least unlikely of the unlikely scenarios, so I want to cash the diamond ace.

I lead the diamond jack to the ace. As expected, everyone follows, so I claim. (East did cover by the way, perhaps guarding against my having started with three small.)

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

Plus 650 is worth 79%. A number of declarers found a way to take only ten tricks, often by taking an early diamond finesse against West. In general, one should postpone critical decisions as long as possible, since you may get information that will prompt you to change your mind. Sometimes taking a finesse early is appropriate. You may have communication problems. Or you may decide that, should the finesse lose, the defense is more apt to make a mistake if you lose it early. Neither of those considerations applies here. Taking an early finesse is a clear error.

Free Weekly Instant Tournament - November 11 - Board 4

Board 4
Both vulnerable

♠ A 9  ♥ Q 10 6 4  ♦ A K J 10 5 3  ♣ K

One spade on my left, pass, pass to me. 

If the one spade bid had come on my right, I would overcall with two diamonds. Some would double for fear of missing a heart fit. But since the opponents have the master suit, missing a heart fit doesn't worry me so much as missing the chance to get my six-card suit into the auction. It is unlikely we can outbid the opponents unless we find a diamond fit.

When the opponents have bailed out at the one-level, however, the situation is different. Now it may well be our hand--possibly for a game--so I'm more concerned about finding a heart fit. That makes doubling more attractive.

I double, LHO passes, and partner bids three clubs. There's not much point in bidding diamonds now. If we don't have a heart fit, our likeliest game is three notrump. Partner probably has some help in spades, so I'm not worried about my single stopper.

I bid three notrump, everyone passes, and LHO leads the king of spades

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

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

Partner is contributing the expected second stopper in spades, so I have time to set up the diamond suit. If diamonds split, I can take five diamonds, three hearts, and a spade, for nine tricks. The opponents can take at most two spades, a diamond, and the club ace. So I make three notrump. A problem arises only if diamonds are five-zero. But, assuming I attack diamonds by taking a finesse against the queen, I can still take five diamond tricks. If I carelessly cash the diamond ace first, however, I'm in trouble.

At IMPs, taking the diamond finesse is clear, since it guarantees the contract. But at matchpoints could it be right to cash the ace-king, trying to drop a doubleton queen offside? West is known to have the preponderance of high cards after all. But he is also known to have at least five of the seven spades.

This is a fairly common problem. When one opponent is known to have most of the high cards but the other opponent rates to be longer in a given suit, how does that change the odds on how to play that suit? Is the high card disparity or the the length disparity more important?

If West has three or more diamonds, cashing the ace-king doesn't help, so we might as well assume that's not the case.What if we knew West had a doubleton diamond? Would it be right to play for the drop then? 

If we knew nothing about the location of high cards, knowing West had a doubleton diamond would make the finesse a three-to-two favorite. If we assume West has at least 11 HCP, then East is restricted to at most three. (Yes, giving West 11 HCP is a simplification. If he is 5332, he probably has at least 12. If he is shapely, he could have nine or ten. But to keep things simple, we'll assume he has at least 11.)

Crediting East with at most three HCP means that if East has three small diamonds, he could have the heart jack, the club jack, neither, or both. If East has queen third of diamonds, then he can have the heart jack, the club jack, or neither, but he can't have both. So, roughly speaking, the high card constraints have eliminated from consideration about a quarter of those hands where East has queen third of diamonds. In other words, the finesse has gone from being a three-to-two favorite to being a two-and-a-quarter-to-two favorite. It's still a favorite--just less of one.

If it's right to take the finesse even if we knew West had a doubleton diamond, then it must be right if we aren't sure how diamonds split. If West has a singleton diamond, the finesse is a heavy favorite. And it is a heavier favorite yet if he has a void.

I play low from dummy at trick one, RHO plays the spade six and I win with the ace. I play a heart to dummy. West contributes the jack; East, the eight. I play a diamond from dummy and RHO plays the deuce. If I play the ten, West will probably assume I have the jack. If I play the jack, I could easily be missing the ten. So if West has queen-nine fourth of diamonds, the jack may conceal the fact that the suit is running.

I play the jack. West wins with the queen and cashes the spade queen. RHO follows with the seven. West now cashes the spade jack. If he doesn't cash the club ace next, I'll make an overtrick. On this trick, RHO pitches the club seven. Perhaps a diamond pitch will make it appear my diamonds aren't running, so I pitch the diamond three. West continues with another spade, and I claim

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

Making four is worth 96%. The overtrick didn't matter much, since the field had difficulty reaching game. Most players balanced with two diamonds and played it there. I find that a little surprising, since I thought the field was fonder of off-shape take-out doubles than I am.

As far as the odds calculation goes, the methodology I described above is fine for an at-the-table approximation. But it assumes all four possible high-card layouts (heart jack, club jack, neither, and both) are all equally likely, which isn't quite the case. For those who care, here is a more accurate calculation:

If we assume East has two spades and three diamonds, then his remaining eight cards are chosen from a population of two jacks and eleven small cards. There are ₁₁C₇ ways he can have one specific jack, ₁₁C₈ ways he can have no jacks, and ₁₁C₆ ways he can have both. Since there are four ways for East to have three small diamonds, the total number of ways for the diamond queen to be offside is 4 * (2 * ₁₁C₇ + ₁₁C₈ + ₁₁C₆). There are six ways for East to hold queen third of diamonds, so the total number of ways for the queen to be onside is 6 * (2 * ₁₁C₇ + ₁₁C₈). That works out to about 51% in favor of the finesse, slightly worse than what we arrived at with our rough approximation.

Free Weekly Instant Tournament - November 4 - Board 3

Board 3
Opponents vulnerable

For the first two boards of this week's tournament, I got 93% for results that should have been below average. If I can manage a result for board three that should be above average, maybe I'll do even better.

I pick up this hand in first seat:

♠ A K Q 7 5  ♥ 10 8 3  ♦ K J 8 7  ♣ 7

I open with one spade, partner bids one notrump, I bid two diamonds and buy it. West leads the heart four.

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

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

If everything breaks, I can take five spades (ruffing one to set the suit up), three diamonds, and a heart. Nine tricks. If spades don't break, I won't score the long spade, but I'll still make eight tricks. A four-one diamond split, however, might prove to be a problem.

Let's say I hop with the heart ace and play a spade to the ace, ruff a spade, and play the diamond queen. It holds. I play another diamond and East shows out. Am I in trouble? West will win and tap me in clubs. Now I've lost control and can no longer run spades. Can I switch to a cross ruff? This is the position.

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

I've taken five tricks and need three more. As long West follows to a spade, I have them. I cash the spade king, pitching a heart from dummy, ruff a heart, and still have the diamond king. So as long as at least one of my suits breaks, I can manage eight tricks. If both suits break, I can make nine.

Back to trick one. I play the heart ace, East plays the jack, and I follow with the three. I assume the jack is intended to signal possession of the king. Since the deuce is missing, a likely lie of the heart suit is queen fifth on my left and king-jack third on my right.

I play a spade--four--ace--six. It's superficially tempting to cash the spade king, pitching a heart from dummy. But that's an illusion. I must ruff a spade to set up the suit, and I don't have the entries to ruff a heart also. So pitching a heart from dummy accomplishes nothing. In fact, it would be a mistake, because playing three rounds of spades before losing to the diamond ace exposes me to a possible uppercut.

Say, for example, I cash another spade, pitching heart, then ruff a spade in dummy. Everyone follows. I play a diamond to the jack. West takes the ace and plays a spade. I've manufactured a trump loser out of thin air.

So I don't take the pitch. I play the spade five and ruff in dummy. West plays the eight; East, the three.

Now queen of diamonds--five--seven--ace. West cashes the club ace, East playing the seven. He then switches to the diamond nine--three--four--king. Here is the current position:

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

This wasn't the best defense. West should have ducked the diamond ace. If he has ace third, he could then win the next diamond and play a third one. If he has ace doubleton, he could play a heart to his partner for a third diamond. After this defense, I may be able to make a second overtrick by ruffing a heart in dummy, which I hadn't planned on doing.

I cash the spade king, pitching dummy's heart. West follows with the jack; East, the deuce. Now I ruff a heart in dummy, ruff a club to my hand, and claim all but the last trick. Making four.

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

I said at the start that I hoped to achieve a result that should be above average. Did I succeed? I suspect most declarers will not see the danger of taking the heart pitch from dummy and will do so routinely. So my best chance is that the error will cost. Unfortunately, it doesn't. The hand with the diamond ace has short spades, so there is no trump promotion. Anyone who takes the pitch will get away with it.

So plus 130 should be a fairly normal result. Still, I might do worse and I can't see doing better. So I suppose this qualifies as "a result that should be above average."

And indeed it is. Plus 130 is worth 100%.

Free Weekly Instant Tournament - October 28 - Board 2

Board 2
Our side vulnerable

♠ A K 9 2  ♥ J 5 4  ♦ 10 8 4  ♣ A K 8

RHO opens with one notrump. I have a one-notrump opening myself, so I could double. Some players don't care for penalty doubles of one notrump--so much so that they give double some other meaning. But I think the penalty double of one notrump is a useful call.

Perhaps, though, "penalty double" is not the best description. It's true that if partner has a flat hand, he will pass and you will defend one notrump doubled. But that's not the main reason you double. You double because it might be your hand, and if partner has a long suit and some shape, you want to encourage him to bid it. The double, paradoxically, tends to work out better when partner pulls it than when he passes.

You do, however, have to be prepared to defend if partner is flat, and with this hand, I have poor defensive prospects. I have four tops tricks and possibly a long spade trick, but no place to look for tricks beyond that. If I knew partner had some shape and was going to pull the double, I would double. It might be our hand and doubling now might be the only way to get into the auction. But if partner passes the double, I won't be happy.

I pass and am quite pleased with my decision when I hear LHO raise to three notrump. Everyone passes, so I must find a lead.

If the opponents have 25 HCP, partner is broke. If one of the opponents has counted a five-card suit as a point, partner might have a jack. My best chance to beat this is to find partner with the spade jack. Either I can lead a low spade, hoping to find dummy with queen-ten, or I can lead the king, hoping to drop a doubleton queen. The latter is more likely, so I lead the spade king.

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

West	North	East	South
Phillip	Robot	Robot	Robot
			1 NT
Pass	3 NT	(All pass)

Queen-ten of spades were in dummy after all. And, since dummy has only nine HCP, partner could have a jack, so I might wind up regretting my opening lead. But it's too late to do anything about that now. Partner plays the three; declarer, the six. Now what?

If I continue spades, declarer can take five diamonds, one spade, and anywhere from three to five hearts, making anywhere from nine to eleven tricks. Since I can't beat this, perhaps I should just cash out to ensure holding declarer to nine tricks.

One thing to consider is that declarer might not know diamonds are running. Partner might have the jack and declarer might have ace doubleton. But even if that's the case, what choice does he have but to try to run the suit? If I'm the one with spade length, I must have a club honor, since I would have led low from ace-king and length with no side cards. Even if declarer doesn't draw that inference, three-three diamonds is a priori more likely than both club honors in the short-spade hand.

So playing on diamonds is declarer's best chance to make this. But will he necessarily try to make it? It's a normal contract, after all. Might declarer drive the clubs anyway, conceding down one to avoid going down more?

If I concede a spade, declarer can count three diamonds, one spade, and three hearts. If he has five hearts, he can cash the ace and king and discover the suit is running. But if he has four hearts, cashing the ace and king doesn't help. When the jack doesn't drop, he doesn't know whether the fourth heart is good or not. In that case, it's possible he will wind up down two if he tries to run diamonds, so he might decide to play on clubs and concede down one.

Still, for me to continue spades hoping for that to be the case is playing for a parlay: Declarer must have ace-small doubleton of diamonds, he must have fewer than five hearts, and he must have two or three spades (else I can't set up a spade trick anyway). And, even if he has all that, he must judge to concede down one rather than try to make it--hardly an obvious decision. It's clearly right for me to cash my four tricks.

I cash the spade ace, then king-ace of clubs, then play another club on the off chance partner has the queen. Making three.

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

Minus 400 is worth 46%. Nine defenders did continue spades at trick two and found declarer with the magic hand where he has a decision to make. Three times, declarer cashed out and made an overtrick but six times he attacked clubs and conceded down one. Presumably there is some randomness build into the program to account for this.

I notice some defenders chose to lead the spade ace rather than the king. The standard approach against notrump is to lead the king from ace-king or king-queen, reserving the ace as a request for partner to unblock an honor (or to give count if he has no honor). The queen also requests an unblock of the jack, so you lead the queen from king-queen-ten-nine but the king from king-queen-ten-small.

Someone--I don't know who or when--came up with the idea to reverse the ace and king leads. In this method, you lead the ace from ace-king and lead the king to request an unblock. This makes absolutely no sense to me. It means you can't afford to lead the king from king-queen unless you can stand an unblock. Perhaps the method makes some sense if you play Rusinow leads against notrump, but it seems unplayable otherwise. Yet I see that several websites for beginners suggest it.

If someone can point me to an article providing a cogent argument for this method, I'd love to see it. Perhaps I'm missing something. Until then, I'm sticking with the standard approach.

Free Weekly Instant Tournament - October 21 - Board 1

Board 1
Neither vulnerable

♠ K J 9 8 6  ♥ A 10 2  ♦ A K  ♣ A 10 3

Two passes to me. I open with one spade, intending to raise one notrump to two. I don't get the chance. LHO bids four clubs, which is passed back to me.

I can hardly pass, since partner could easily have a hand that will produce game. While I'm not a fan of offshape take-out doubles, they are less of a problem at a high level, since partner is freer to pass the double without a clear direction. Let's hope that if partner bids diamonds, he won't be disappointed with ace-king doubleton for support.

I double, and partner bids four hearts. Everyone passes, and RHO leads the club seven

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

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

If I pick up the trump suit, I have six hearts, one club, and two diamonds for nine tricks. I should be able to find a tenth trick in either diamonds or spades.

How should I play trumps? Since East has at least seven clubs and probably eight, West is a favorite to hold the heart queen. So my best play is a low heart to the king then a heart to the ten. Even if this finesse loses, all is not lost. At least I'll have a trump left in dummy to ruff a diamond with.

I play the heart deuce from dummy--seven--king--five. Now a low heart--nine--ten--club eight. On the heart ace, East pitches the club five.

I'm up to nine tricks. I can set up a diamond trick on most layouts and two diamond tricks on some. The only danger is that East has a small singleton. Is there anything I can do if he does?

Suppose I cash the ace and king of diamonds and East shows out. Now what? The spade ace is surely onside, but setting up the spade king does me no good, since I no longer have a dummy entry with which to reach it. Perhaps I should cash one diamond, then ruff a club to my hand and play a spade. Now I have an entry to the spade king, and I still have two trumps left, so I still have enough entries to my hand to make five if the diamonds behave.

But what if I'm wrong about the spade ace? What if West plays low on my spade play and the king loses to East's ace? Now I'm in trouble. East will tap me and, with only one trump left, I can no longer establish a diamond trick. So I'm down one. It's embarrassing to go down with normal breaks by trying to guard against bad ones.

I could take the position that West will always hop with the ace if he has it and play the jack if he ducks. But if I'm wrong about that and the jack loses to the queen, I again get tapped out and go down. In fact, even if the jack loses to the ace, I could get a poor result. I make four, but if the diamonds lie favorably, declarers who unimaginatively cash the ace and king will be making five.

Cashing only one diamond doesn't seem to be a good idea. Is there another way to handle a bad diamond break? Let's say I cash both diamonds and East shows out. I ruff a club to my hand, ensuring West is out of clubs, then lead the diamond ten. West wins and, if he has the spade ace, he must give me either a diamond trick or the spade king for my tenth trick. So long as West has the spade ace, there is no need to lead a spade toward the king early.The need to retain a dummy entry was an illusion.

I cash the ace of diamonds. East plays the deuce; West, the eight. Maybe I should have cashed one diamond before doing all that thinking. Now that I've seen the eight, I have no further problems. I cash the king of diamonds, and East drops the jack. Good. Now I'm making five. I ruff a club to my hand as West pitches the spade three.

But hold on. Maybe I can make six. I still have two trumps left, so I can afford to lead a spade before driving the diamond queen in case West sees a reason to duck. Actually he might have a very good reason. What if I held a second spade instead of the diamond ten? From West's perspective, this might be the end position.

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

If West hops when I lead a spade, the defense can take only one diamond trick. If he ducks, they get two. It's worth a shot. Let's hope West thinks of this layout.

I play the spade deuce, and West plays the seven. Did this actually work? Or was East overstrength for his pre-empt? I play the king, and East takes the ace. He taps me with a club and I claim eleven tricks.

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

96%! This board should be average. Even if you take "eight ever, nine never" too seriously and cash the top hearts, you still make five. You can ruff out the diamond queen, trading a diamond loser for a trump loser. It's strange that this is such a good result.

Incidentally, I don't care at all for East's four-club bid. He could easily be missing three notrump. Pre-empts are supposed to be bad hands.