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.

Free Weekly Instant Tournament - October 14 - Board 8

Board 8
Neither vulnerable

♠ A 6  ♥ 10 9 5  ♦ K 6 5  ♣ A Q J 9 8

LHO passes, partner opens with two spades, and RHO passes.

Playing opposite myself, I would pass. While game is possible, it's remote enough that I wouldn't want to risk going minus at the three-level. With three trumps, going minus at the three-level isn't so bad, since you have the protection of the Law: If you go minus, chances are the opponents can make something. With only two trumps, that is less apt to be true, so it pays to be conservative.

Playing opposite robots, however, passing is less clear. Robots often pre-empt with hands I would open at the one-level, so the chance of game is greater. I have missed games passing robot weak two-bids with worse hands than this.

Ron Klinger, in The Modern Losing Trick Count, recommends that, when holding a doubleton in support of partner's weak two-bid, you should invite game with three and half or four cover cards. My aces and king provide three cover cards, and the club queen provides a half. So this hand is worth an invitation by that standard. Since my record opposite robots is poor in these situations, I'll follow Ron's advice.

I bid two notrump, and partner bids three clubs, showing a maximum with a club feature. If spades are solid, we have eleven tricks. The question is whether the opponents can cash four first.

Let's hope not. I bid four spades and everyone passes.

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

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

Do you want to be in four spades with these cards? Against best defense, game is worse than a finesse, since we might have a trump loser. But in practice it's better than that, because the opponents might lead a black suit or might fail to solve the cash-out problem. It's not clear whether that consideration boosts the odds to better than fifty percent. But I don't mind being in game, so I have no quarrel with Klinger's rule.

Unfortunately, the opening lead is the diamond queen, so the ace is offside. And, since my auction revealed my club king to the defense, they know they must cash four red cards immediately. My only chance to make this contract is to convince the opponents I have a singleton in one red suit so they will try to cash three tricks in the other one. 

What's the best way to do that? Since the opponents know they are facing a cash-out problem, all their signals should be count. If I duck this trick, East should play a count card. If that card happens to be higher than the four and is intended as low, I can obscure the message by dropping the ten. But most of the time his card will be readable. Perhaps it's better to cover the queen, forcing East to take his ace and preventing him from signaling.

The defense should be able to solve their problem even after I cover, but it will be more difficult and the opponents might not be on the same wavelength. Of course, robots aren't on any wavelength. They don't signal at all nor do they draw inferences from the play, so this whole discussion is moot. But, just for practice, I might as well pretend I'm playing against real bridge players.

I  play the king and East takes the ace. Should I drop the ten or the four? The ten tells East I have a singleton or doubleton diamond, since I would have ducked the queen with ten third. The four leaves open the possibility that I have one, two, or three diamonds. The more possible layouts I give East to defend against, the harder it will be for him to find a defense to cater to all of them, so the four is the correct play.

I play the four, and East shifts to the heart ace. So far, so good. I play the six; West, the deuce. East now shifts to the diamond deuce. It's all over. West, seeing my ten, isn't going to try to cash a third diamond, since I can hardly have ten third. And indeed he doesn't. He takes the jack and cashes the heart king, as East follows with the seven.

West continues with the heart jack. East follows with the four, and I ruff. My only chance for a good board is to hope that other declarers will be minus in a partscore. Does it makes sense to finesse the spade, hoping East has jack fourth? Could I conceivably get back to average that way?

That might make sense if I thought the field was in three spades. But it's hard to see three spades being a popular contract. Either you make a game try and get to game or you don't. So the contract will be either two spades or four at most tables. I can neither beat nor tie anyone in two spades, so I'm competing only against other pairs in four. That means I should simply take my percentage play. I play a spade to the ace and back to the king. They split. Down one.

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

East's heart ace at trick two was a poor play. If I had three hearts and a stiff diamond, West would have to unblock his heart king to beat me. A better play would be to shift to the heart three (showing an odd number of hearts). West would now know what to do.

This works if West has two or three hearts, but what if he has four? How will he know whether West's odd number of hearts is five (in which case he must cash two diamonds) or three (in which case he must cash two hearts)? He will know because East shouldn't lead low with three hearts. He should cash an honor, allowing West to play a count card. Then he will know himself what tricks to cash. An interesting wrinkle: From ace-queen third, East should lead the queen. If West has king sixth, he knows only one heart is cashing, so he can overtake and play diamonds.

The defense must cater to three critical cases: declarer's holding a singleton heart, a singleton diamond, or two red doubletons. Since signals are binary, you can't cater to three cases by signaling alone. (That's why it was important for declarer to play the diamond four at trick one.) But you can often cater to three cases by combining signaling with logic.

I get 4% for this result, which seems a bit harsh for bidding a decent game. Only two other players reached game, and they both made it. One raised two spades to four and got a club lead. Yes, my auction was revealing. But if I was afraid to invite for fear of tipping off the defense, I think I would prefer passing to blasting a game.

The other player bid two notrump, then three notrump over three clubs and also got a club lead. Given the robots' preference for passive leads against notrump, there is some merit to this decision. I did briefly consider it but decided it was too much of a gamble.