Weekly Free Instant Tournament - Feb. 11, 2022 - Board 3

Board 3
Opponents vulnerable

♠ A J 10 8  ♥ A J 9 7  ♦ 8 4  ♣ J 8 4

I don’t open balanced 11-point hands. But is this hand really worth only 11 points? It would be a clear opening bid if the jack-ten of spades were the queen. And if partner doesn't have the spade king, this is actually a better hand. (Ace-jack-ten of spades will be worth two tricks 75% of the time, whereas ace-queen will be worth two tricks only half the time.) That fact plus the good heart spots persuades me to evaluate this hand as 12 points and open with one club. 

As in the past, I'm studiously avoiding the term "upgrade." To me, "upgrade" implies you are, for one reason or another, elevating something to a higher category than the one to which it actually belongs. You might, for example, upgrade an airline ticket to first class as a reward. Or you might upgrade a 14-point hand to a strong notrump to avoid rebid problems. That's not what's happening here. I'm not upgrading this hand to 12 points. Nor am I treating it as 12 points. I'm judging 12 points to be an accurate evaluation.

Partner bids one diamond. I would like to rebid one notrump rather than one heart, since I don't want to hear a preference to two cubs. But the tooltip tells me that denies a four-card major. I wish I knew under what circumstances partner would respond one diamond with a four-card major. I know the robots sometimes bypass a longer diamond suit to bid a four-card major, because I've seen them do it. If I knew they did so whenever they had less than a game force, I would rebid one notrump even though it's non-systemic. But I don't know enough about the robots' tendencies to risk it. If we have an eight-card major-suit fit, it rates to play better than one notrump. So I bid one heart. Partner bids one notrump, which I pass. West leads the nine of spades.

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

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

The lead is presumably from a doubleton or singleton. I have only four tricks off the top. I’ll need to develop three more before they can take seven. Since both spade honors are offside, I'm not off to a good start. There is a variety of possible approaches, but I need to know more about the layout before I can evaluate them.

I play the spade jack. East wins with the queen, and I play the deuce. East shifts to the club three. West wins with the queen and cashes the king. East follows with the nine. West continues with the ace. Now I know enough to do some planning.

Since this is a best-hand tournament, West has at most 11 HCP. He has shown up with nine already, so he can’t have the heart king. He might hold the diamond queen, but I have to hope he doesn’t, since I don’t have much of a chance if the diamond finesse is losing. I will assume, out of necessity, that the diamond queen is onside.

Under that assumption, I have five tricks and will need two more. And if West began with five clubs and cashes them, I will need to avoid losing any more tricks to the defense. My prospects are actually pretty good as long as East has at least three diamonds. If he has exactly three, my diamonds are good. If he has four, perhaps I can gain two tricks via a triple squeeze. 

There are two ways a triple squeeze can yield two tricks: by means of an extended threat (if your opponent abandons a suit, it gives you two tricks instead of just one) or by having the squeeze repeat (he gives you a trick in one suit, then you cash that trick, squeezing him in the remaining two).

Let's see if that works here. Suppose I come down to this position after East cashes his fourth club.

(A)

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

East must hold four diamonds, and king doubleton in both majors. If West cashes his fifth club, I pitch a spade from dummy. A diamond pitch by East gives me two tricks, since I have an extended threat in diamonds, so he must stiff a major-suit king instead, giving me one trick. When he does, I don't need the fifth diamond any more, so I pitch it. Whichever suit West shifts to, I win and cash two tricks in the major East stiffed the king of, squeezing him in diamonds and the other major. The squeeze trick is played from the North hand, and I have a diamond entry to the South hand. So, yes, the squeeze repeats, and I gain two tricks.

Note I need to keep all five diamonds for this to work. If I have only four diamonds in the above position, East can afford to pitch a diamond. This gives me one trick, but West simply plays a spade, killing the entry for the spade-heart squeeze, and the squeeze doesn't repeat. I can gain one trick but not two.

Sometimes the best defense in these situations is to avoid correcting the count by refusing to cash the last winner. What happens if West doesn't cash the fifth club? Since the opponents have taken only five tricks,  I can now afford to concede a trick to one of East's kings. That gives me my sixth trick. Then perhaps I can execute a simple squeeze to get one more.

Let's say in the above position West shifts to a heart instead of cashing his fifth club. I duck, establishing a heart as my sixth trick. Eat wins and returns a red suit. I win and cash my heart tricks, squeezing East in spades and diamonds. If West shifts to a spade in the above position, the result is similar. I duck and eventually squeeze East in hearts and diamonds. 

What if West shifts to a diamond? Since the squeeze card lies in the North hand, attacking the entry to the South hand might work. Let's play it out. Low diamond--low--queen--king. I pass the heart queen to East's king. This is the position:

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

A second diamond play by East kills the spade-diamond squeeze. The squeeze card, the heart jack, is in the North hand and I have no entry to the diamond threat.  I can still make my contract by guessing whether to finesse the diamond nine or to play for West's ten to drop. But I no longer have a sure thing.

For the spade-diamond squeeze to operate I need to be able to cash the squeeze trick in my hand. That means I can't afford to pitch a heart. Suppose I come down to this position instead of (A) after the fourth club is cashed.

(B)

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

I can still handle either major-suit shift. What if West shifts to a diamond? Then I win and play a heart to the jack. East wins and plays another diamond. I win and cash hearts, ending in my hand. The squeeze card is in the South hand, and North has an entry to the spade threat. So the squeeze now works. East is squeezed in spades and diamonds.

But we have already decided I need to keep all five diamonds for the triple squeeze to yield two tricks. So I can't cater to both scenarios. If I come down to (A), West shifts to a diamond. If I come down to (B), West cashes the fifth club.

If West has five clubs, it seems my best chance is to come down to (A) and hope West woodenly cashes the last club. If, instead, he finds the killing diamond switch, I will simply have to guess who has the diamond ten. But if clubs are four-four, West won't have a fifth club to cash. So I can come down to (B). I need to be flexible. I don't know which position I want to reach until I know how clubs split.

Where were we? West has just cashed the club ace. Dummy follows with the jack, and East follows  with the six. No matter which position I aim for, I can afford a spade pitch.  So I pitch the five of spades. West cashes the club ten. I pitch the heart seven from dummy, and West follows with the club seven.

So clubs are four-four. That means I must come down to position (B). I pitch the diamond six. West shifts to the four of hearts. I play the nine from dummy, East covers with the ten, and I win with the queen. That's a surprise. I wasn't expecting East to duck the heart king.

We have now reached this position:

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

I doubt East would have ducked with king doubleton of hearts, so he is probably 4-3-2-4. I now have six tricks (assuming the diamond queen is onside). All I need to do is concede a trick to the spade king to set up my seventh trick.

Since I'm home if the diamond queen is onside, it's time to revisit that assumption. Especially since the queen is now two to one to be offside. Is there anything I can do if it is? Can I squeeze East in the majors, using the heart eight in my hand as a threat? 

I could try playing East for ten doubleton of diamonds. Say I lead the jack. West takes his queen and plays another heart. I hop with the ace and cash my diamonds, squeezing East in the majors. But all West has to do to break up the squeeze is shift to a spade--or a diamond for that matter, since the squeeze doesn't operate unless I cash the heart ace before running diamonds. If I knew the diamond queen was offside, it would be worth a try, hoping West misdefended. But East is just as likely to have a doubleton queen as a doubleton ten, so there is no reason to adopt that line.

I play a spade--seven--eight--king. East shifts to a diamond. Since I know East has the heart king, the elegant line is to hop and cash dummy's major-suit winners for a show-up squeeze. East will have the heart king and a diamond for his last two cards.

That diamond isn't the queen, so I'm down one.

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

Minus 50 is worth only 7%. My score is down to 63% and I have dropped to second place.

Almost every table passed the board out. I stand by my decision to open the bidding. I reached a contract that went down only one after four finesses lost. That strikes me as a bit unlucky. Note that if you change my spades to ace-queen forth, one notrump is not as good a contract, but the whole room would be in it.

I misplayed the hand at the very end. Go back to the last diagram before the full deal and see if you can find my error. Recall what I know: East has the spade king and the heart king and at most two diamonds.

By conceding a spade, I make if East has the diamond queen and go down one if he doesn't. But I can achieve those same results another way. I cross to the heart ace, then cash the ace and king of diamonds. If the queen drops, I cash the jack, then toss East in with the heart king to lead into my spade tenace. Making one. If it doesn't drop, I still toss him in with the heart king to lead into my spade tenace. Although now I will lose the last trick for down one.

What do I gain by doing this? I gain if East has queen-ten doubleton of diamonds. Now I have four diamond tricks to cash, and East is squeezed in the majors. Not only do I make an overtrick, but I also get to watch East kick himself for ducking the heart king.

Weekly Free Instant Tournament - Feb 11, 2022 - Board 2

Board 2
Our side vulnerable

♠ K 10 5 2  ♥ A 6 3  ♦ Q 10 2  ♣ A 7 3

RHO passes. I open with one club and LHO overcalls with one heart. Partner passes and RHO bids one notrump. I have nothing further to say. I pass and LHO bids two clubs. 

Not everyone would play two clubs as natural. Some players make it a rule that, with a few specific exceptions, bids in suits bid by the opponents are never natural. As a Lowenthal disciple, I go to the opposite extreme. ("Often the best trump suit on a misfit is the suit that splits five-one," John would say. "It's the only suit where the opponents can't crossruff.") But even if you prefer the former approach, this bid should be one of the exceptions. Partner has shown something in clubs with his one notrump bid. If you have shortness in spades or diamonds and four or five clubs, why shouldn't clubs play better than notrump? The robots agree; the tooltip says this bid is natural.

Partner passes over two clubs, and RHO corrects to two hearts, ending the auction. Partner leads the club five.

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

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

Declarer plays the club nine from dummy.

What’s declarer’s shape? The club five looks like a doubleton, so declarer is probably 2-5-1-5. Or maybe not. Partner would have doubled one heart with four spades unless he is almost broke. So it's more likely declarer is 3-5-0-5.

I could win this trick and continue clubs. But perhaps ducking makes more efficient use of our entries. Suppose partner has queen third of hearts, for example. If I play two rounds of clubs, declarer will win in dummy, pitch a spade on the diamond ace, and play a heart. If I play low, he might (and arguably should) go up with the king and play another heart. Then there is nothing partner can do. If he hops with the queen, he can’t reach me for a club ruff. If he ducks to my ace, he’s ruffing with a natural trump trick.

What if I hop with the heart ace to  give partner his ruff? Now declarer may guess to drop partner’s heart queen. Ducking the club, then ducking when declarer plays a heart off dummy leaves declarer with no winning options. He can’t stop us from scoring two heart tricks and a club ruff.

There are two layouts where I may regret ducking both aces:

 (1) Declarer is 2-6-0-5. I can afford to duck the club ace, but if I duck the heart, we lose our club ruff. Is that a possible hand for declarer? It gives partner four spades and king-jack fifth of diamonds. With as much as the queen of spades, he would have doubled one heart. So if declarer is 2-6-0-5, he must have ace-queen doubleton of spades. That means, when the club nine holds and declarer cashes the diamond ace to pitch a spade, that spade will be the queen. If that happens, I'll hop with the heart ace. If he pitches a low spade, I know he can't be six-five, so I can afford to duck. 

(2) Declarer is 2-5-0-6. Now we can take two club ruffs if I win the first trick. Again, declarer must have ace-queen tight of spades if that's his shape. But now I won't find out in time. I'll just have to pay off to this case. It's too specific a hand to worry about.

Actually, come to think of it, there is another way that ducking the club ace might cost. What if we have spade tricks to cash? Can it be right to win and shift to spades before declarer gets his pitch on the diamond ace? If declarer has queen third of spades, the pitch doesn't matter. And if he has ace third, we can't stop it. It appears the only time a spade shift is necessary is when partner has both spade honors. Is that possible? It would give partner

♠ A Q x  ♥ x x x  ♦ K J x x x  ♣ x x .

I wouldn't pass over one heart with that hand, but a robot might. Still, I can't cater to that hand. If I win and switch to a spade, we might lose our club ruff altogether. Suppose, for example, declarer has both spade honors instead of partner. Again, this is a layout I just have to pay off to.

Back to trick one. I encourage with the club seven, and declarer plays the six. As expected, declarer cashes the diamond ace. I play the deuce, declarer pitches the spade eight, and partner follows with the diamond four. Declarer plays the deuce of hearts from dummy. I duck as planned. Three—queen—four. Partner had no trump honor, so my careful defense has made no difference. Declarer continues with the eight of hearts—seven—jack—ace. I play ace and a club, which partner ruffs. Eventually, we score a spade trick. Making three.

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

Minus 140, surprisingly, is worth 82%. Most defenders failed to navigate the club ruff. A couple of players found a strange one diamond opening and were severely punished. Over one diamond, South bid an unusual two notrump. Responder raised to three diamonds, and North doubled for penalties. The one diamond opening failed, weirdly, because it enabled you to find your fit.

The usual reason for opening the "wrong" minor is to inhibit the lead against a notrump contract. Some might choose one diamond for this reason if you move the diamond queen to the club suit. With this hand, however, I see no reason to inhibit a diamond lead, so I'm not sure what the point was. Perhaps they just wanted to do something random to increase the standard deviation of their results. If that was their objective, they succeeded.

Incidentally, the South hand is a good advertisement for playing two clubs as natural in this auction. I would hate to have to find a sensible call if it weren't.

My running score is 91%. I'm still in first place.

Weekly Free Instant Tournament - Feb 11, 2022 - Board 1

I am starting a new set of posts this week, discussing boards from the Weekly Free Instant Tournament on BBO. You might find these posts more meaningful if you try playing the boards yourself first. You have until Thursday of this week to do that. Just go to the "Solitaire" section on BBO and click on "Weekly Free Instant Tournament." Please comment below if you had an interesting result or if you think of some play or inference I missed. 

You can also get a different perspective by viewing Pete Holland's video. He plays the tournament in real time with a running commentary. His video will be on BBO on Tuesday and can also be found on YouTube. I'm sure he will have different points to make, since we don't think about the game the same way. For one thing, I have never once played a hand where I was even alert to the possibility of scoring the beer card.

Board 1
Neither vulnerable

♠ Q 9  ♥ A 10  ♦ A Q 6  ♣ Q 10 8 5 3 2

Partner opens with one heart and I bid two clubs. Partner bids two hearts. This is a catch-all bid in the robots' methods and does not guarantee a sixth heart. Partner might be balanced without a stopper in one of the unbid suits. Or he might be four-five in the majors, since a two spade bid by him would show extras.

My choices are two notrump or three clubs. Three clubs shows the sixth club, but it's not clear how important that is. And it requires partner to bid past three notrump to show club support. Two notrump leaves room for partner to show support by bidding three clubs. Another advantage of two notrump is that it may right-side notrump. Both my spade and diamond holdings suggest notrump may play better from my side. 

I bid two notrump, and partner bids three spades, showing four spades. Arguably this should promise a sixth heart. I wouldn't bid two notrump with four spades, so with a 4-5-2-2 or 4-5-3-1 opener has no reason to introduce the suit and should simply raise to three notrump. Choosing three spades instead suggests he has reason to suspect notrump is the wrong strain. But I have no confidence partner knows this. I would bid four hearts if I trusted partner. But opposite this partner I think it’s better to bid three notrump. This could conceivably be the right contract even if partner has six hearts, and it is almost surely right if he doesn't. 

I bid three notrump, which ends the auction. West leads the diamond three.

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

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

I'm glad I didn't bid four hearts. This certainly looks like a better contract.

The diamond deuce is missing, so the lead could be from a five-card suit or even from a doubleton. I have seven tricks ready to cash, so I need two more. I also need to prevent the opponents from taking three diamond tricks. 

If diamonds are five-three, it could be right to go after hearts, attempting to establish two tricks while losing the lead only once. But that’s unlikely to work, and, if it doesn’t, it could result in my going down two or more, since it establishes heart tricks for them they won't get if I attack clubs instead.

Attacking clubs, assuming I don’t run into bad luck in the club suit, will work if diamonds are four-four or if I can tangle the opponents' communications so they don't take all their diamond tricks. And, if it doesn’t work, I rate to go down only one. So my plan will be to work on clubs.

What should I play from dummy at trick one? The eight is right if West has the ten and nine, a 25% chance. It might also be right if East plays the king from king-ten or king-nine. When will he do that? He will do that if he thinks it's possible I have queen doubleton. But he should be able to tell from the lead that I don't. He might also do that if it looks right to win the first trick and shift to a different suit. But this doesn't look a deal where that's the right approach. So I'll assume he will always insert the ten or nine from those holdings. Playing low, then, is right 25% of the time.

For the jack to be right, West must have the king, a 50% chance. But that's not sufficient. Even if the jack holds, if East wins the first club trick and plays a diamond through, playing jack will have gained nothing. So if I expect that to happen more than half the time, playing low is the percentage play. Will it happen more than half the time?  If I win the diamond jack and play a small club from dummy, it might not be obvious to East that he needs to hop, especially if he has the king and not the ace. In fact, it might be impossible for him to hop, since West might have both honors. 

Let's make the assumption that East will never hop with the king alone, probably a fair assumption against this East. In that case, I will lose the first club to West whenever West has ace-king or the ace alone and will lose it to East whenever East has ace-king or ace alone, in other words, half the time. This makes it a tossup which card to play at trick one. But, in fact, sometimes East will duck the club even when he has the ace. He's not looking at my hand after all. That possibility makes it percentage to play the jack.

I play the jack, and East covers with the king. I see no reason to win this trick. I don’t see any reason to duck it either—unless perhaps the lead was from a doubleton. But a general principle of declarer play is that any time it can’t gain to win a trick, you should duck. Sometimes the opponents make a mistake when you leave them on play. Sometimes you tighten up the end position for a squeeze you didn’t see coming. Sometimes you simply get more information. In general, good things seem to happen when you follow this principle. So I duck.

East continues with the diamond deuce. Since East has the deuce, I now know West began with three or four diamonds. Which card should I win with? From West’s perspective, the queen is the card I’m known to hold, so the queen is more deceptive. From East’s perspective, the ace is more deceptive. If I play the queen and it holds, East will know I have the ace also. But if I play the ace, his partner might have the queen. 

So my right play depends upon which defender I want to keep in the dark. If West has three diamonds, he will need to hop on the first club. East, on the other hand, has no critical decisions to make. Since West is one I want to conceal information from, the queen is the right play. How will playing the queen persuade West to duck the first round of clubs? I have no idea. Probably it won’t. Like my duck it trick one, it’s just good technique. You want to conceal information from the opponent who will make the critical decision. 

I play the diamond queen, and West follows with the four. I play the club three. West plays the seven, and East wins dummy’s jack with the king. I expect East to continue diamonds, but he surprises me by leading the club four. Hmm. It appears East had five diamonds and West failed to hop with the club ace to lead his last diamond. Did my play of the diamond queen work for some reason?

I play the club queen, and West takes his ace. I have the rest. Making four.

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

Diamonds were four-four. Perhaps East thought his partner had led a three-card suit, so continuing diamonds would not be productive. What was he playing me for instead? Maybe something like

♠ Q x  ♥ A x  ♦ A Q 6 5  ♣ A 10 8 x x ?

Who knows? It’s not important. What’s important is that, if I had won the first trick, East surely would have continued diamonds on winning the club king. By ducking, I created the opportunity for him to construct a layout where something else was more attractive, and he did. 

Plus 430 is worth 100%. No other declarer in three notrump ducked the first trick, so East always continued diamonds when he gained the lead. It’s nice when proper technique is rewarded.

Some statements I made earlier proved to be wrong. "East... has no critical decisions to make," I said.  Wrong. "You want to conceal information from the hand who will make the critical decision," I said. Wrong again. Advertising my double diamond stopper made abandoning diamonds more attractive. Had I made the deceptive play of the ace, East might have continued diamonds. While I will happily take credit for ducking at trick one, I can't take credit for the play of the diamond queen. It was a lucky accident. I chose the right play for the wrong reason.

Zenith Daylong - Oct 14, 2021 - Board 16

Board 16
Opponents vulnerable

♠ K 7 3  ♥ A 8 6  ♦ Q  ♣ K Q 9 8 4 3

LHO passes. Partner opens with three diamonds in second seat, and RHO passes. Even if our diamonds are solid, a heart lead will probably defeat three notrump. And if they aren't solid, three notrump will have little play. So I pass, as does LHO. West leads the king of hearts.

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

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

I have seven diamond tricks, a heart, and a club. Nine tricks. If the spade ace is onside, I can take one more--possibly two more if they allow me to establish a second club trick for a spade discard.

I win the heart lead with dummy's ace, and East plays the five. I play the queen of diamonds--deuce--three--five. I ruff a heart. East plays the heart ten; West, the seven. I draw two more trumps. West follows with the nine, then pitches the spade deuce. East follows with the six, then the ten.

West appears to have a good heart suit and a doubleton diamond and chose not to bid over three diamonds. He probably doesn't have both aces, so the prospect of setting up a second club trick for a discard is not good. I play the six of clubs--deuce--queen--ace. West might have led a stiff club, so unless that's a stiff ace, clubs are probably breaking. If so, and if the spade ace is onside, the defense must knock out dummy's spade king to keep me from making five. That shouldn't be hard for East to see. So if he doesn't lead a spade, I'm going to assume he has the ace.

He plays the heart nine, and I ruff. West follows with the four. Here is the current position. I am assuming the spade ace is offside and would like to find some way to lose only two tricks.

	NORTH Phillip ♠ K 7 3 ♥ -- ♦ -- ♣ K 9 8
	SOUTH Robot ♠ 9 8 4 ♥ -- ♦ J 8 ♣ 7

If East is out of hearts, I may be able to endplay him. I have two ways to attempt that: (A) Play a club to dummy and another club. If East follows, pitch a spade. (B) Play a club. If West follows low, insert the eight. When East wins, he must give me my spade king or return a club to dummy, letting me pitch two spades. 

(B) works whenever (A) does, and it also works when East began with ace-jack or ace-ten doubleton of clubs and has no more hearts. The problem with (B) is that if East has a heart to return, I may never score the club king, in which case I've gone down in a cold contract. I have no particular reason to believe East is out of hearts, so I'll play for (A). It gives me some chance to make an overtrick without the risk of going down.

I lead the seven of clubs--five--king--ten. On the next club, East pitches the five of spades. Oh, well. No endplay. I ruff, and East follows with the jack. Here is the position now:

	NORTH Phillip ♠ K 7 3 ♥ -- ♦ -- ♣ 8
	SOUTH Robot ♠ 9 8 4 ♥ -- ♦ J ♣ --

I could be wrong that East would have shifted to spades without the ace, but it's a reasonable assumption. If I'm right that the ace is offside, is there any chance of scoring the king? 

East began with three-two in the minors. If he is out of hearts, as he needs to be for me to have any hope of an endplay, he was 5-3-3-2 and is now down to four spades. West pitched the spade deuce earlier, so he has one spade left. If it happens to be the six, then I can duck a spade to East. Of course, I'll look silly if West turns out to hold ace-six of spades. But there is no need to worry about that unless he plays the six. If he does, then I can decide how confident I am in my inference.

I lead the spade nine. West plays the ten. There is no reason not to play the king now. East takes the ace, then cashes the queen and jack. Making three.

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

48%.  It's below average because a few Norths tried 3NT and, even after a heart lead, the robots weren't able to find the right defense.

It feels as if I should have been able to do something in the end position. In the diagrammed position above, East's last four cards are AQJ6 of spades. Shouldn't he be in some kind of trouble? Yes, of course! I don't need West's stiff spade to be the six. A stiff ten works as well. All I have to do is cash my last trump. If East comes down to AQJ of spades, I duck a spade and endplay him. If he pitches the queen or jack, my nine of spades sets up. I had him in a one-suit squeeze. That's annoying. One-suit squeezes don't come up often, so it's a shame to miss one when it does. Plus 130 would have been worth 87%. 

Why didn't I see that? Possibly it's because I hadn't fully committed to placing the spade ace offside. If the thought "the spade ace might be onside after all" weren't floating around in my head, I might have stopped to ask myself if cashing the last trump would accomplish anything. Alternatively, I could have arrived at the solution from a different direction. If I had seen the possibility of a one-suit squeeze first, I might then have asked myself how confident I was that the spade ace was offside. I've internalized most squeeze matrices, so that the possibilities jump out at me without my having to look for them. But apparently one-suit squeezes aren't among those I've internalized. I need to make an effort to be more alert to them.

I finish with 59%, putting me 159th out of 1562 players. The best-hand robot individuals usually take in the high 70s or even low 80s to win. The winning score in this tournament was 68%. I would have come very close to that if not for my two egregious errors--the one on this board and my misplay on board eight.

For the next event, I'll try something different. Every Friday, BBO posts a Weekly Free Instant Tournament, which is available through Thursday of the following week. I'll play in the one they post this Friday, February 11, and will discuss the boards here. If you want, you can play the same boards and compare your results with mine. You can find the tournament under the Solitaire menu on BBO.

You can also watch Pete Hollands' video on YouTube or on BBO and get a different perspective on the same boards. He plays and discusses the deals in real time and posts the video on Tuesday. I admire anyone who can do that. Not only am I a very slow player, I can't talk and think at the same time. So if I tried that, the video would consist of me starting at the screen in silence for ten minutes, then telling you what I was thinking about.