Zenith Daylong - Oct 14, 2021 - Board 2

Board 2
Our side vulnerable

♠ A J 8 4 2  ♥ K 8  ♦ Q 5  ♣ A J 10 6

Pass to me. Some will open one notrump with this hand. I'm happy to open one notrump offshape when I have rebid problems. But with this hand, I don't. If I open one spade and partner responds one notrump, I see no issue with rebidding two clubs. So I open one spade. 

Partner bids two hearts. I can rebid three clubs or two notrump. I would bid three clubs with the spade queen instead of the diamond queen. But with scattered values, this hand looks more like notrump than like spades-and-clubs. Furthermore, there is a variety of diamond holdings partner might have where notrump is better from my side. If I bid three clubs, I may miss my chance to bid notrump first. If I bid two notrump, on the other hand, we haven't precluded getting to a club contract. Partner can still introduce clubs over two notrump.

I bid two notrump, and partner raises to three. West leads the jack of diamonds.

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

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

If partner had ace third of diamonds, I would be happy we were playing this from my side. Opposite ace doubleton, I'm not sure yet. I play low from dummy; East follows with the four and I win with the queen. Now I'm sure.

I have seven cashing tricks. I need two more. Either hearts or clubs looks promising for two additional tricks. Which one should I try first? If both finesses are working, I don't care. If one is losing, which one would I prefer to take first? If I take the club finesse and it loses, I will win the diamond return and run clubs. This might put the opponents under some pressure. Imagine West's discomfort if he holds queen fourth of hearts, for example. On the other hand, if I take the heart finesse and it loses, it's not clear they will feel the same degree of pressure when I run the heart suit. Admittedly, this is more instinct than rigorous logic. I don't have any specific plan in mind. But it looks better to take the club finesse first.

I play the spade deuce; West plays the ten. That looks like queen-ten. West is afraid I'm looking at his hand and will insert the nine. I play the king, and East follows with the three.

Should I lead the club queen or a low one? Low is better if East has a stiff king. But the queen allows me to repeat the finesse if it wins. Say I lead low to my hand and it holds. I play king of hearts and a heart to the jack. It loses and they clear diamonds. Do I risk repeating the club finesse or not? If I find myself facing that problem, I will be wishing I had led the queen.

But maybe I shouldn't worry too much about West's ducking. Ducking a trick is unattractive when you have a suit ready to establish. And if I play the jack rather then the ten, ducking will be even less attractive, since West can't be sure repeating the finesse is even an option. So I decide to guard against a stiff king by leading the deuce. East plays the three. I play the jack; West plays the seven.

Now for the heart finesse. King of hearts--six--four--nine. Eight of hearts--queen--ace--five. That makes eleven tricks. If a club to the ten holds, that makes twelve. If clubs break, that's thirteen. If they don't break, I can cash the club ace and execute a show-up squeeze, taking all the tricks if East has the spade queen or if the queen is doubleton offside.

I play the club four--eight--ten--nine. I claim. Making seven

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

62%. I beat most of the pairs who played three notrump. Some played it from the other side and didn't get the gift at trick one. Others played it from my side but got a club lead after my hand opened one notrump. The reason this result isn't better is some Souths opened one spade and rebid three clubs over two hearts, thereby reaching and making six clubs. It's hard to say whether three notrump or six clubs is the better matchpoint spot.

Note, by the way, East's play at trick one: the four from 742. That's neither count nor attitude. It appears to be random. That's what makes it hard to defend with robots. Even their trick-one plays aren't helpful.

Zenith Daylong - Oct 14, 2021 - Board 1

I recently discovered the Zenith Daylong tournaments on BBO. The BBO and ACBL Daylongs are best-hand tournaments, meaning no one at the table has more HCP than you do. This isn't true in the Zenith Daylongs. Perhaps it's more fun always to have a good hand. But sometimes having a bad hand gives you more difficult problems. When you are defending and have fewer high cards than partner, it can be hard to work out what is going on. This is especially true playing with robots, who make no effort to help you. You must work everything out by drawing inferences from declarer's play and from partner's line of defense. That's a good thing if your objective is to hone your skills.

Let's give it a try.

Board 1
Neither vulnerable

♠ --  ♥ Q 10 6  ♦ A 9 6 3 2  ♣ A J 7 4 3

Partner opens one heart. Normally, when you have two five-card suits, you bid the higher-ranking one first. That assumes, however, that you intend to bid both suits. With this hand, I intend to support hearts next. For that reason, it makes sense to start with two clubs. Partner might raise clubs or he might bid two diamonds, revealing a double fit. Starting with two diamonds could prevent us from finding a secondary club fit.

I bid two clubs; partner rebids two hearts. This is the default rebid in the robots' methods. It does not promise six. Three spades would be a possibility now if the robots played that as a splinter, but they don't. I raise to three hearts, and partner goes on to four. I pass, and West leads the diamond jack.

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

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

If West has led a short suit, as seems likely, I want to play to minimize the chance of a diamond ruff. If East has the heart ace, it doesn't matter what I do. If West has it, I want to rise if the lead is a singleton and duck if it's a doubleton. Doubletons occur more often than singletons. Plus there is some chance West has led from king-jack-ten. So I duck.

East wins with the king, and I play the five. East returns the diamond four. Assuming this doesn't get ruffed, which hand do I want to win the trick in? I see no reason to take a finesse against the heart jack. So if either opponent has ace-jack third of hearts, I'm losing two heart tricks. If hearts are two-two, I'm losing one heart trick and, potentially, a diamond ruff. The only time my heart play matters is if someone has a stiff ace. A stiff ace in East's hand doesn't help. I'm losing the heart ace and a diamond ruff however I play the suit. But if West has a stiff ace, I want my first heart play to be from my hand. So I play the diamond queen. West plays the ten. I'm past the first hurdle. At least the lead wasn't a singleton.

Now deuce of hearts--five--queen--ace. East returns a diamond, which West ruffs with the heart seven. There is only one trump outstanding, and I can ruff my spade loser in dummy. So I have the rest. Making four.

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

This result is worth a mere 39%. And for a weird reason. If I respond two diamonds instead of two clubs, West chooses a club lead, and I make five.

It's annoying to get a below-average board for a completely random reason. Some would claim I got what I deserved. Two clubs was anti-field, since most players would bid the higher-ranking suit reflexively. And I should avoid anti-field actions in the auction so I can fully exploit my edge in declarer play--assuming I have one. 

I've never bought that argument. If I think bidding two diamonds has a lower expectation than bidding two clubs--and I do--why should I accept that lower expectation out of fear that it will work out poorly for some reason having nothing to do with the relative merits of the two choices? Randomness works both ways. Two club is just as likely as two diamonds to work out better for some unforeseeable reason. And it is more likely to work out better for a foreseeable reason. I believe you should simply do what you think is right and let the random effects balance themselves out in the long run.

What about my play at trick one? While it didn't matter. I'm not entirely sure I did the right thing. One possibility I didn't consider at the time is that West might have jack-ten third of diamonds. If so, and if West has the heart ace, I need to hop to block the suit. There is also some chance West led from jack-ten fourth and East has a singleton king. Finally, hopping may also save a trick if West has a singleton and East has the stiff ace of hearts. In that case, I lose two ruffs if I duck but only one if I hop. Whether those additional cases tip the scale in favor of rising with the ace is hard to say. If we assume West would never lead from king-jack-ten, then hopping looks like the better choice. The more likely he is to lead from king-jack-ten, the more attractive ducking becomes.

ACBL Daylong 1 - Jul 29, 2021 - Board 12

Board 12
Our side vulnerable

Last chance to beat the other couples.

♠ A 9 6  ♥ 7 4  ♦ K J 6 3  ♣ K 9 7 2

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

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

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

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

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

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

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

♠ K x x x x  ♥ Q x x x  ♦ x  ♣ A Q x

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ACBL Daylong 1 - Jul 29, 2021 - Board 11

Board 11
Neither vulnerable

♠ A Q 2  ♥ Q 10 5  ♦ 9 8  ♣ A Q 10 8 7

I have 14 HCP with two tens, no jacks, and a good five-card suit, so I open 1NT. I'm consciously avoiding the term "upgrade." I'm not "upgrading" to 1NT. I am judging the hand to be worth a strong notrump. It doesn't need "upgrading." 

Partner bids two hearts, a transfer to spades, and RHO doubles. I bid two spades, promising three spades. Partner passes, and RHO balances with three hearts. Since I have confirmed three-card spade support by accepting the transfer after the double, I can leave any further competitive decisions to partner. I pass, and partner chooses to defend. 

I see no hurry to cash our spade tricks. The club suit isn't a threat. If the diamond suit is, perhaps my ability to ruff the third round will suffice to keep our spade tricks from disappearing. I'd prefer to avoid leading a spade in case declarer has the king. So I lead the diamond nine.

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

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

Declarer doesn't have the spade king, but I'm still happy I didn't lead a spade.

Partner would compete with three spades on most hands with six of them. So I suspect declarer is one-six or one-seven in the majors. He plays the five of diamonds from dummy, partner plays the queen, and declarer plays the four. Partner shifts to the four of clubs, declarer plays the five, and I win with the queen. The club four should be from a singleton, 43 doubleton, or K94. But partner's carding when he shifts is unhelpful. He could have 943. 

Since declarer has no dummy entries, it won't hurt to cash the club ace. If declarer doesn't play the king, I will know partner is ruffing the third round. Unfortunately, he does play the king. Partner plays the three. Partner might be ruffing the third round, but he could easily have the nine left. 

With ace-queen of diamonds, there is no way partner would sell to three hearts when we have a nine-card spade fit, so it's safe to cash the spade ace. Actually, come to think of it, it's safe to play a diamond also. And it might be more productive. One diamond ruff won't help, since I have a natural trump trick, but perhaps I can get two. If declarer is 1-6-3-3, I can play a diamond, get a ruff, cash the spade ace, give partner his club ruff, then get a trump promotion on the fourth diamond. 

I play the eight of diamonds--king--ace--ten. It suddenly occurs to me that was an error. Partner might return a spade instead of a diamond. I should have cashed the spade ace first to remove that option. Fortunately, partner returns the three of diamonds. Declarer plays the jack, and I ruff. Now ace of spades--five--nine--eight. I play the seven of clubs. Partner follows with the nine. See? I told you he might have 943. Declarer has the rest. Down two.

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

I would have been tempted to double three hearts with partner's hand. But it's hardly clear. Maybe I'm just being swayed by the result. Fortunately, plus 100 is good enough to score 90%. Most pairs defending three hearts beat it only one, and quite a few players in my seat made an undisciplined decision to compete to three spades. They got what they deserved, going minus when they were entitled to go plus. 

The decision to open one notrump didn't matter much. If you open one club, partner bids one spade, and you make a support double over two hearts, showing your three-card support that way. Then partner bids two spades and RHO bids three hearts. So you are in a similar position, except that now there is no chance partner will find a double.

How did the defense lose a trick at other tables? It seems they trusted partner's carding and tried to give him a club ruff at trick three. Of course, even if partner does have a doubleton club, giving him an immediate ruff is the wrong defense. 

It's interesting that some Easts shifted to the club nine instead of the four. Does this mean their carding in this situation is random? Sometimes they lead the nine, sometimes the four (but never, for some reason, the correct three)? No. It seems East returned the nine when West's opening bid was one club but the four when his opening bid was one notrump. 

I doubt there is any logic behind that. It's probably just an accidental consequence of the fact that the program traverses a different path depending on the precise auction. So, while I doubt East used a random number generator to select his card, it's random for all practical purposes. In other words, it's determined by factors we aren't privy to, so we have no way of predicting which card partner will choose.

ACBL Daylong 1 - Jul 29, 2021 - Board 10

Board 10
Both vulnerable

♠ A J  ♥ 8 4 2  ♦ K Q J 3  ♣ A J 9 4

Pass to me. I open one trump. Partner transfers with two diamonds, I bid two hearts, and partner passes. RHO hasn't had enough yet. He balances with two spades. With three-card heart support and short spades, it's probably right to compete. Unless partner has four spades, then, according to the Law, it's unlikely both two spades and three hearts are going down. 

I bid three hearts and buy it. West, somewhat surprisingly, leads the king of hearts.

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

N

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

How are spades splitting? The balance would be more attractive with six spades, and the robots like to have good suits for their weak two-bids, so East's failure to open two spades doesn't mean much. But if East has six, that means West didn't lead a doubleton in his partner's suit. A trump lead makes some sense with three spades, since West expects me to have a doubleton and he wants to stop my ruff. So I'm inclined to think spades are three-five.

I have three top losers. Assuming the spade king is onside, I can avoid a spade loser by pitching dummy's third spade on a diamond. I can then concede a trick to the club king to make my contract. I'll wind up taking nine tricks: three heart tricks and two tricks in each of the remaining suits. 

If the club king is onside also, what are my chances of finding a tenth trick? I might be able to take three clubs tricks, either by dropping a doubleton king or by double finessing against king-ten. Or, if the diamond ace is onside, I might be able to take three diamond tricks. But taking all those finesses is going to require a lot of dummy entries, which I don't have. Probably my best chance for three diamond tricks is to hope East has four diamonds and comes under pressure when I cash dummy's hearts. I'm not sure of the details yet. Maybe I'll have a better picture of the hand after a few more tricks.

I don't need entries to my hand, so I see no reason to unblock in hearts. I play low. from dummy. East pitches the nine of spades. A five-zero trump break! I've never figured out how the robots card at trick one. Sometimes they play attitude; sometimes, count. So I'm not sure what to make of the nine of spades. It seems unlikely East wants a spade shift with a suit headed by king-nine, so perhaps he intends it as count from six. I have conflicting inferences now, and I'm not sure which is stronger. I'll have to keep an open mind about the spade split.

West shifts to the deuce of clubs. That's one dummy entry I no longer need. I play low, East plays the ten, and I win with the jack. If that shift was from three small, my clubs are now good. But a shift from three small clubs doesn't make much sense. A shift from a singleton or doubleton, looking for a ruff, makes more sense. The robots frequently lead low from doubletons in the middle of the hand, so the fact that West led the deuce is immaterial.

I play a heart. West hops with the ace, and East discards the spade four. That was surely an error. Ducking this trick would make it difficult for me to reach dummy to draw the remaining trumps. 

West persists with the three of clubs. His urgency to continue clubs suggests he was, in fact, looking for a ruff. I'm pretty sure now he has a doubleton club. I play low from dummy. East plays the eight, and I win with the nine. Thanks to West's club plays, I can now make an overtrick if the spade king is onside. 

It appears West is either 3-5-3-2 (making East 5-0-4-4) or 2-5-4-2 (making East 6-0-3-4). I play a heart to dummy, and East discards the diamond ten. The robots' first discard in a suit tends to be count. If East has four diamonds, that means he is 5-0-4-4. Here is the current position.

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

If my construction is correct, I don't need the spade finesse, since I have three diamond winners after East's diamond pitch. I can pitch a spade and a club from my hand on dummy's two hearts, then, once I've knocked out the diamond ace, my hand is good.

It makes me nervous when I have multiple winning lines, all of which seem to be virtually 100%. If you choose one of them and it turns out to be wrong, you look foolish. "What?" partner will say, "Why didn't you just do such and such? Wasn't that virtually 100%?"

I've never seen the robots pitch false count cards as their first discard in a suit. But that doesn't mean they won't. Perhaps the programmers have been reading my blog and have changed the code. On the other hand, I'm quite confident the spade king is onside. If East had

♠ 9 x x x x  ♥ --  ♦ A 10 9 x  ♣ K 10 8 x,

why would he hand me an overtrick by pitching a diamond? He probably shouldn't be pitching a diamond even with the spade king, but it's a gross blunder without it. So I'm sticking with my plan of taking the spade finesse.

On the next heart, East pitches the six of spades. I might as well hold onto my club. If East pitches a club on the last trump, I can pitch my spade and claim. So I pitch a diamond. On the last trump, East pitches the nine of diamonds. I let go of my small club and play a spade to the jack. It holds. I knock out the diamond ace and claim. Making four.

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

Plus 170 is worth 88%. Several Souths in three hearts made only three or even went down. Quite a few sold to two spades.

Apparently the spade nine at trick one was attitude, although I'm still not sure why East would want to encourage in spades. At least I was right that West's club shift was from a doubleton, despite the fact that he chose to lead the deuce. 

Could West have stopped the overtrick by ducking the second round of hearts? It doesn't appear so, since I don't actually need to draw trumps. I can lead a spade to my jack and drive the diamond ace. East wins and returns a spade or a diamond. I cash my pointed-suit winners, pitching a club from dummy. Then ace of clubs, club ruff, and ruff dummy's last spade with my eight of hearts.