Board 39

Board 39 (click to download pbn file)
Both sides vulnerable

♠ A K 10 3 ♥ 5 4 ♦ Q 5 3 ♣ Q J 7 4

I open one club in first seat, partner responds one diamond, and RHO overcalls with one heart. I bid one spade, and partner bids three notrump, which ends the auction. West leads the three of hearts.

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

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

Partner seems to be pretty aggressive with these three notrump bids. I'm not sure what was wrong with two notrump. I play the four from dummy, and East plays the ten. Falsecarding with the king wouldn't work too well here. West has no reason not to play hearts from the top once he gets in. So I win with the jack. I know from the lead that hearts were five-three.

I have essentially two ways to make this: (1) Hope West has all the missing high cards. I play diamonds out of my hand. When West is in with the king of diamonds, he can't afford to clear hearts, since that gives me my ninth trick. So I have ample time to establish my ninth trick in clubs. (2) Try to run the diamonds. I cash out the spades, then lead the queen of diamonds from dummy, hoping West has ten doubleton or East has king-ten doubleton.

Neither line is especially good. Which one is better? Let's start by assuming diamonds are three-two. (We'll relax this assumption later). In that case, line (2) is easy to calculate. There are 20 possible three-two breaks (the combinations of five things taken two at a time--times two, since either hand can have the doubleton), and our play works in four of them (three doubleton tens in West's hand plus one king-ten doubleton in East's hand). That makes line (2) 20%. Line (1) is little harder to calculate. It works when West has three out of three critical cards. Normally this would be 12.5%, but it's better here because some layouts are contra-indicated by East's failure to raise hearts over one spade. Let's assume East can't have all three honors, that he can't have the ace-king of clubs, and that he can't have the ace of clubs and the king diamonds. We'll allow him to have both minor-suit kings. This is a simplification. Depending on his shape, he might sometimes pass with the club ace and the diamond king and he might sometimes bid with both kings. But it's a reasonable approximation. We've eliminated three of the eight possible ways for the honors to be split. So West will have all the missing honors one time out of five, making line (1) also 20%.

In our first approximation, then, both lines are roughly equal. Next we consider what chances each line might offer above what we've already calculated. Line (1) will work on certain four-one diamonds breaks. Specifically, it will work when West has a singleton king or when East has either singleton honor and West has both club honors. Line (2) has an advantage that's hard to quantify, namely, flexibility.  Depending on what happens when you cash the spades, you may change your mind about how to play diamonds.  You may wind up leading a diamond to the jack, essentially reverting to line (1) with some extra chances against king doubleton of diamonds on your right.  And if the jack of spades happens to fall, allowing you to put pressure on the opponents by cashing four rounds of spades, additional possibilities arise.  I decide I like line (2).  Line (1) is too committal.  When you stay flexible, good things tend to happen.

I cash three spades, pitching a club from my hand. East plays deuce--four--five. West plays nine--six, then discards the deuce of hearts. So West is already under pressure. What's going on?

____

West might be 2-5-4-2 with ten fourth of diamonds. He might also be 2-5-3-3 with ten third of diamonds and ace-king third of clubs. It's not immediately obvious that he can't afford a club from the latter hand. But, in fact, he can't. After leading the queen of diamonds to the king and ace then cashing the jack, I can simply exit with a diamond, and he has to give me my king of hearts for my ninth trick. To escape the endplay, he must keep an exit card in clubs.

One thing for sure. He doesn't have the ten doubleton of diamonds I was about to play him for, since has no reason not to pitch a club from four. So I'm changing my mind about leading the queen of diamonds. Suppose I play a low diamond to the jack, cash the ace, presumably dropping East's king, then play a diamond to dummy's queen and exit with the queen of clubs. I've taken seven tricks. I need only two more, and West must give them to me.  He can either play hearts, giving me an entry to my diamonds, or he can play clubs, giving dummy two club tricks.

I play the three of diamonds--seven--jack--deuce. Ace of diamonds--eight--five--ten. Ten? That's disappointing. I was sure this was going to work. I play the eight of clubs. West hops with the king, cashes the diamond king and the club ace, then plays a club to dummy. I have to lose the last two tricks for down one.

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

When West didn't pitch a diamond, I thought he had ten third. But he had king third, and the reason he couldn't afford to pitch one was he needed to duck the first round. Nice play. It turns out line (1) would have worked. But I still think line (2) is better.  There's no particular reason the king and ten of diamonds couldn't have been reversed.

I was impressed with Jack's defense.  Assuming I work out to abandon my original plan of leading the diamond queen, this defense was necessary. He had to hold a diamond so he could duck the first round, and he had to hold a small club to avoid being endplayed. I gave this problem to several gargoyles, and no one found this defense. For once, I think I went down against Jack when I might have succeeded against most humans.

At the other table, the auction and lead are the same. Jack wins the jack of hearts, cashes the spade queen, and, strangely, leads a club. West hops with the king and plays ace and a heart. Declarer plays another club. West hops with the ace and cashes his hearts. Declarer has the rest. Down one for a push.

I'm not sure what Jack was up to. Did he consider it so unlikely he could make this hand that he was simply playing to hold the undertricks? It's true that, if you give East one of West's club honors, Jack would have been down two, while I would have gone down five, losing seven imps. I risked a lot of extra undertricks for a line that had little chance of working.  In this case, perhaps my customary single-minded devotion to finding a way to make the hand was wrong?  Perhaps Jack's line makes more sense?

I don't think so, at least not under normal conditions.  The game is thin, and you have no reason to expect your opponents to reach it at the other table.  If your opponents are going plus at the other table, the cost of going down a few extra tricks is minimal compared to what you rate to pick up by making the game.  In this match, however, the same South is sitting at both tables, and all of my own actions were routine.  So maybe it's fair to assume they will reach game at the other table as well.

Me: -100
Jack: -100

Score on Board 39: 0 IMPs
Total: +96 IMPs