Board 73

Board 73
Opponents vulnerable

♠ 7 6 ♥ A K 6 3 2 ♦ 8 ♣ A 9 8 5 4

Partner passes and RHO opens two spades. Perfect! To try for a swing on this deal all I need to do is to bid normally. I know from earlier deals that Jack will bid four clubs (leaping Michaels) with this hand. In my opinion, this hand is worth only three hearts. Even if I did think this hand qualified for four clubs, I would still bid three hearts given the state of the match, since three hearts is by any standard a reasonable call and one I know my opponent won't choose.  This is perhaps our best example yet of an Edgaresque swing action.

Over three hearts, LHO bids three spades. Partner bids four hearts, and everyone passes. I suspect they will play four hearts at the other table, but they will play it from the other side, so I still have a chance for a swing. West leads the queen of spades.

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

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

So West broke the Law by raising with a doubleton. I cover West's queen with the king. East wins the spade ace, cashes the jack, then plays a third spade.

I can pitch a diamond and make this any time West began with a doubleton heart, since I will be able to draw trumps in one round and will have four trumps left to ruff clubs with. I can also make it if West began with a singleton queen, since if he ruffs with the queen, I won't need to draw trumps.

But why did East give me this chance? Given the raise, he knew his partner's spade queen wasn't a singleton. If East is looking at a small singleton heart, why not play a diamond at trick two? His partner can win and switch back to spades, and a third round of spades will defeat me. How hard could it be to find that defense? Admittedly, East can't be sure his partner has the diamond ace. But how does he plan to beat this if he doesn't?

If East's defense means he can't have a small singleton heart, I should ruff with the ace and play a diamond toward the king. If I develop a diamond trick, I can afford to play two rounds of trumps (finessing against East's queen), since I will need only three ruffs in dummy. This line is considerably against the a priori odds. Given the six-two spade break, West is almost twice as likely as East to have a doubleton heart. So, before I decide to adopt this line, I need to be fairly certain of my inference.  Just how difficult is it for East to find a diamond shift?

First of all, could a diamond shift ever be the wrong defense with a small singleton heart? Yes, it could. I could have:

♠ x x ♥ K x x x x ♦ A ♣ A x x x x.

The defense has four tricks off the top, but a diamond shift lets me pitch my spade loser. Or I could have

♠ x x ♥ K Q x x x ♦ A x x ♣ A K x.

Again, the defense has four tricks, but East must play jack and another spade in order to take them. So the diamond switch isn't 100%. It might still be the best play, but it's not so obvious that I can assume East would always find it.

Another thought occurs to me.  A diamond shift is never necessary unless I have a singleton diamond. East may well think I'm unlikely to have a singleton diamond since I didn't bid four clubs.  If so, he is very unlikely to find the switch.

I pitch a diamond, and West ruffs with the seven of hearts. He shifts to the three of clubs. I ruff in dummy as East plays the six. I play a diamond--three--ruff--deuce. I cash the trump ace, and West pitches the four of diamonds. Terrific! I considered the winning play, but I talked myself out of it.

Since I must draw a second round of trumps, I can ruff only three clubs in dummy. That means I need clubs to be four-four or the diamond ace to be doubleton. I ruff a club and play a diamond. If East plays the ace or shows out, I'm home. Otherwise I'm going down. He plays the jack. Down one.

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

At the other table, South bids four clubs, as I suspected he would, and North bids four hearts. East leads the jack of diamonds to West's ace, and West shifts to the queen of spades. North ducks this. This is an error.  He should cover in case it's queen-jack doubleton. West continues a spade to East, and East plays a third round. Since the defense has already taken three tricks, declarer has no choice. He ruffs with the ace, ruffs a club, and floats the ten of hearts. Making four.

As the cards lie, my opponents played this from the correct side. But that didn't have to be the case. If West had queen doubleton of hearts, my opponent would have gone down, whereas I would have made it (assuming I got the same defense). So playing it from a different side produced a random swing, which I is exactly what I was trying to accomplish. Of course, I would prefer to have won the random swing than to have lost it, but you can't have everything.

What about my play? Was I unlucky to go down or should I infer that East can't have a small singleton heart and find the winning line? A priori, ruffing high is superior in only two cases: when East has queen-nine or queen-seven of hearts. Pitching the diamond is superior in three cases: When West has queen-nine, queen-seven, or a singleton queen. But, since West is more likely to have a doubleton heart than East, I need to give his doubletons more weight.

I said earlier that West is almost twice as likely as East to have a doubleton heart.  That was a seat-of-the-pants guess.  If you work it out, the exact number is five thirds as likely.  To account for this, we count each of West's doubletons as five thirds of a case instead of one case. The a priori odds, then, work out to 13 to 6, or a little more than two to one,  in favor of pitching a diamond. What my decision boils down to is this: If I ruff high, I am essentially laying two to one that East, when looking at a small singleton heart, will find a diamond shift. Is that a good bet or not?

In a real match, a hand like this might keep me up all night wondering whether I did the right thing. One of the nice things about playing against Jack is I don't have to wonder. I can find out if I did the right thing.  I switch the queen of hearts and the deuce of clubs and play the board again.  The auction and lead are the same.  I cover with the spade king.  East takes his ace.  Will he find the diamond switch?  If he does, then I made a mistake. He doesn't!  He plays jack and another spade just has he did with queen doubleton of hearts.  So I'm exonerated.  I can sleep tonight.

Me: -50
Jack: +420

Score on Board 73: -10 IMPs
Total: -145 IMPs