Stuart Rachels


Chances

Playing in a team game, at unfavorable vulnerability, I am dealt:

AK74 J52 A43 K65

My spots are poor, my shape is bad, but I'm not willing to downgrade these 15 points and thus risk missing a vulnerable game at IMPs. So, playing weak no-trumps, I am obliged to open 1.

My partner Kevin responds 1, so I rebid the obligatory 1NT. Kevin alerts this and explains to the inquiring opponents that I am 15-17 balanced, and I might have one or two 4-card majors. He now bids 2, which I alert as artificial and game forcing. Usually this convention (2-way new minor forcing) is employed with something undisclosed in the majors. So, if I have 3 s or 4 s, I need to speak up. I have both, and I bid the cheaper asset: 2.

Kevin now bids 3. What is that? Well, presumably he doesn't have 4 s, because he bypassed 2. Does he have 5 s? Probably. Is this a cuebid showing the A, or is he just bidding his shape? I'm not sure, but I have nothing more to say. We don't have a 4-4 fit, I've shown 3 s, and given my flat distribution and lackluster spot cards, I've already come close to overstating my values. So I bid 3NT.

Do you dislike that bid? Me too. When you're not sure what your partner is up to, just keep describing your hand and let him pick the spot. I should have bid out my shape with 2. At the time, I couldn't see what could go wrong by bidding 3NT. Partner contemplates the situation and bids 6. This was a surprise to me, but of course he hadn't limited his hand. Nobody doubles, and after a is led, the dummy comes down:

9
KQ106
KJ97
AQ102
 
AK74
J52
A43
K65

Ah, so this is what can go wrong. As Philip Larkin once wrote, "Well, useful to get that learnt." We're missing an ace, we have no 8-card fit or 5-card suit, and our 7 measly trumps are not solid. This is my fault: given that I opened 1, showed exactly 3 s, and then seemed to deny 4 s, partner reasonably inferred that I had 4+ s. (After all, with only 3 s, 3 s and 3 or fewer s, I would've had 4+ s and would have opened 1. The shapes consistent with my bidding are 3=3=3=4, 3=3=2=5, 2=3=4=4, and 2=3=3=5.) Since Kevin thought we had a fit, he judged well to bid 6: 15 points, a fit, and a singleton are enough for slam opposite a strong no-trump. But all this is now your problem. Plan the play.



The first thing is not to panic. You'll be in worse contracts that can make. Also, you should know how to play the suit, absent any other considerations about the hand: A, K, small, and if West follows small, play the Q. Essentially you hope for a 3-3 split, and because of the 10 you will also pick up the suit if the J is doubleton. Now about the play. After you win the lead in hand, how might you make 11 more tricks?

KQ106
KJ97
AQ102
 
K74
J52
A43
K65

Think of the dummy as the master hand, since its trumps are longer. Essentially, there are two possibilities: you can draw trump (whether in three rounds or four, if the J is doubleton), knock out the A, and then later try to get your twelfth trick by finessing the J. (If you want to visualize this in terms of one of the hands being set up, focus on the North hand: aside from the A, you have two potential diamond losers: one will go on the K, and the other will disappear with a successful finesse.) Alternatively, you can try a dummy reversal: ruff two s, hope trumps can be drawn in three rounds, and then knocking out the A will generate 12 tricks without any finesses. (If you want to visualize this in terms of one of the hands being set up, focus on the South hand: the two losers are ruffed, and a little will go on a long .) Which plan is better?

Reversing the dummy seems better, since no finesse is required. However, there are two complicating factors. First, note that ruffing twice in the dummy gives up on the possibility of picking up trumps when they split 4-2 with the jack-doubleton; once you start ruffing, someone's trumps will be longer than yours. Second, do you have the entries to do all this? You can begin the reversal at T2 by ruffing a , yielding:

KQ106
KJ97
AQ10
 
K7
J52
A43
K65

To pull off the reversal, you need to come back to your hand twice: once to ruff another , and then again (after cashing dummy's high trumps) to pull the remaining trumps with your K. Do you have the entries? It's not clear. You have the A, but you can't use the trump suit, and the J is only a quick entry if the A is on your right.

A danger lurks here. Suppose you play to the A, ruff a , and then cash dummy's high trumps. The position is now:

KQ106
KJ9
 
K
J52
43
K

You can play to the J, but suppose it loses to the A. When West returns a you're stuck in the dummy: even if trumps are 3-3, you can't get to your K to extract them. (An even worse fate for you is possible: West wins the A, returns a which East ruffs, and then East puts you in dummy with a , and you still can't draw the remaining trump. Ha ha ha!)

Is your head hurting yet? Do you have any idea which line is better? Do you notice how, when things go badly, suddenly the hand is yours and not mine?

Things become clearer when you realize that we've misplayed the dummy reversal line. We can combine our chances by playing more flexibly. Again, win the opening lead with the A and ruff a small one:

KQ106
KJ97
AQ10
 
K7
J52
A43
K65

This time, however, don't cross to the A; that line of play puts all of your eggs in the basket of East's holding the A. Instead, try to cross to the J. There are three possibiIities. If it wins, you can reverse the dummy, now holding a sure entry in the A. If East rises with the A, he cannot hurt you, since he would be leading into dummy's tenaces, and you can continue with your plan to ruff another ; finally, if your J loses to the A--this is the interesting case--you are in much better shape than before: a lead is unlikely to be ruffed (since this is only the third round of the suit), while a return won in dummy leads to this position:

KQ
KJ97
AQ10
 
K7
5
A43
K65

The extra trump in dummy now gives you the flexibility to revert back to the first plan: cash your top s (hopefully drawing trump), and sooner or later you can try the finesse. You win some, you lose some.

What is the upshot of all this? Line 2 lets you avoid the finesse with a dummy reversal when East holds the A, which he will half the time. The only thing you give up to Line 1 is the ability to draw trumps when the J is doubleton. But that possibility is slightly less important than what you gain. Here is how to quantify the comparison: s will split 4-2 48% of the time, with the J being doubleton in one-third of those cases, or 16% of the time. But picking up that 4-2 trump split only matters when the finesse is on, which brings us down to 8%. So, Line 1 gains over Line 2 in 8% of the cases. By contrast, consider the dummy reversal line, which can only bring home the contract when trumps split 3-3, which they will 36% of the time. The A will be favorably placed half the time, or in 18% of the cases. However, the ace's being onside will affect the number of tricks taken (as against Line 1) only when the finesse was going to fail, which it will half the time. And half of 18% is 9%. So, Line 2 gains over Line 1 in 9% of the cases. Thus, Line 2 is superior by 1%. (There are factors we haven't considered, but they're too remote to change our conclusion.)


What Actually Happened


I made all these calculations as swiftly as I could, and then I went for Line 2. Very funny, don't you think? In reality I did go for Line 2, but my thought process cannot be rationally reconstructed. (If you put enough monkeys in front of enough typewriters, eventually one of them will hammer out the sentence, "To be or not to be; that is the ishblurb.") Here's what happened:

9
KQ106
KJ97
AQ102
 
AK74
J52
A43
K65

T1: A; T2: ruff; T3: low off the board (perhaps better technique is cashing the A first?) with my J losing to the A (too bad).

KQ10
KJ97
AQ10
 
K7
52
A43
K65

West returned a trump (earlier I mentioned a ) to the 10, J and K. I still have an 18% chance: hope that trumps split 3-3 (which they did), and later try the finesse (it worked). Partner looked surprised that I made it, and later he asked me why on earth I began the hand by ruffing a with my long trumps. I said without conviction that I had hoped to ruff another one, but I never got around to it.


Final Thoughts


9
KQ106
KJ97
AQ102
 
AK74
J52         (dealer)
A43
K65

The actual auction: 1-1-1NT(Alert!)-2(Alert!)-2-3-3NT-6.

After Kevin bid 3, I was wrong to think he might have 5 s. If he'd had 5 s, he would have set the trump suit by bidding 3 (forcing, since 2 put us in a game-force auction). Thus, I should have placed him with exactly the sort of hand he had. And so, I should have known to bid out my shape with 3. Here is the proper bidding sequence, on our methods:

1-1-1NT(Alert!)-2(Alert!)-2-3-3-4NT(quantitative)-pass.

Yes, our opponents got fixed: we bid too high and were rewarded. I've gotten fixed a time or two.

When Kevin looked at my analysis of this hand, he found a flaw: I overlooked an advantage of line 1 (where trumps are pulled straightaway) over line 2 (the dummy reversal): line 2 will fail if the opponents can find a ruff, which would require a 5-1 or 6-0 split (and the A must not be singleton, since then the suit would get blocked). This is an obscure chance, for several reasons, but instead of saying that line 2 was 1% better than line 1, I should have called it a dead heat.