Law of Restricted Choice?
That Figure 33
No Trump vs. a suit slam
|
 K J 10 |
|
 Q 10 |
|
 K Q 9 7 5 2 |
|  4 2 |
| Q |
|
9 7 4 3 2 |
| 9 8 7 6 3 | |
4 2 |
|
| 6 4 3 | | J 10 |
| A J 10 5 | |
9 7 6 3 |
|
A 8 6 5 |
|
|
A K J 5 |
|
|
A 8 |
|
|
K Q 8 |
Opening lead: A of clubs |
| North | East | South | West |
| 1 |
Pass |
1 |
Pass |
| 2 |
Pass |
4 NT |
Pass |
| 5 |
Pass |
7 NT |
All pass |
[The hand fit a number of categories as the above headings indicate. As originally entered, the part about no trump vs. a suit was way down at the bottom, virtually an afterthought. I've moved that up front for this category. The remainder is valid, but the reader who is interested only in the discussion of no trump slams is invited to skip the rest after the break.]
Two of the advantages of no trump over a suit (matchpoint scoring) are illustrated here when you have all suits stopped by high cards and a long suit in one hand (as opposed to a balanced fit). That long suit will take just as many tricks in no trump as in diamonds (well, by and large, of course). And here was the rundown: 6 no with an overtrick: 84%. Six no without an overtrick: 60%. 6 diamonds with an overtrick: 48%. 6 diamonds without an overtrick: 40%. There is a significant disparity here, I would say.
The other possible advantage wasn't germane: If diamonds don't split evenly (as on a 4-1 split missing the J 10), you still have your slam in no trump by looking elsewhere for your winners: Four spades (having a bit of luck with the Q), four hearts, three diamonds and a club). Tain't so in a diamond contract. But here that was not a factor.
It would look to be a fairly routine hand as far as the play went. You won't need the spade hook, and even if you take it, you'll get a pleasant surprise if you avoid a first-round finesse. Yet, down at the bottom of the scroll were four or five minus scores. One of the four had nothing to do with the play of the hand but with the bidding, and I have given that above. Not a good idea to be in 7 no missing an ace, particularly when it's held by the person on opening lead.
I'm not sure why North with no aces responded five diamonds to Blackwood. But some who play RKC, Roman Key Card Blackwood, play what they term 0314, meaning clubs indicate zero or 3 aces, and diamonds one or four aces, and some 1403, meaning the converse of that, which is to say 5 diamonds would mean zero or three aces. I suppose it was a mixup on that account, North thinking they were playing the latter, South the former. Not a good idea to get mixed up on that elementary decision. But I would recommend the former so that the lower figure is consistent with straight Blackwood, leading to less forgetfulness and confusion.
However, I would call South the goat here for thinking grand slam in the first place. The bidding goes one diamond, one heart, two diamonds. Now the hand has been defined. North has advertised a minimum opening bid, about 13 hcp's, give or take one, maybe give or take two with a long suit (as here), but a minimum nevertheless. South has 21 hcp's, so the Figure Thirty-Three, q.v., when the combined hands have perhaps 34 hcp's (they actually have only 32, but the 6-card suit does help), advises or calls for a little slam. It doesn't matter if you have all the aces, even all the aces and all the kings. You need the infrastructure to carry you from those 8 tricks to the 12 needed for slam, or the 13 needed for the grand. And the Thirty-three point principle will tell you a whole lot more than Blackwood will on this type of hand (fairly balanced). Indeed, I came across an OKBridge hand in the past year where a pair with every ace and every king couldn't make game!
I'm not asking anyone to take my word for it. This figure has been adduced by such luminaries as Charles Goren and Oswald Jacoby, but I'm not even asking you to take their word for it. I would say, however, that you can do a lot worse than accept their word for just six months, during which time you keep your eyes peeled for whether that figure makes sense or not. I can only say that from my observation, it makes a helluva lot of sense.
Indeed, let's give North the ace of clubs to warrant his 5 diamond response. But we're going to subtract 4 hcp's for that gift, and I'm going to take the easiest 4 hcp's to take, namely the two queens. Now would you like to be in grand slam? You've got 3 club winners instead of one, but the diamond suit is useless beyond the top two winners. That's five, so you're going to need four tricks in each major. Four you can generate in spades, yes. In hearts? Ten doubleton opposite A K J 5? You're going to need a lot of luck to generate four tricks there, though, yes, it's mathematically possible. [Well, come to think of it, only picking up a stiff Q without wasting the 10 on a lead would do it. But this is all academic anyway. The hand just isn't grand slam material and South should have known it.]
Wait a minute, fella! I wanna give up the K J of spades for that ace of clubs. Now I wanna be in grand slam! You've got me. But there's the rub. You'd have grand slam on 32 hcp's because diamonds break evenly and more importantly, nothing is wasted. Unfortunately, or fortunately if you wish, you can't shift points around that way. You have to take your 32 or 33 hcp's where they are, and that is the essence of the 33-hcp principle, that that point count favors a little slam, though you could have a grand on occasion when everything breaks right and could go down on others when nothing breaks right, but in the long run it'll bring in satisfactory profits.
Then three people went down in little slam, two in no trump, one in diamonds, which plays substantially the same as 6 no, and one went down in five diamonds. How did they do that? It looks as if it would be a cakewalk for making 6, as most declarers did. How did they lose a second trick? Ah, there's the culprit. They cashed the ace of diamonds, drawing the jack from East, and evidently following the Law of Restricted Choice, now finessed the 8, overtaken by the 9, into the 10! And that'll do it.
When we come across discussions of that Law, it's almost always illustrated by this situation:
|
K 9 7 6 |
|
. . . . |
|
A 10 5 3 2 |
You cash the king, getting the queen on your left. Now the proponents of the Law of Restricted Choice tell us that we'd do better (by and large) now to finesse the 10 of spades. Okay. I was originally very skeptical of that Law, but when I checked it out, and for the life of me, I don't recall how I checked it out, it panned out as claimed. So that Law has withstood the scrutiny of decades and I'm not here to quibble with it. But you must bear in mind that when you pick up the queen on your left and finesse the 10 on the next round, in addition to paying your respects to that law, you're also playing for a 3-1 spade split over a 2-2. And the mathematical tables tell us the former is a 50% chance over the latter's 40%!
But when you apply that law in the above situation, you're necessarily playing for a 4-1 split as opposed to the far more likely 3-2. I admit I don't have the savvy to work out the odds for each line here, but I'm very, very doubtful that the Law of Restricted Choice would override the odds favoring a 3-2 diamond split over a 4-1.
Further, there's one more factor to consider, at least by the no trumpers, though not by the pairs in diamonds. And that is, you don't need to test the diamond suit just yet, especially the declarer who got the ace of clubs opening lead. It's a common principle in bridge that when you have a key finesse you want to take, which, losing, would defeat your contract, you first want to try for a drop of honors in other suits if there is such an opportunity, and if that doesn't work, then take that finesse. Can you live with just the top three diamonds?
The answer is clearly yes, if you can pick up just three spade tricks (for the declarer has two club winners on the lead of the ace), though without that lead, one needs four spade winners, which wouldn't seem to be so likely to be achievable, even if we can see it would be.
So if you're hooked on that 9 of diamonds finesse based on what I suspect is a misreading of that Law, you might first test spades for the drop of the queen, and not getting it, then take your ill-conceived finesse. But here you wouldn't have to. As for myself, I would test in the other direction. I would test diamonds for a 3-2 split first, and not getting it would then see if I can finagle enough tricks out of the spade suit for my contract.
The other declarer in no trump didn't get the ace of clubs opening lead. I went back to see what he got and found it was . . . the queen of spades! Simple counting would have told him he didn't need the diamond suit beyond the top three. Nor would two leads have endangered him. He's got four spade winners, 4 hearts, three diamonds if the suit splits 4-1 and time to knock out the ace of clubs for a 12th winner. When diamonds split evenly, he could have made an overtrick.
The declarer in five diamonds also didn't count well. Opening lead a low spade. Now the second-round finesse into the 10 of diamonds allowed East (above, but the hand of course was played from North) to give his partner a ruff along with the ace of clubs. Declarer would have had a guaranteed contract by continuing the top diamonds. If they split 4-1, the defense can only take a diamond and the ace of clubs and he just might have beat a few in slam. Indeed, you might even say he should have been glad if diamonds split 4-1 for that reason, instead of going for an overtrick (perhaps not consciously so) by that second round diamond hook, an overtrick that wouldn't have meant a whole lot if the field is largely in a no trump slam.