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Restricted Choice
When a defender plays one of two missing touching honors on the first round of the suit then there is a presumption that the defender is less likely to have the other touching honor. Please read on.
Related Extracts from Past Wednesday Games
Playing in 4♠, it won’t be obvious whether Declarer should cash the ♠A or the ♠K on the first round of trumps. If he cashes the ♠A first then he always has 11 easy tricks. So let’s see what happens if he is predisposed to cash lead a Spade to the King on the first round of trumps. Some possibilities: - North’s opening lead is the ♦K and then she cashes the ♦Q and (belatedly) shifts to a Heart. If N-S play Ace from Ace-King then Declarer has a ruffing finesse in Diamonds which will allow him to ditch his Heart loser. So, he’ll abandon his plan to lead low to the ♠K, instead he will play the ♠A and then the ♠K (arranging to be in Dummy after the second round of trumps), which works out just fine when the Spades oblige. - In the previous line, North’s defense pushed Declarer into the winning play. But suppose that, after cashing just one Diamond, North fiendishly shifts to a Heart! Declarer wins that and leads a Spade to the King, and when North plays an honor, Declarer is faced with a dilemma. If he follows the Principle of Restricted Choice and the trump finesse loses (as in the actual case), then the defense will cash a Heart for down one. An alternative is to disregard the aforementioned Principle … if the trumps are 2-2 then it’s 11 tricks … if not then perhaps the defender with the long trumps (South in this hypothetical case) has three or more Clubs, allowing Declarer to get rid of his Heart loser and make 10 tricks. Playing matchpoints we think that Declarer should adopt the best line for 11 tricks, and that is to finesse in trumps, tragically going down one! Oh, well! Declarer at least can reassure himself that his play was reasonable and that he was also the victim of fine defense by North.
OK, just how good is the slam? It’s so-so. Let’s hope (for the sake of the defense) that South avoids the disastrous trump lead and starts out with a Heart. Dummy’s Ace wins that, and the ♠J is led, covered by the King and Ace. Now, back to Dummy with a Club, then a losing trump finesse. South continues with Hearts, again won in Dummy. A Club is ruffed and all of Declarer’s Spades are played. Declarer is hoping that someone is being squeezed in the red suits but that turns out not to be the case. The ♦K and ♦Q are cashed, and Declarer notes the fall of the Jack and Nine from North. Should Declarer finesse the Diamonds now, playing South to have started with Txxx? We think so! There are Restricted Choice considerations here … with ♦JT9, North had numerous different ways to play the suit … with ♦J9 doubleton he didn’t. So, Declarer takes the finesse and 12 tricks it is!
There’s not much to the play, it will be 10 or 11 tricks, depending on how Declarer plays the trump suit. If Declarer is burdened with knowledge of the Principle of Restricted Choice then she will finesse the second round of trumps and make 10 tricks … but if Declarer is blithely unaware of said principle then she will play for the drop and make 11 tricks.
The auction should persuade North that a trump lead is called for, so the defense starts out with three rounds of trumps. In with the third trump, Declarer cashes the ♣A, ruffs a Club (noting the fall of the Ten), and cashes ♦Q, ♦A, ♦K (removing the defense’s exit cards). At this point, should West lead a low Club, hoping that South started with KTx? … or the ♣Q, hoping that South started with JTx? There are two good reasons to lead a low Club. Firstly, there are Restricted Choice considerations (as South might have played the Jack from JTx), and secondly Declarer would prefer to lose the lead to South (he does not want a Heart lead through Dummy). So, Declarer leads a low Club, felling South’s King. At this point South is down to nothing but Hearts and must lead one to North’s Ace. Now, North is forced to hand Declarer his 9th trick, either by leading into Declarer’s Clubs or by letting Dummy’s ♥K score a trick. Nicely played, Mr West!
In 3♠, Declarer is destined to lose 3 Hearts and a Club, and it all depends on how she plays the trump suit. She’ll start with the Ace, and the Queen will pop out on her left. Should she now play the King, hoping that West started with QJ doubleton? Or should she cross to the board and finesse against the Jack? The answer is that the finesse is very much the percentage play, it’s the so-called Principle of Restricted Choice in action. The logic is a tad obscure, but it goes something like this: - If West had started with the singleton Queen he would be forced to play it - If West had started with the QJ doubleton, he might reasonably have played the Queen or the Jack - The odds of West starting with Q or QJ are approximately the same - So, after we play the Ace and the Queen appears on our left, it would be a mistake to play for the drop, that is hoping for two things … firstly, that West was indeed dealt the QJ, and, secondly, that he would have chosen to play the Queen from that holding, rather than the Jack - If, instead, we take the finesse on the second round, we are playing for just one thing, namely that singleton Queen, which had to be played because the choice was restricted to that.
Yes, it’s an elusive argument, but also a fairly frequent situation, and one that is worth remembering. Anyway, the Principle of Restricted Choice tells us to take the finesse and this works two times out of three, as indeed it does here.
It’s true that 9 tricks can be made but that requires the winning Heart finesse and successful guesses in both black suits. Of course, an opening Spade lead from North would eliminate one of those guesses, with a less helpful J♥ lead Declarer will have little to guide him to the location of the Q♠. Anyway, making 9 tricks in No Trump, with or without bidding the optimistic game, will surely result in an excellent board for E-W.
We mentioned the Spade guess, but more interesting is the guess in the Club suit. At some point in the play, Declarer will cash Dummy’s KQ♣, and North will play the Ten on the second round. Until the appearance of that Club honor, Declarer would have been obliged to play for a 3-3 break, but now the option of a 3rd round finesse has presented itself. Do you finesse, playing for the 4-2 break, or do you play for the 3-3 break? It may seem like a close guess, one way or the other, but the Principle of Restricted Choice tells us that the percentage play is to take the finesse. The logic is convoluted, but it goes something like this: - If North started with Tx he would have had to play the Ten on the second round, he would have had no choice. - If North started with JTx he had a choice on the second round of the suit, either play the Ten or play the Jack. Therefore, if we play for the drop on the third round, we are betting for two occurrences, namely the specific holding and North’s choice to play the Ten. But, taking the third round finesse is betting on just one thing, and that is the specific holding where there was no choice of plays. Well, we did warn that it was convoluted. But valid, nonetheless.
South does not have an attractive opening lead against 4♠ and may well start out with a trump. Declarer draws three rounds of trumps, and must then decide how to play the Diamonds. Declarer will have noticed that South had 3 Spades, and also the Heart length, so it’s fair to assume that if Diamonds are not 2-2 then the length is likely to be in the North hand. Accordingly, he lays down the A♦ and sees the Q♦ appear from the South hand. Now, Declarer has two good reasons to finesse against North for the Jack: - As already mentioned, North rates to have Diamond length - The Principle of Restricted Choice tells us that North is more likely to hold the J♦.
So, Declarer successfully finesses in Diamonds, runs the suit pitching a Heart, and then leads towards the K♣. When the A♣ turns out (as expected) to be over the King, it’s 11 tricks for Declarer.
North no doubt considered bidding 5♥ as a sacrifice, and that will be either a spectacular success or a spectacular failure, nothing in between. The difference between triumph and disaster will be the play of the Club suit. The defense starts out with Diamonds and Declarer ruffs the second round. Declarer cashes the A♣, noting the fall of the Ten from East, then plays three rounds of trumps ending on the board. The bidding suggests that the K♣ is with East (though it’s no certainty), and the play of the T♣ is a further indication for Declarer to run the 9♣ on the second round of the suit (it’s another application of the Principle of Restricted Choice). It was nice play by Declarer to cash the A♣, rather than take a first round finesse. A well-earned top for those N-S pairs who escaped for -300!
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