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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
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 finesse against the missing honor? 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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