RC Squared

Author: Larry Cohen
Date of publish: 04/01/2018
Level: Intermediate

This deal was played in a Junior Practice match, for which I was giving live on-line commentary. After South's 1NT, he ended in 3NT (North investigated a possible 8-card major fit, but found none). The J was led in this layout.

 Q952 K102 84 K962 AK7 AJ75 K3 J1073

East encouraged and South took the K. Playing on clubs is conceding the contract (the defense will have too many diamond winners). Declarer needs to take 9 tricks without losing the lead. That means each major needs to produce 4 tricks.

In spades, you can hope for either a 3-3 break, or that the jack/ten cooperate (more on that later). In the heart suit, there is a 2-way guess for the queen. If the suit splits 3-3, it is just a pure 50-50 guess. What if they are 4-2? Since it is easier to pick up Qxxx with East (you can cash the king first and lead the 10), let's say you lead a heart to the king at trick two (all following low).

Do you agree with trying the hearts first? Decide before you read on.

You continue with the 10. RHO thinks for a moment and covers with the queen. On your ace, LHO follows with the 9. You are left with J7 opposite 2.  The opponents have 8x. You can lay down the jack (hoping LHO started with 98x), but "restricted choice" says that 9x was more likely. The theory goes like this: "With 98x, you might have seen the 8 on the second round--West would have had a choice. When he played the 9, assume his choice was restricted; he played it because he had to." Mathematicians would prefer that I explain it as just plain odds--that exactly 986 opposite Q43 is only one holding and statistically not as likely. Are you still with me?

Say you want to go back to dummy to finesse against the 8 (which assumed you carefully watched the spot cards and can calculate the odds). So, you start with the AK. All follow low, but on the second round, RHO follows with the 10. You play a third round, and when LHO plays low, do you finesse the 9, or play the queen to try to drop the jack? Here we go again. Using all the same Restricted Choice analysis (or probabilities), the odds favor the finesse. Let's look at the Real deal:

 Vul:NoneDlr: South Q952 K102 84 K962 J643 96 AJ105 AQ5 108 Q843 Q9762 84 AK7 AJ75 K3 J1073

After the K, declarer can indeed take his 8 major-suit tricks if he relies twice on Restricted Choice. A heart to the king, followed by the 10 covered (East's best play here), drops the 9. Now, the AK drop East's 10. A low spade goes to the 9. After the Q, a low heart is led to finesse the 7. Pretty fancy footwork and use of those spot cards.

Remember the question about spades first or hearts first? If you played spades first and then laid down the K and 10 covered, there would be no way back to dummy to finesse to the 7. If declarer did play spades first, he could recover by starting hearts with the 10 (without cashing the king first, possibly losing to a singleton queen with West).

This month's deal was really for the mathematicians and Restricted Choice fans out there, which is why I named it RC squared.