Barry Crane’s Kxx Rule–Assessment

Original Example 1:  Missing K 7 2. You lead the Q and second hand plays the 7.

Barry’s rule says to play small from Dummy. Is the rule right here? What justification is there for the finesse?

Example 1 [LHO plays 7] Assesment-–
If East/West are novice defenders then by Patrick’s principle of novice defenders, the 7 is LHO’s smallest card in this suit, i.e. RHO has the 2. This means that the drop cannot succeed. Finesse this suit.
Against expert defenders the rule of restricted choice halves some apriori relative probabilities. The three relevant distributions are
LHO     RHO      %        wins
K 7 2     —         5.5%   finesse
K 7        2          13%    finesse
7 2        K          6.5%    drop
For the first two, the finesse succeeds and for the third, the drop succeeds. Thus the finesse is more likely to succeed. Barry’s rule is correct for example 1. [The other distribution, LHO holding singleton 7, loses a trick to RHO’s K regardless of what we do.]

Original Example 2:  Missing K 7 2. You lead the Q and second hand plays the 2.

Barry’s rule says to play the ace. Is the rule right here? What justification is there for the drop?

Example 2 [LHO plays 2] Assesment-–
Applying the same novice/expert analysis as in example 1:
LHO     RHO     novice   expert   wins
K 7 2     —         11%       5.5%     finesse
K 2        7          13%       13%      finesse
7 2        K          13%       6.5%     drop
The finesse appears to be better here, contrary to Barry’s rule.

To help Barry out, I am going to posit that some of the time LHO covers the Q with the K. Let that fraction be x. Now our revised table is
LHO     RHO     novice            expert          wins
K 7 2     —         (1-x)11%       (1-x)5.5%     finesse
K 2        7          (1-x)13%       (1-x)13%      finesse
7 2        K          13%                6.5%             drop
After a little algebra we see that Barry needs x to be greater than 46% for novices and 65% for experts. The problem with x > 65% is that makes Barry wrong about example 1!
Another consideration is that if Barry is right, then an expert LHO holding doubleton 7 2 would play the 7 not the 2 causing you to take a losing finesse (see example 1 above). So if Barry were right about his rule, then the drop would never work for him.

I conclude that Barry Crane’s Kxx rule is wrong. So who is right– Barry Crane (one of the greatest bridge players of all time) or Patrick the Idea Hamster?

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