Eight Never, Nine Ever?

You have to play this combination (the trump suit) for no loss:

AKJ76
5432

The rule “eight never, nine ever” asks you to eschew the finesse against the queen holding nine cards in the suit. You surely know that the correct play is to cash Ace and King, hoping to fell the queen, rather than to finesse against the queen on the second round.

But do you know how close the percentages are? Say you cash Ace, then lead low toward the KJ, and LHO produces a low club. At this point, the correct guess will lead to no loss in the suit. The chances of LHO holding the queen are about 48 %, which makes the two lines so close that the correct conclusion is not “nine ever”, but “other considerations rule”.

Let me give you an example. Suppose you and dummy have 24 HCP between you, and you landed in this contract after East had passed as dealer. If you simulate this situation, giving you and dummy a total of any 24 HCP and making sure East does not have 12 or more HCP, you find that the chances of the finesse succeeding are now up to 51 %, making it the better line.

The constraint imposed on the opposing cards was very mild. Of the 16 outstanding HCP, RHO could not hold 12 or more (which limit is 4 more than his average of 8), and that was enough to tip the scales in West's favour. In actual play, there are countless factors that tip the scales by similar amounts.

Hugh Kelsey states in some book that one must not despise the 3 % margin because gambling houses have grown fat on margins much smaller. His idea is preposterous. Gambling houses have the same slim margin (never higher) every single time someone bets, and they do despise 0.01 % margins (e.g. the dirtying of cards leading to an imperfect shuffle). The bridge player is typically dealing with percentages much higher than that through the bidding and play. I don't blame Kelsey, however, because no doubt that was marketing for the 4-volume treatise he was planning, Miscellaneous Throw-In Squeezes Against Both Opponents Involving Three Suits without an Entry To the Hand with Two Menaces

[Update: I just realized that the rule goes “eight ever, nine never”. In other words, it seeks to answer the question, Should I finesse against the queen. The way I've used it, it answers the question, Should I play for the drop?]