[Yu18772]

We all know that the "9 never" rule is secondary to having any reasonable hint in favor of the finesse. This is because with 9 cards a priori it is 52-48% for the drop which is pretty close. Thus, if one of the opponents is known to hold more points, or have shortness in other suit, finessing considered at least as good as the drop. However in "8 ever" the amount of information needed to tip the % in favor of the drop is obviously more, because the % difference is 50 vs 34 - yet it is obvious, for example, that if only one of the opponents holds all of the outstanding high cards finessing into him will not succeed, and you can only hope for the drop.

My question is if you dont have any particular information about distribution, but do have information about high card split (for example one opponent opened, and you are playing a 26 HCP game), what would be the minimum difference between the opponents to make playing for the drop a % line in 8 card fit? Assuming it has something to do with the form of these points - how many high cards can be potentially assigned to the weak hand that would make it worth finessing into the strong hand?
Yu

[Phil]

Y(o)u might find this interesting: The Majority Rule

[semeai]

Phil, on 2012-August-13, 09:38, said:

Y(o)u might find this interesting: The Majority Rule

An interesting read. I enjoy his articles.

The Majority Rule by Phillip Martin said:

When you have an eight-card fit missing the jack, if a partial count of the hand (e.g., a count in two other suits) suggests playing one opponent, say West, for jack-fourth, consider the implications of a four-one break on the lie of the unknown suit. When the four-one break would still leave West with a majority of cards in the unknown suit, finesse.

This is a pretty good rule but not completely general. It works when the total length in the unknown suit held by the opponents is 5 or 6, but fails in a way for boundary cases for total lengths 4 or 7, as well as for some more extreme lengths.

To be more precise with the exceptions:

If the unknown suit would be 2-2 when the 4-1 break occurs, then he says play for the drop. In fact, if you can play one top honor before committing to the finesse, it's slightly favored. [More extreme example: If the unknown suit would be 1-1 when the 4-1 occurs, then it's always correct to play for the finesse, even if you must commit on the first round.]

If the unknown suit would be 4-3 when the 4-1 break occurs, then he says finesse. This is correct if you can play one top honor before committing, but if you have to decide on round one you should play for the drop. [More extreme example: If the unknown suit would be 5-4 when the 4-1 occurs, then it's always correct to play for the drop, at least just doing the math (some of the cases for the drop involve 7 or 8 card suits).]

[semeai]

Yu18772, on 2012-August-13, 00:06, said:

My question is if you dont have any particular information about distribution, but do have information about high card split (for example one opponent opened, and you are playing a 26 HCP game), what would be the minimum difference between the opponents to make playing for the drop a % line in 8 card fit? Assuming it has something to do with the form of these points - how many high cards can be potentially assigned to the weak hand that would make it worth finessing into the strong hand?

To have a definite example, let's say we have 26 HCP and are missing A K K ♥Q J J, with the ♥Q being the card of interest.

Let's say East opened and has 12+ points, i.e. is missing ♥Q or J or JJ or nothing. Then there are 26-10 = 16 remaining non-heart non-high-cards.

Finesse:
Qxx-xx (6 ways) times ♥Q-AKKJJ (1 way) times 10-6 remaining cards (16 choose 6 ways)
Qxxx-x (4) times ♥Q-AKKJJ (1) times 9-7 remaining cards (16 choose 7)

Drop:
xxx-Qx (4) times -AKK♥QJJ (1) times 10-6 remaining cards (16 choose 6)
xxx-Qx (4) times J-AKK♥QJ (2) times 9-7 remaining cards (16 choose 7)
xxx-Qx (4) times JJ-AKK♥Q (1) times 8-8 remaining cards (16 choose 8)

We have 16 choose 6 < 16 choose 7 < 16 choose 8 (even split is most likely) so without even adding anything up we can see the drop is a winner. If you consider AKKQ♥Q as the missing high cards instead, though, you find that the finesse is still better.

[Yu18772]

Thank you

Yu