Principle of restricted choice

[xx1943]

[hv=n=sak1098&w=s&e=s&s=s7654]399|300|[/hv]

 

You play the A and EAST produces the Q.

Next time you play the 7 and WEST contributes the 2.

 

Other things being equal (no hints from bidding or further play, or ... ) do you finesse or play for a drop.

 

Imo the finesse has a success of 65%, my regular partner always states it is 50/50.

 

What do you think about?

 

Regards

 

Al

[hotShot]

If WEST produces the 2 over the 7, you should call the TD because it's EAST's turn to play a card.

It would be nice to know what card West put into the first trick, and if East has a second card (J) over the 7.

[MickyB]

The Principle of Restricted Choice IS correct.

 

There are twice as many combinations where the finesse is correct (Q singleton, J singleton against QJ doubleton), however QJ doubleton is slightly more common than a singleton (12:11 by Empty Spaces - LHO has 11 other cards, RHO has 12 other cards) so it is more likely to be in LHO's hand by 22:12 = just under 65%.

[LH2650]

At the time you must make the decision, there are only 2 cases that must be considered - J32 opposite Q, and 32 opposite QJ. Originally, there were 8 cases of a 3-1 split, with a total a priori probability of 49.74%, and 6 cases of a 2-2 split, with a total probability of 40.70% (Encyclopedia of Bridge, Mathematical Tables). The relative probabilities for the two remaining cases hold. Therefore, the 2-2 split is more likely. However, RHOs best strategy is to randomly play the Q or J from the QJ doubleton. (If he always plays the Q, you are entitled to this information.) The probability of interest is that he held the QJ AND he played the Q. If he follows the optimum strategy, this is only half as likely as holding the QJ originally, so your best strategy is to play for the 3-1. It comes to about 64.7%. I remember reading an article by Jeff Rubens about what happens when he follows a non-optimum strategy, and would like to hear if anyone can identify it.

[han]

This is not a matter of opinion.

[Guest Jlall]

yep, this is math.

[Free]

This has nothing to do with thinking, it's just a fact, pure math.

[paulg]

Just for reference, a couple of articles on the subject:

 

ABCL District 13's explanation of Restricted Choice

 

The Rule of Restricted Choice from The Bridge Companion

[pclayton]

Interesting that we have two threads on bridge 'myths' - this and the Law of Symmetry.

 

I can't find my old Gold Book; I think Culbertson had a a mention about it in there.

[Flame]

Its not a question of being right, just a question of wather you understand why its right.

BUT i do think there is one thing that is sometime overlooked, its the distibution chances, restricted choice attack the problem of one suit only but in bridge we have 4 suits which must come up to 13 cards in each hand, so one suit effect the other suits too. In general if there are less cards left they will rate to be evenly distributed between the hands and that may effect the overall chances.