Rule of restricted coice and the quack

[leswt]

I was reading and article on the rule of restricted choice and the nine card fit missing the QJ (quack) case was discussed.

 

The author talked about how the queen is played half the time and the jack half the time from a doubleton

 

Is this actually the case? Many experienced players play random but what is your experience as to the actual play of the general bridge population?

[han]

I think that most decent bridge players are able to play this one randomly enough. I wouldn't know which I or my partner plays more often.

[1eyedjack]

I remember calculating a while back that someone who (otherwise) consistently plays a specific card from that holding only has to deviate from that routine by more than one time in 12 for the odds to favour your finessing the second round, so you don't really have to approach pure randomness for the rule to work.

[akhare]

This is somewhat orthogonal, but are defenders with such holdings (stiff quack or QJ tight, etc.) required to consider potential tempo issues?

 

In a recent club game, I could have made a contract by not using restricted choice because there it appeared that there was a perceptible delay before RHO followed suit with a quack (A in the closed hand, KTXX on board, 9 card suit fit).

 

On the bidding, it was reasonable to use restricted choice (RHO took the 5 level sacrifice). However, I would have been rather peeved if I had decided to not use restricted choice because of RHO's perceived hesitation and RHO had a stiff.

 

My solution to the problem is to identify the quack I want to play in advance and put it at a pre-determined location in deck so that I can play in tempo and declarer can't tell whether it's a stiff or a two card holding...

[gnasher]

This is somewhat orthogonal, but are defenders with such holdings (stiff quack or QJ tight, etc.) required to consider potential tempo issues?

You're always required to consider tempo issues. To be precise, "players should particularly careful when variations [in tempo] may work to the benefit of their side".

[mycroft]

I play the one on the left. The way I sort my cards does the randomness for me (no, that does not mean "top to bottom in every suit", thanks)

[aguahombre]

My record is perfect, always losing to the doubleton quack.

 

With ten of them, I occasionally get it right.

[rogerclee]

It's irrelevant anyway.

 

Let's say you have AKTxx opp xxxx and cash a high one and they drop an honor, let's say the jack. Suppose from QJ that they play the J p% of the time, and that from stiff J they always play the J. The event that they have the J is P(J) and the event that they have the QJ is P(QJ).

 

Then for any p, we win when they have J and lose when they have QJ, so our win rate by finessing is:

 

P(J) / (P(J) + p * P(QJ))

 

If you substitute P(J) = P(QJ) = 1/2, which is basically right assuming we have no bidding inferences, then this gives us

 

1/(1+p) >= 0.5

 

So we will always do at least as well to hook no matter what p is.

 

In reality, the probabilities are about P(J) = 0.48 and P(QJ) = 0.52. If we substitute those values, we get that

 

0.48 / (0.48 + p * .52) > .5 if p < .923

 

So as long as you think they are randomizing more than 7.7% one way or another (everyone), you shouldn't worry about it.

 

Note that p = 0.5 gives the well known approx. "2-1" statistic, but it's a myth that it's actually necessary to randomize, since even if it was well known that you played the Q from QJ say 90% of the time, it's still to declarer's advantage to hook when you follow with the Q.

[rogerclee]

My record is perfect, always losing to the doubleton quack.

 

With ten of them, I occasionally get it right.

Really? There are many cases where you should not take a restricted choice finesse (like you have a complete count).

[1eyedjack]

I worked it out by a slightly different method. It came to roughly the same conclusion but the difference was slightly outside what I would expect to be explained by rounding differences:

In a vacuum, the a priori odds of a specific defender having a specific stiff honour is 6.22% to 3 sig fig. The odds of that defender having QJ tight is 6.78%. The ratio 6.22/6.78 is 0.917 which is 11/12 to 3 sig fig. Hence my conclusion that varying your habit by 1/12 is sufficient to justify the hook. This is slightly different from rogerclee's figure, but I expect my method is flawed.

[aguahombre]

Really? There are many cases where you should not take a restricted choice finesse (like you have a complete count).

thanks...was feeble attempt at humor.

[rogerclee]

I worked it out by a slightly different method. It came to roughly the same conclusion but the difference was slightly outside what I would expect to be explained by rounding differences:

In a vacuum, the a priori odds of a specific defender having a specific stiff honour is 6.22% to 3 sig fig. The odds of that defender having QJ tight is 6.78%. The ratio 6.22/6.78 is 0.917 which is 11/12 to 3 sig fig. Hence my conclusion that varying your habit by 1/12 is sufficient to justify the hook. This is slightly different from rogerclee's figure, but I expect my method is flawed.

Actually I erroneously used 0.5 in the inequality when it should really be compared to 0.52 (probability of QJ tight). Solving gives me .147 < p < .853 now.

 

I could be wrong, not that any of this is terribly relevant to the main point.

[gnasher]

Roger, your figures of 0.48 and 0.52 are incorrect. Those are respectively the probabilities that LHO has any combination containing both honours (QJ, QJx, QJxx), and any combination containing one honour (Q, J, Qx, Jx, Qxx, Jxx).

 

The chance of a specific singleton honour with LHO is

13/26 x 13/25 x 12/24 x 11/23 = 0.0622

 

And the chance of QJ doubleton with LHO is

13/26 x 12/25 x 13/24 x 12/23 = 0.0678

[JLOGIC]

Agree with clee that it doesnt matter. If someone always plays the same card, and you figured it out with a reasonable sample size (would take a lot of time), you could gain a very small edge. In practice, surely someone always plays the other honor 1 in 10 times or whatever it is.

 

People like to discuss whether random opps play the queen or jack more often but since there is little/no edge to be gained from figuring this out it is not that interesting to me personally.

[rogerclee]

Roger, your figures of 0.48 and 0.52 are incorrect. Those are respectively the probabilities that LHO has any combination containing both honours (QJ, QJx, QJxx), and any combination containing one honour (Q, J, Qx, Jx, Qxx, Jxx).

 

The chance of a specific singleton honour with LHO is

13/26 x 13/25 x 12/24 x 11/23 = 0.0622

 

And the chance of QJ doubleton with LHO is

13/26 x 12/25 x 13/24 x 12/23 = 0.0678

 

We are assuming it's either J or QJ, so their relative probabilities are 48-52. You could substitute .0622 and .0678 respectively and the answer would be the same, it's just a scaling issue.

[gnasher]

Sorry, I think I misunderstood how you got to the figures. I assumed you'd calculated

(13/26*13/25) / (13/26*13/25 + 13/26*12/25) = 0.52 (exactly)

 

but if what you actually did was

13/26*12/25*13/24*12/23 / (13/26*12/25*13/24*12/23 + 13/26*13/25*12/24*11/23) = 0.521739

and then rounded it to 0.52, then I agree.

[rduran1216]

I play the Q against bad players and the J against good players, works every time haha.

[JLOGIC]

I play the Q against bad players and the J against good players, works every time haha.

 

What does "it works" mean? They play restricted choice? Well done!

[cherdano]

Holding a singleton Q, no play is ever working for me :(

[AlexJonson]

I remember a long time ago finding the debate about restricted choice, really interesting.

 

But as several players here have said, it just doesn't matter.

 

In the normal world believe it,

it's only a short hand for the possible distributions, and if people are a bit routine and not random,

it doesn't matter enough, take the finesse.

 

If they are completely routine, take the finesse anyway, because maybe they changed since last week, and they are a bit less routine.

[rduran1216]

What does "it works" mean? They play restricted choice? Well done!

 

easy turbo, just highlighting that its had success playing this scheme. This is one of the few poker aspects of bridge. Also helps to not keep your cards in sight when playing since most hawks stare at where u play from.

[rogerclee]

easy turbo, just highlighting that its had success playing this scheme. This is one of the few poker aspects of bridge.

http://www.dailyhaggis.com/wp-content/uploads/2009/08/o_rly.jpg

[NickRW]

Is this actually the case? Many experienced players play random but what is your experience as to the actual play of the general bridge population?

 

 

To answer your actual question, which I am not sure anyone has really done, the general population (in my experience) play Q from QJ tight a lot. I wouldn't like to put a figure on it - but they think it is clever or something and do it a lot.

 

Nick

[CSGibson]

I play the Q against bad players and the J against good players, works every time haha.

 

I can just imagine the table questions to highlight this understanding... "In your experience, does your partner play any specific pattern from QJ tight"... "Have you ever discussed whether I'm a good or bad player?"...

[leswt]

Thanks for all of the great replies