Rule of restricted coice and the quack
#1
Posted 2011-April-28, 07:59
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?
#2
Posted 2011-April-28, 10:55
- hrothgar
#3
Posted 2011-April-28, 11:32
Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mstr-mnding) tr. v. - Any bid made by bridge player with which partner disagrees.
"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"
"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
#4
Posted 2011-April-28, 12:26
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...
#5
Posted 2011-April-28, 15:34
akhare, on 2011-April-28, 12:26, said:
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".
#6
Posted 2011-April-28, 16:54
#7
Posted 2011-April-28, 16:58
With ten of them, I occasionally get it right.
#8
Posted 2011-April-28, 17:33
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.
#10
Posted 2011-April-28, 18:40
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.
Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mstr-mnding) tr. v. - Any bid made by bridge player with which partner disagrees.
"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"
"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
#11
Posted 2011-April-28, 18:51
rogerclee, on 2011-April-28, 17:34, said:
thanks...was feeble attempt at humor.
#12
Posted 2011-April-28, 20:16
1eyedjack, on 2011-April-28, 18:40, said:
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.
#13
Posted 2011-April-29, 01:04
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
#14
Posted 2011-April-29, 01:23
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.
#15
Posted 2011-April-29, 01:50
gnasher, on 2011-April-29, 01:04, said:
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.
#16
Posted 2011-April-29, 03:18
(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.
#17
Posted 2011-April-29, 09:56
www.longbeachbridge.com
#18
Posted 2011-April-29, 11:55
rduran1216, on 2011-April-29, 09:56, said:
What does "it works" mean? They play restricted choice? Well done!
#19
Posted 2011-April-29, 13:16
#20
Posted 2011-April-29, 14:38
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.