Linda Lee — My personal bridge blog

Do you “believe” in Restricted Choice?

On Wednesday, against my advice Ray, whose turn it was to teach the intermediate class, decided to teach them “restricted choice”. This is based on the “Monty Hall” principle from Let’s Make A Deal.  The contestant gets to pick one of three doors (A, B, or C). Only one has a prize.

 Let’s call the door selected by the contestant Door A.

Monty then reveals one of the doors which will always be a loser (he can’t reveal the prize door or the game would end).  Say he picks Door B.

Now the contestant must is given a chance to switch doors. He can hold onto Door A or switch to Door B. What should he do? 

Restricted choice says its 2 to 1 to switch.

In the beginning each door has a 1 in 3 chance of being right. So the contestants Door A is 1 in 3 and Monty’s 2 Doors B and C are have 2 in 3 chance of bring the prize. When Monty removes a loser that whole 2 in 3 chance is invested in that remaining door/

And in theory this applies in certain situations in bridge. The most common one used is this one:

You are missing five cards including the Q and J in a suit.  You have a holding like say, A1084 opposite K972. You lay down one of your top honors, say the king planning to lead towards the ace-ten combination. The offiside hand drops the queen. Do you finesse through the A108 or do you play for the drop.

Theoretically it is twice as good to play for the finesse (in the absence of other significant information) because if the offside hand held the Queen and the Jack they could drop either. And theoretically even if they ALWAYS drop the queen from queen-jack doubleton you should finesse when they drop the queen. (Of course you would comfortably finesse if they dropped the jack since our predictable opponent would never have the queen).

I know most of you know this – but do you really believe it in your heart? I am not sure I do especially in the case where they would always drop the queen. Is this really the SAME as the Monty Hall Principle?

I think he probably bewildered most of the students. My friend who has a mathematical bent was still thinking about it the next day.

Okay, okay as the Monkees used to say “I’m a Believer” (I think). 

If you’d like to read a great response on Restricted Choice check out Bob MacKinnon’s post  Restricted Choice: What Lies Behind It on


ray leeFebruary 8th, 2013 at 10:39 pm

Bob MacKinnon discussed this (including the ‘always drops the Q’ case) in ‘Bridge, Probability and Information’. He also gives a fascinating account of the media circus that surrounded the game show when various mathematicians started writing about the correct strategy.

Bill CubleyFebruary 11th, 2013 at 6:13 pm

Also as the Monkees sang – “Not a trace of doubt in my mind”

Made a grand slam when one opponent had shown she always plays queen from QJ doubleton. The other opponent mentioned that declarer bravely ignored restricted choice when she dropped the jack. We never corrected him.

Alsa, we lost that GNT distict final by one IMP. It was the flight B. But our unit won Flights A and C that year. Flight A had Hugh Ross so that was an expected result.

David GoldfarbFebruary 21st, 2013 at 5:10 am

I commented on this earlier, but my comment somehow was deleted or not posted:

The example given above here is incorrect. The restricted-choice finesse is a two to one favorite when missing FOUR cards, not five. With five out, it’s true that Restricted Choice applies, but since a 3-2 split is about twice as frequent as a 4-1 split, that counterbalancing factor makes the finesse versus the drop very close to even money.

lindaFebruary 21st, 2013 at 1:50 pm

Thanks David. Your comment is interesting. But aren’t there really only two cases relevant assuming rationale play.

In the example you cash the King and the offside hand drops the jack. Now I think we can assume that LHO does not do this with JX. So at this point he can only have either a singleton jack or the QJ. If he had a singleton jack he would have to play it while if he had the QJ he could have played either the Q or J.

Am I wrong?

[…] This blog is in response to Linda Lee’s post Do you “believe” in Restricted Choice? […]

Alvin P. BluthmanMarch 2nd, 2013 at 5:08 pm

Mrs. Lee:

Restricted Choice is a valid mathematical concept. But I write on a different aspect of the matter, to point out the error Marilyn vos Savant made in her Parade magazine article, which first discussed the advantage of switching doors (on which the public wrote in expressing disbelief), and which prompted repeating the same error on the rules of Lets Make a Deal, which has been stated numerous times since.

The actual rules are the final round differ from Ms. vos Savant’s version. In fact, when the New York Times interviewed Monty Hall about this question, he pointed out that on the actual show, contestants are never permtited to switch doors. Rather, in developing the show, he and Stefan Hatos rejected door switching because of the advantages it would offer to the contestant; and then as host he (and subsequent hosts) have not allowed it. What actuallty happens is that the host offers the guest a cash settlement to end the game; and the contestant takes either the cash offer or what is behind the selected door.

Alvin P. Bluthman

John WoodMarch 31st, 2013 at 11:41 pm

I expect that most Bridge players know and believe in restricted choice – but don’t always appreciate when it applies and when it does not.

Apologies if teaching granny to suck eggs, but suppose you have

KQ2 opposite A9863

You cash the King (or Queen) in dummy and the person on your right plays the Jack.

Do you run the 9 next time, based on restricted choice (if they had had the 10 they might have played it)?

The answer is (probably) no! Although the person would have been restricted if they had had a singleton honour they might easily have held J,10,X and thus weren’t restricted at all in their play.

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