The other day, Sue and I went to the movies to see "21" - the movie about MIT students who systemically beat the odds in Las Vegas.

 

There was a scene where they discussed what they called "variable change." Mickey, the mathematics professor, gave Ben, the student protagonist, a hypothetical problem.

 

A contestant on a game show is offered his choice of three doors: Door 1, Door 2 or Door 3. Behind one of the doors is a sportscar. Behind the other two doors are goats and he is asked to pick a door at random. The contestant chooses Door 1. The host then opens Door 3 and reveals that it has a goat in it. He then asks if he wants to keep his initial choice of Door 1, or switch to Door 2.

Ben explained that it would double his chances of winning if he switched doors.

 

I whispered to Sue, "I didn't realize I was going to get a bridge lesson today at the movies." She wondered what I meant and I told her they just explained the bridge theory of restricted choice, which is based on conditional probability.

 

Restricted choice is a rule influencing the play of certain card combinations, first discussed by the Alan Truscott and later developed and named by Terence Reese in his book The Expert Game.

 

A classic example of restricted choice is:

How do you play this suit for no losers? You plan to cash the Ace and King and hope for a 2-2 split. But when you cash the Ace, your right-hand opponent  follows wih the Jack (or Queen). Do you lead to the King as planned, playing RHO for QJ doubleton or do you now finesse the 10, playing him for a singleton honor?

 

Surprisingly, the answer is that the odds are 2:1 to finesse. For a more comprehensive explanation of the theory of restricted choice, see: restricted choice.

 

So, it appears that if you want to learn more about our favorite game, all you have to do is go to more movies!

 

Best of luck to those of you playing at the Bahia Mar tournament. I hope you win bushels of gold points!

 

Cheers,