Friday Puzzler -- Not Monty Hall

Alex Y
This may be a repeat, but my memory was not good enough to help on it, so I'll post, maybe again.

A game show offers the winning couple, Alan and Becky,
the grand prize, a chance to win a car. Behind three curtains are:
* a car
* the keys to the car
* a goat
Placement behind curtains 1, 2, and 3 is random, unknown to the contestants, and does not change during the course of the contest.

Becky will be taken offstage and kept in a sound-proof booth while Alan chooses two curtains to see what is behind them. He is then taken to another sound-proof booth, the curtains are closed, and Becky comes out. She also gets to open two curtains.

The couple wins the car if and only if the car is behind one of the curtains Alan picks and the keys are behind one of the curtains Becky picks.

Knowing how the game will work, Alan and Becky are given some time to come up with a strategy to pick doors to increase their chance of winning.

What is the best chance they have for winning, and what is their strategy?

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