Double Russian roulette

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Here is a puzzle similar to one that was on Car Talk.

Puzzle

As often happens to time traveling spies, you have been captured by the Cold War era Russians. They have decided to release you, but only if you survive their game of Russian roulette: they load bullets into the first and second chambers of an old six-shooter revolver. The other four chambers are empty. They spin the wheel and take a shot. You hear a click. But you are not out of the woods yet, as you must pull the trigger one more time. However, your captors offer you a choice: you can either pull the trigger right now, or spin the wheel first. What should you do?

References

Car Talk Puzzler - sometimes automotive, sometimes more math/logic based.