AClue to Puzzle #54: Two Bullet Russian Roulette

54. We are to play a version of Russian Roulette, the revolver is a standard six shooter but I will put two bullets in the gun in consecutive chambers. I spin the chambers, put the gun to my head pull the trigger and survive. I hand you the gun and give you a choice...
You may put the gun straight to your head and pull the trigger, or you may re-spin the gun before you do the same.

What is your choice and why? How does this differ from the case with only one bullet?
picture of a revolver containing two bullets for russian roulette If you have never thought about the analogous question with 1 bullet, (and why would you?) going through it now may help you work on the 2 bullet problem. The working below is also in the answer. . One bullet can be in 6 positions as shown.
1 B-----
2 -B----
3 --B---
4 ---B--
5 ----B-
6 -----B
Obviously you would, with a randomised gun, have a 1 in 6 chance of dying. However, if someone has just fired and survived then we have eliminated the first scenario, B-----, it definitely wasn't that. And we are on the second chamber. We have essentially reduced the game to the following (removing the first row, because it wasn't that, and the first column because that chamber has been fired.):
2 B----
3 -B---
4 --B--
5 ---B-
6 ----B
Which is just the same as a standard game of Russian Roulette if there were only 5 chambers in the gun. A 1 in 5 chance of dying is worse than a 1 in 6. So in the case of one bullet it would be in your interest to spin and re-randomise the gun.

If you apply the same technique to the 2 bullet problem I'm sure you will be OK.

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