Dice probability, Heaven or Hell

Question

You're at the gate of Heaven and St. Peter asks you to play Dice with him. If you roll a 5 or 6, he'll let you into Heaven. However, if you roll a 2,3 or 4, you'll be sent to hell. If you roll a 1, he will let you re-roll. What is the chance of you entering Heaven?

Answer 1

I'm gonna play the devil here an give you a torturous hint.

You could avoid me if

1. You roll a 5 or 6 in the first roll, with chance $p_1 = 2/6$.
2. Or land a reroll on the first and then get a 5 or 6 on the second roll, with chance $$p_2 = \frac{1}{6}\cdot\frac{2}{6}.$$
3. Or you land a reroll twice and then 5 or 6 with chance what?

Can you take it from here?

Bwahaha!

Answer 2

We can ignore occurrence of 1 as they just reset the gamble.   So of the results that matter $3$ are bad and $2$ are good.

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Then there's the theological question on whether Saint Peter would actually allow you to gamble on salvation or damnation with such odds, or whether perchance it is either a test or a trick?