Is the probability of dying in Anthropic Snake Eyes 1/36?

Question

Background: the Snake Eyes Paradox market.

The anthropic version of the Snake Eyes Paradox is like so:

Initially the universe is empty. God creates 1 person and rolls fair dice. If they come up snake eyes, God kills the person and the game ends. If they don't come up snake eyes, the person lives and God creates 2 new people and rolls the dice again. Once again, those people die on snake eyes and the game ends. This repeats as long as non-snake-eyes are rolled, with the group size doubling each time. As soon as snake eyes is rolled the latest group dies, and the game ends.

The question: Suppose God has created all the requisite people, rolled all the dice, and is about to kill the final group that eventually got snake eyes. You're one of those people, with no idea which group you were in or how many other people were created. What's your subjective probability that you'll be killed?

Argument for YES: No one ever dies except by fair dice roll. So your chances of dying are the chances of rolling snake eyes on your round: 1/36.

Argument for NO: Due to the doubling, the final group that dies is slightly bigger than all the surviving groups put together. So if you exist, you could be anyone and so you have about a 50% chance of dying.

Resolution criteria: I'll defer to Martin Randall's opinion unless I can articulate why I'm certain he's wrong. Since this could be subjective, I won't trade in this market.

FAQ

1. What if snake eyes is never rolled?

Eventually, with probability 1, snake eyes will be rolled but if hypothetically we rolled non-snake-eyes forever then an infinite number of people would be created and none would die.

2. What if the probability is undefined?

That's a no in this market. (I tragically failed to anticipate that possibility in the original snake eyes market, which caused lots of consternation!)

3. Should we use the self-sampling assumption (SSA) or the self-indication assumption (SIA)?

TBD -- please discuss in the comments if it's necessary to clarify this. So far SSA seems to me to miss the whole point of anthropic reasoning but let's discuss.

4. Is this different from the regular Snake Eyes Paradox?

I think so but the point of this market is to clarify that. In my interpretation of the original, there's a fixed pool (maybe an infinite one) of people, a subset of which is chosen to play. In this version you don't exist at all unless you're chosen to play. I meant the original to be as realistic as possible. This version is explicitly in philosophy-thought-experiment-fantasy-land. But, again, I'm hoping that understanding the differences between this version and the original will help pull us out of the rabbit hole (or push through it to come out the other end?).

5. Priors?

Uniform. And the dice are fair and i.i.d.

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Please ask other clarifying questions before trading! And huge thanks to everyone for all the work on resolving this paradox.

Manifold Markets · Answer

Unlikely — Manifold Markets prediction market estimates a 19% chance (24 traders, as of Feb 22, 2025).