If the deity is answering questions, you know it’s before the roll, so it’s clearly 1⁄36. The current size of the population (50% blue-eyed and 50% not-yet-determined) is irrelevant—this game has no upper bound, and past dice outcomes do not change the probability of future ones. This holds as well if you know that you’re in the most recent batch.
The conundrum is if you are a snake whose age is unknown who just doesn’t know their eye color yet. It’s 100% blue if the game is ongoing, and 50% if the game is ended, so the question is “what is the probability that the game has ended”. There’s no uncertainty about that to the deity—they know whether the game is ongoing or ended. There is definitely uncertainty to the player, and it will be resolved when they discover their own eye color.
In this case, I support SSA and would wager 50%. Note that this is a pretty specific setup, and doesn’t apply to even similar-sounding anthropic arguments.
If the deity is answering questions, you know it’s before the roll, so it’s clearly 1⁄36. The current size of the population (50% blue-eyed and 50% not-yet-determined) is irrelevant—this game has no upper bound, and past dice outcomes do not change the probability of future ones. This holds as well if you know that you’re in the most recent batch.
The conundrum is if you are a snake whose age is unknown who just doesn’t know their eye color yet. It’s 100% blue if the game is ongoing, and 50% if the game is ended, so the question is “what is the probability that the game has ended”. There’s no uncertainty about that to the deity—they know whether the game is ongoing or ended. There is definitely uncertainty to the player, and it will be resolved when they discover their own eye color.
In this case, I support SSA and would wager 50%. Note that this is a pretty specific setup, and doesn’t apply to even similar-sounding anthropic arguments.