There is no finite number of lives that reach utopia, for which I would accept Omega's bet at a 90% chance of extinction.
This does not mean I would accept Omega's bet at 89% chance of extinction (I wouldn't), but 90% is far above my ceiling, and I'm very sure of it.
Inspiration came from Against the Linear Utility Hypothesis and the Leverage Penalty
Place a value on the utility of a utopia with 1 human, let's call this X.
Place a value on the negutility of all of humanity going extinct. Let's call this Z.
Decide if your utility function is linear in number of lives saved.
Place a value on the utility of say humans achieving a perfect utopia. Call this K.
Omega offers you a bet. This bet has a 50% chance of humanity reaching a Kardashev type V civilisation (colonising the multiverse) and a perfect utopia, and a 50% chance of human extinction this instant.
Omega is an omnipotent entity that always tells the truth, you know (and believe this), etc.
Do you accept the bet?
What about 1:3 odds?
What about 3:1 odds?
What is the highest probability of extinction at which you would accept Omega's offer?
What does this say about your utility function?