I think I have a decent solution for this interesting paradox.
First, imagine a bit of a revised scenario. Instead of waiting until you finish the bet, the demon first creates a universe and then adds people to it. In this case, I would claim the optimal strategy is betting forever.
I think the intuition here is similar to the quantum immortality thought experiment. In most universes, you will end up with 0 people created. Still, there will be one universe with infinitesimal probability where you will never get three sixes. You and the demon will forever sit throwing the dice while countless people will be living happily in this universe. And in terms of EV, it will beat stopping at any point.
But in the original formulation, this strategy has an EV of 0 - and that’s not due to weaseling out, but because the only condition that will create a universe with any amount of people is when you stop betting, and this will only happen after you get three sixes. So the 0 EV is a trivial conclusion in this case.
The way out of this trap is to add a random stopping mechanism. Before every throw of the dice, you will roll a random number generator, and if you hit a very specific number (The odds to hit it will be infinitesimal, e.g., 1/(9^^^9)), you will stop betting. To maximize EV, you should use the lowest probability to stop you can practically generate while making sure it’s > 0.
Wouldn’t the EV be 0?
My reasoning:
- The condition for the universe to be created is when you stop betting.
- Under this strategy, the only way where you stop betting is when you get three sixes.
So there is no plausible scenario where any amount of QALY is being created. Am I missing something?