I’m not sure what you mean by it. Law of large numbers is just a fact from probability theory, it doesn’t require utility functions or betting.
I meant that the law is just a statement about probability, not about simulations confirming it. To conclude anything from simulations or any observations you need something more than just probability theory.
For now, it’s suffice to say that we can easily talk about different probabilities for Heads: on average awakening and on average experiment
Or on average odd awakening, if you only value half your days. Or on whatever awakening you need to define to minimize product of squared errors. I feel like the question confused people want answered is more like “can you get new knowledge about coin by awakening?”. But ok, looking forward to your next posts.
I meant that the law is just a statement about probability, not about simulations confirming it. To conclude anything from simulations or any observations you need something more than just probability theory.
Or on average odd awakening, if you only value half your days. Or on whatever awakening you need to define to minimize product of squared errors. I feel like the question confused people want answered is more like “can you get new knowledge about coin by awakening?”. But ok, looking forward to your next posts.