I feel like if Bob has enough money, he ought to just be able to raise the stakes if he has enough money. In your example, if Alice is 50% sure, then she will never bet more than a quarter of her money, regardless of how certain and rich Bob is.
Even if I do have to let Bob go down a little, I still feel like it could be worth it. I don’t know before-hand if I’m going to be Alice or Bob, so it’s automatically fair. I want to maximize the sum of their expected profits.
I feel like if Bob has enough money, he ought to just be able to raise the stakes if he has enough money. In your example, if Alice is 50% sure, then she will never bet more than a quarter of her money, regardless of how certain and rich Bob is.
Even if I do have to let Bob go down a little, I still feel like it could be worth it. I don’t know before-hand if I’m going to be Alice or Bob, so it’s automatically fair. I want to maximize the sum of their expected profits.