Well, Omega doesn’t know which way the coin landed, but it does know that my policy is to choose a if the coin landed heads and b if the coin landed tails. I agree that the situation is different, because Omega’s state of knowledge is different, and that stops money pumping.
It’s just interesting that breaking the independence axiom does not lead to money pumping in this case. What if it doesn’t lead to money pumping in other cases too?
Well, Omega doesn’t know which way the coin landed, but it does know that my policy is to choose a if the coin landed heads and b if the coin landed tails. I agree that the situation is different, because Omega’s state of knowledge is different, and that stops money pumping.
It’s just interesting that breaking the independence axiom does not lead to money pumping in this case. What if it doesn’t lead to money pumping in other cases too?