You have not cheated Omega, you have just changed the terms of the problem so that it suits you better. Probabilistic Newcombs are a totally different beast: if we introduce uncertainty in our behaviour, then one must consider also uncertainty in Omega outcomes, for example saying that Omega puts a million in the box 75% of the times that it predicts that you’ll choose only box A 75% of the times.
You have not cheated Omega, you have just changed the terms of the problem so that it suits you better. Probabilistic Newcombs are a totally different beast: if we introduce uncertainty in our behaviour, then one must consider also uncertainty in Omega outcomes, for example saying that Omega puts a million in the box 75% of the times that it predicts that you’ll choose only box A 75% of the times.
Then to maximize expected value, we should one-box 50% of the time for an expected 250k.