I choose Box B.
This is because taking into account that Omega is a superintelligence with a success rate of 100% and no margin of error and is the one offering the problem to me. The only logical reason for this is an ability to predict variables that I have no current understanding of. This is either through an ability to analyze my psyche and see my tendency to trust in things with 100% success rates, the ability to foresee in time my decision, or the ability for Omega to affect things backwards in time. Omega has not provided any reasoning for its 100% success rate, so these are the three logical things that I see. If you would argue to take both in the instance of the assumption that Omega has no extraordinary powers with time, and so the decision is already made, I think this is actually the irrational stance. Reasoning from a standpoint that doesn't consider the past facts is actually irrational. I would take Box B, because even if that assumption that he's guessed wrong is correct, and I take both boxes and get both sets of money, then I'm really not that much better off than if I took Box B. To me, the irrational decision is to take both boxes, if the probability is as follows: if I take Box B, I presumably have a 100% probability of 1,000,000 dollars. If I take both boxes, I have a 50% chance of 1,000 dollars and 50% chance of 1,001,000 dollars. Taking both is therefore not the logical choice, as 1,001,000 dollars versus 1,000,000 dollars is not worth the 50% chance of reducing my payout to 1,000 dollars. If you would put this into perspective in Prisoner's Dilemma in game theory, and put this decision in front of me 10 times, the outcome and my decisions become a lot clearer. Let's say that Omega has the ability to guess wrong. If every 10 times I take both boxes, there is a 50% chance of the money being in Box B, then numerically I lose versus if I choose Box B every time, even if Omega has the ability to be wrong and therefore it's not in there one of the times. However, one time out of ten would be the most logical error rate to assume, if any, coming from the fact that if he's been correct 100/100 times, and if he would be wrong with me, then he's been correct 100/101 times, in which failure rate out of 10 chances really only has the possibility of being either 0/10 or 1/10. Therefore, by taking Box B 10 times, the minimum payout I receive is 9 million. If I take both all 10 times, then the most payout I can really hope to achieve is 1 million and ten thousand. If Omega had a failure rate of even 5%, then that would definitely effect my decision, but as it stands, the only logical choice is choosing only Box B. Furthermore, if I only take Box B, and he's wrong and it's empty, then I believe Omega would be curious enough in its failure to reward me with the million dollars afterwards. Furthermore, the 1,000 dollars outcome is simply not enough money to me to "need it" in a way that makes it so I have to play safe.
I choose Box B. This is because taking into account that Omega is a superintelligence with a success rate of 100% and no margin of error and is the one offering the problem to me. The only logical reason for this is an ability to predict variables that I have no current understanding of. This is either through an ability to analyze my psyche and see my tendency to trust in things with 100% success rates, the ability to foresee in time my decision, or the ability for Omega to affect things backwards in time. Omega has not provided any reasoning for its 100% success rate, so these are the three logical things that I see. If you would argue to take both in the instance of the assumption that Omega has no extraordinary powers with time, and so the decision is already made, I think this is actually the irrational stance. Reasoning from a standpoint that doesn't consider the past facts is actually irrational. I would take Box B, because even if that assumption that he's guessed wrong is correct, and I take both boxes and get both sets of money, then I'm really not that much better off than if I took Box B. To me, the irrational decision is to take both boxes, if the probability is as follows: if I take Box B, I presumably have a 100% probability of 1,000,000 dollars. If I take both boxes, I have a 50% chance of 1,000 dollars and 50% chance of 1,001,000 dollars. Taking both is therefore not the logical choice, as 1,001,000 dollars versus 1,000,000 dollars is not worth the 50% chance of reducing my payout to 1,000 dollars. If you would put this into perspective in Prisoner's Dilemma in game theory, and put this decision in front of me 10 times, the outcome and my decisions become a lot clearer. Let's say that Omega has the ability to guess wrong. If every 10 times I take both boxes, there is a 50% chance of the money being in Box B, then numerically I lose versus if I choose Box B every time, even if Omega has the ability to be wrong and therefore it's not in there one of the times. However, one time out of ten would be the most logical error rate to assume, if any, coming from the fact that if he's been correct 100/100 times, and if he would be wrong with me, then he's been correct 100/101 times, in which failure rate out of 10 chances really only has the possibility of being either 0/10 or 1/10. Therefore, by taking Box B 10 times, the minimum payout I receive is 9 million. If I take both all 10 times, then the most payout I can really hope to achieve is 1 million and ten thousand. If Omega had a failure rate of even 5%, then that would definitely effect my decision, but as it stands, the only logical choice is choosing only Box B. Furthermore, if I only take Box B, and he's wrong and it's empty, then I believe Omega would be curious enough in its failure to reward me with the million dollars afterwards. Furthermore, the 1,000 dollars outcome is simply not enough money to me to "need it" in a way that makes it so I have to play safe.