So say it’s repeated. Since our observable universe will end someday, there will come a time when the probability of future flips is too low to justify paying if the coin lands tails. Your argument suggests you won’t pay, and by assumption Omega knows you won’t pay. But then on the previous trial you have no incentive to pay, since you can’t fool Omega about your future behavior. This makes it seem like non-payment propagates backward, and you miss out on the whole sequence.
I wouldn’t trust myself to accurately predict the odds of another repetition, so I don’t think it would unravel for me. But this comes back to my earlier point that you really need some external motivation, some precommitment, because “I want the 10K” loses its power as soon as the coin comes down tails.
So say it’s repeated. Since our observable universe will end someday, there will come a time when the probability of future flips is too low to justify paying if the coin lands tails. Your argument suggests you won’t pay, and by assumption Omega knows you won’t pay. But then on the previous trial you have no incentive to pay, since you can’t fool Omega about your future behavior. This makes it seem like non-payment propagates backward, and you miss out on the whole sequence.
I wouldn’t trust myself to accurately predict the odds of another repetition, so I don’t think it would unravel for me. But this comes back to my earlier point that you really need some external motivation, some precommitment, because “I want the 10K” loses its power as soon as the coin comes down tails.