You are right that the presence or absence of alien civilisations (especially those that expand to settle very large regions) can change things. I didn’t address this explicitly because (1) I think it is more likely that we are alone in the affectable universe, and (2) there are many different possible dynamics for multiple interacting civilisations and it is not clear what is the best model. But it is still quite a plausible possibility and some of the possible dynamics are likely enough and simple enough that they are worth analysing.
I’m not sure about the details of your calculation, but have thought a bit about it in terms of Jay Olson’s model of cosmological expanding civilisations (which is roughly how Anders and I think of it, and similar to model Hanson et al independently came up with). On this model, if civilisations expand at a constant fraction of c (which we can call f), the average distance between independently arising civilisations is D light years, and civilisations permanently hold all locations they reach first, then delaying by 1 year loses roughly 3f/D of the resources they could have reached. So if D were 1 billion light years, and f were close to 1, then a year’s delay would lose roughly 1 part in 300 million of the resources. So on my calculation, it would need to be an average distance of about 3 million light years or less, to get the fraction lost down to 1 part in 1 million. And at that point, the arrangement of galaxies makes a big difference. But this was off-the-cuff and I could be overlooking something.
>Aliens
You are right that the presence or absence of alien civilisations (especially those that expand to settle very large regions) can change things. I didn’t address this explicitly because (1) I think it is more likely that we are alone in the affectable universe, and (2) there are many different possible dynamics for multiple interacting civilisations and it is not clear what is the best model. But it is still quite a plausible possibility and some of the possible dynamics are likely enough and simple enough that they are worth analysing.
I’m not sure about the details of your calculation, but have thought a bit about it in terms of Jay Olson’s model of cosmological expanding civilisations (which is roughly how Anders and I think of it, and similar to model Hanson et al independently came up with). On this model, if civilisations expand at a constant fraction of c (which we can call f), the average distance between independently arising civilisations is D light years, and civilisations permanently hold all locations they reach first, then delaying by 1 year loses roughly 3f/D of the resources they could have reached. So if D were 1 billion light years, and f were close to 1, then a year’s delay would lose roughly 1 part in 300 million of the resources. So on my calculation, it would need to be an average distance of about 3 million light years or less, to get the fraction lost down to 1 part in 1 million. And at that point, the arrangement of galaxies makes a big difference. But this was off-the-cuff and I could be overlooking something.