Mild dissent, or at least a caveat. If your distribution is already consumer, an existing audience or a community you are part of, then 200 hobbyists may be reachable next month while twenty businesses might take a year of cold outreach you have no time for. The best price is partly a function of the door you can already open.
Statistically that is the normal outcome rather than bad luck, which is exactly the argument for buffers.
If your country offers an expedited service, price it out now rather than in week eight when it becomes an emergency. It is usually a modest fee compared with rebooking a whole trip.
Also worth checking whether that programme has decent short haul or partner redemptions you would not have considered. Sixty thousand miles sitting in an unloved account has sometimes turned into three domestic hops for me that I would otherwise have paid cash for.
Follow up. One short follow up four days later, then one more a week after that, then stop. My replies roughly doubled from the second email alone and nobody has ever been annoyed by two polite messages.
If none of that works, long distance coaches on major intercity routes are usually bookable much later, cost less, and take maybe 60 to 90 percent longer. Not glamorous, but it keeps your fixed hotel date intact and you can sleep on it.
So the 1 is arbitrary? Could I have used 1/2 and gotten a different bound?
The two documents framing is what I was missing. I kept trying to derive it in the proof itself and getting tangled.
That was my grandmother's advice and I did not want to argue with her, but I am glad I asked here first.
The always choose local currency thing is not something anyone told me and it sounds like the sort of trap I would have walked into every single day.