I met Charles Snead Houston, who lead the first two American attempts on K2 and became a doctor. (He fell the furthest in "The Belay", the most famous belay in mountaineering history.)

He asked me to explain my work on card shuffling, so we traded. He taught me about altitude sickness, for which he was the foremost expert. I then read his books before my own mountaineering, and his advice worked for me.

In a nutshell, where you sleep matters. 7,000' is free, and a conservative pace is to sleep 1,000' feet higher each night. (Good luck finding a Kilimanjaro ascent that climbs that slowly, but have you met anyone who was comfortable at the summit?)

My wife's brother lives at 10,000'. As it happens the last hotel is at 8,500'. One night does the trick for her.