For a month MTTH, after 30 days you get an expected value of 0.685200947
For a 25 year MTTH, after 25 years you get an expected value of 0.693120489
And so in all cases in EUIII, the expected value will equal 1 at 1.45*MTTH.
Technically not a constant, but for the purposes of EUIII it might as well be. (Just wanted to quantify the "hangs" in your "in practical cases hangs around .69 usually" bit.)
...
Wow. 4.32*MTTH for 95% probability of event happening at least once is a long time in the case of the great men.
And if you had 3 great men, you could just simply divide that 4.32 by 3 if I am understanding what is going on here correctly?
So you could say there is a 95% chance that one of those great men would fire at least once within (4.32/3=1.44) 1.44*MTTH?
Damn. So if Kanitatlan's Ming turbo AAR relies on great men is going to be something of a crapshoot
.
But when you drop it down to a 75% chance of one great man firing at least once it goes down to:
log(0.25) / log(0.5) = 2
And then (2 [75% chance of great man firing]/3 [total great men])*25 years [Great man MTTH] = 16.67 years.
Booooooo. Still much longer than I'd like.