Nice calculation.
The average multiplier is a little bit higher 1.9375 if you play a lot of rounds ( http://forum.c-rpg.net/index.php/topic,2394.msg40222.html#msg40222 )
But that does not help a lot... so chadz succeded in making retirement much harder.
Read it through and about the first part:
It doesn't end at X5, you want to be staying at X5. Every round there after you have 50% chance to stay at X5 or drop back to 1.
I did it to 7 levels of prob before.
Here's the first 5, to show you what I mean.
1
2 1
3 1 2 1
4 1 2 1 3 1 2 1
5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
Level avg and total avg as per each level:
1. 1, 1
2. 1.5, 1.333
3. 1.75, 1.5714
4. 1.875, 1.7333
5. 1.9375, 1.8387
6. 1.83870968, 1.83870484
7. 1.85245902, 1.84552602
8. 1.84166667, 1.84362017
As you can see, he's right up until the 5th line, but he's wrong about it staying at 1.9375x.
1.84x is starting to look pretty good, though.
Anyway, later on he describes the effects of win streaks on the average multiplier. It increases it a bit, so I have to agree, it's closer to 2 and I think it's safe to take 1.94 for the equation.
Redoing the math with 1.94 you end up with roughly 52 hours on average to get from 1 to 31 with the max possible gen bonus.