Random Magic Paths - is it truly random?

[Ivan Pedroso]

BigDaddy said:
Thats funny because i'm not bone daddy and Ivan's posts where nerdier. No offense intended Ivan.

Hehehe none taken

"20 sages in a row with exactly 1 path missing":
(7/8)^20 *8 = 0.554

Explanation:
the (7/8) is the chance of getting one of the 7 "good" paths when you hire a sage.
^20 is just 20 such sages in a row.
*8 stems from the fact that you can choose your pool of 7 "good" paths from the 8 possible paths in 8 different ways.

General formula:
(chance of one good)^(number in a row) * (ways to make a good pool)

Getting 20 in a row with exactly 2 paths missing:
(6/8)^20 * 28 = 0.0888
(28=(8!)/(6!2!) is the number of ways of taking 6 from a sample of 8)

Getting 20 in a row with 1 or more paths missing:
~65%

Surprisingly high ? or ?