Quote Originally Posted by Slashley View Post
Assuming that the 20x Rate is true, then coin-flip chance on Thanatos specifically is 1200 dollars. And remember, that's a COIN CLIP. You can lose a coin flip multiple times. Even at 3600 dollars, your chances are not 100%.
Where are you getting $1200? My calculations yield $990 as an upper bound for a 20x rate. Only when I do the calculation with a 15x rate does the cost reach $1136.

There are 8 * 8 +3 = 67 SSR kamihime in the pool. There are two ways to interpret 20x; either the typical rate has been amplified to be 20x, or the hime is weighted to over 20x what she normally would be. The latter is obviously the less favorable interpretation. With the outdated assumption that himes and eidolons are weighted 1:1 (with the gacha rates thread suggesting otherwise), we obtain:

Amplified by 20x: (0.03/2) * 20/67
Weighted by 20x: (0.03/2) * 20/143

(1 - rate)^N = 0.5 --------> N = log(0.5) / log(1 - rate)

Amplified by 20x: N = 153.456 ---> $460.37
Weighted by 20x: N = 330.053 ---> $990.16

The cost lowers to $385.97 and $824.96 respectively if we weigh kamihimes to take 0.6 of the SSR pool instead of 0.5.