I have been playing for a bout a year now and have been lucky enough to get 3 HOM. Margaret, Seshat, and Tellie. I have seen players with 3 of the same HOM.
Is it truly luck? or is it $$$$$? or is it up up, down down, left right, left right,…?
Love this game and am just getting into this forum now!
It’s a combination on all of the above in varying degrees. Some don’t spend much or at all with far greater luck while others spend a 
ton with lousy luck but get similar results.
It is a lottery as most aspects of this game. You do summons and depend on Random Number Generation. It might happen that your computer would conjure you 3 HOTMs in one 10x summon or you might spend considerable money for 5 10x summons and get no HOTM as all.
In a long run it all fits declared odds, but in a short term it can all be called luck.