I had to restart on a new world because I was being farmed while I was on hiatus and all my troops were gone. Rather than trying to defend myself and waste time building up troops I decided it would be better to just start fresh since I wasted pearls on pretty much useless things. By the way save your pearls for high star gods. It'll be more worth your time that way.
Anyway while I was trying to farm the cave I realized that the math from the Mystic Cave Part 2: The Math was slightly off. When I was taught that math it hadn't accounted for the fact that you didn't have any upgrades to your soldiers. The math does start to work better at later games but early game is when you really feel tight on money. So I think you should multiply by 2.5 instead of 2 for the power of the needed attackers and that's what you should be using to attack so you don't lose any troops to be sure. At least during early game.