# Given consumer grade hardware,what is a reasonable upper bound for size of search space?

There's a gacha RPG I'm trying to get better at.

I estimate there are about 10^15 states for the 3 opening rounds of a match for which I am trying to evaluate damage output.

The equations themselves aren't complicated: mostly linear ones, with the odd division and factorial with small integers (less then n=10) thrown in.

I'm trying to differentiate between "easy", "tough but doable if you know what you're doing" and "don't even think about it".

I suspect I'll have to simplify the problem further, but is there a way to know at which point brute force becomes unreasonable before committing to code? I only have access to consumer grade hardware (and google colab).

• A rule of thumb I have used in programming competitions is about 10^9 "simple" operations per second. This might give you some idea of what a reasonnable search space is, depending on how complicated it is to test a state and how much time you are willing to let the code run. – Tassle Jan 14 at 19:17
• – Yuval Filmus Jan 15 at 12:38