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Cake day: July 4th, 2023

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  • Depending on the specific game itself, we can boil down the multiple-stat problem in a few ways. If the goal is to get all the stats as high as possible evenly, then we can assign each stat a multiplier based on how low it is. Fixing lower stats becomes worth more than buffing higher stats. That multiplier would depend on the game, on how much it punishes the low stat. The multiplier itself might end up being a whole new problem to solve, but for now I’ll just say its not my problem and call it X.

    Whatever X is though, every stat can then be reduced to a single value using it. Super-low fortitude should be buffed over already-high mana according to X, so all of the numerical values in the game become directly comparable at any stage in this problem. Then I expect it will be equivalent to the knapsack problem. Each item in the game will boost several stats in certain ways, and all of those boosts can be combined using X to become our item value in the knapsack problem.

    So I consider it to be the knapsack problem + figuring out X (which might be NP-complete on its own, depending on the game).