Is it safe to say those optimizations are performed ad hoc? That is, you're manually in control of the optimization process instead of wiring it up to some kind of automation?
Yes! In particular, it is usually to create some concrete data/parameters to be used towards creating the final product.
In the usual Excel Solver case, for a simplified example, I want to create a biased coin where getting heads doubles your money and tails loses your money, with expected payout 90% in the long run. The parameters to change are heads/tails coin weighting, to target a value 90%. A fair coin gives a long run payout of 100%. It turns out that if a biased coin hits heads 45% of the time and tails 55% of the time, we end up with this 90% payout. Excel solver can come up with these two values.
In this example, we can come up with these 45% and 55% values theoretically. With more complex systems, we may want to see the effects of changing a subset of parameters that have an indirect effect on payout.
For example, if we extend the “biased coin game” to instead be “win your money back, 2, or 3 times your wager each with some probability” on a heads result, there are more parameters (and many solutions!) to get to 90% payout. Changing the heads probability has a further, second-order effect on the payout. Using Excel solver it’s straightforward to fix some parameters (heads/tails probability) and allow others to change (1x/2x/3x odds) to get desired results (90% payout).
If we further extend this methodology for a biased coin game, we can end up with a coin game that pays with distribution exactly like a slot machine in a casino, though it would not look like one!
