So I'm thinking about what the best order to buy things is. I feel sure that a lot of research has been put into this problem (though the funded research has probably been for less-frivolous trappings), and I'm hoping that my friends (especially glenbarnett and bluelang) can help me navigate the theory.
So, to abstract the problem a bit:
- let's say that there's an abstraction called "winnitude". Team winnitude is a monotonically increasing (or at least nondecreasing) function of the winnitude of the players (and other factors like team experience and cohesion), and player win is a nondecreasing function of the winnitude of the gear (and skill and whatnot).
- My real goal is to increase the winnitude of the team as quickly as possible. For this problem, I'm trying to increase the winnitude of the team by increasing the winnitude of my gear.
- The rate of badge acquisition is more or less directly dependent on team winnitude. (In fact, that rate might be the metric of team winnitude.)
- Team winnitude, player winnitude, and gear winnitude all increase over time (gradually), even if I don't spend badges to increase my gear winnitude.
- Let us suppose that for each item I might buy, I know a) the cost in badges, b) the contribution in gear winnitude, and c) the chances that I'll get something of comparable winnitude as a drop.
How, then, should I choose which item to save toward next?
Some edge cases are obvious:
- I should never buy an item that doesn't increase my winnitude.
- If I have more badges than the cost of any single item on my shopping list, I should probably buy something instead of continuing to save.
- If two choices on my list have the same cost and chance of replacement, I should buy the one with greater winnitude first. If two choices on my list have the same cost and winnitude, I should buy the one that is less likely to be replaced.
Some strategies I can think of:
A. As soon as I have enough badges to buy something that will increase my winnitude at all, go ahead and buy it.
B. Sort my shopping list by (winnitude / cost). Buy things in the order given by that ratio.
But I don't know how to compare these two strategies, much less think of other strategies to evaluate.