Let's say that a player has some general idea of a distribution that random numbers will be drawn from. The player will be presented a number and he can either accept or decline it. He will be offered a maximum of 10 numbers and needs to accept exactly 5. The goal is to maximize the total of the 5 numbers. I'll need to solve this (or simulate?) in a general case for N numbers presented and having to take T numbers.
Feels like game theory to me a bit, but it's been too long since I've done any real math so I could be totally off base. I'd love to hear thoughts on how to reason and try to solve this problem in the general case. I'm not sure where to even start. Any help or advice would be greatly appreciated.
Thanks!