We have $n$-players in a game. We have a population of players we can choose from. Each player score is a normally distributed random variable and each player has a cost to add to the team. We are limited to $n$-players and the total cost must be less than or equal to $m$.
The total score for a team is calculated as the sum of all of the individual player's score on that team. Our goal is to maximize the expected team score while staying under our allowed player weight and number of players.
Now, suppose that in this game we drop the score of the player that has the lowest score on the team and do not consider it in the total team score.
Does a deterministic algorithm exist that will allow us to reach the optimal solution?