I have a row of case values with a total of 100 difference cases. I play a game with someone else and I get to go first. Each player takes turns taking a case from either end of the row. All values are known to both players and assuming the other person behaves in the most logical manner (perfect logicians), what is the best strategy for me to ensure that I end up with the majority of the money? How does it change, if at all with $n$ number of cases?
I'm thinking maybe split row in half and take from side with higher combined total? However, what if say case 1-50 sum to 1001 and case 51-100 sum to 999 but with case 100 having the value of 999? I'm also thinking that strategy may change with how many initial starting values odd vs even $n$?
Take the cases and number them from 1 to 100 (from one end to another). Then look how much the odd cases add up and how much the even cases add up. If the odd ones add more take number 1. After this your adversary will only be able to take even cases. This will lead to you being able to take an odd case, which again will lead the other person to only pick evens. the strategy is almost the same if the even ones add up more.