I was solving this problem :https://codeforces.com/contest/1841/problem/A ,I know it is a programmingm problem but inherently it does involves principles of game theory. What I don't understand is that if suppose Alice is starting in the question , then won't he always win if he selects the (n-1) cards , replaces the sum (n-1) back , now if n>2 then he should always win. Also, can anyone give me on what metric is the optimal decision for a player is decided?
Thanks