LeetCode 486 Predict the Winner - Problem Statement

Two players take turns picking numbers from either end of an array. Each player adds the picked number to their score. Both play optimally. Can Player 1 win (or tie)? Example: nums $= [1, 5, 2]$. Player 1 picks $2$, Player 2 picks $5$, Player 1 picks $1$. Scores: $3$ vs $5$. Player 1 loses.

But if Player 1 picks $1$ first, then $5$... try it yourself. This is the classic Game Theory DP problem. The array shrinks from both ends, and we need to track who's winning at each subarray.