In Predict the Winner with an even-length array, the first player can always at least tie. Why? Split the array into even and odd indices.
First player can always take all even-indexed elements (or all odd-indexed). Strategy: compute sums of even-indexed and odd-indexed elements. Take from whichever set has larger sum. This proves first player \geq second player. But the DP finds the exact margin, not just win/lose.