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Let F[i] = best sum you can achieve when it's your turn and there are i elements left..
You can make a simple observation that if player A takes F[N] points then player B will have Total Points — F[n].
Based on that let Sum[i] be the sum of the last i elements in the stack then F[i] can be one of these 3 cases:
F[i] = A[i] + sum[i-1] -F[i-1].
F[i]= A[i] + A[i-1] + sum[i-2] -F[i-2].
F[i]= A[i] + A[i-1] + A[i-2] + sum[i-3] -F[i-3].