To play optimally, both players would first move towards each other and then from the point of their intersection they will take all the numbers from that point to their nearest boundaries.
Let Player 1 start from X and Player 2 start from Y.
Then,
if (X < Y), player 1 will take all the numbers from A[1] to A[X] and player 2 will take all the numbers from A[Y] to A[N] and also player 1 will take the numbers from A[X] to A[(X+Y)/2] and player 2 will take the numbers from A[(X+Y)/2+1] to A[Y].
if (X > Y) same as above but now player 1 will work from X to N and player 2 will work from 1 to Y.
if (X == Y), calculate the sum from A[1] to A[X-1] and another sum from A[X+1] to A[N],
add A[X] to the greater sum and give it to player 1.