KGS math club/solution 1 2

Another solution:

Colour every second item in the sequence blue and the rest red. Sum up the blue items and the red; which one is bigger, start playing that colour. Always take the item of the chosen colour; only one end will be that colour since the length of the sequence is even. The opponent will be forced to take the other colour, since after your move both ends will be the same colour. You will be the numbers of the better colour, whereas your opponent will get the numbers of the worse colour; you win (or at least score a tie).