Jon P. answered 02/26/15
Tutor
5.0
(173)
Harvard honors math degree, experienced tutor in math and SAT prep
The average of the numbers 1 to 5 is 3. So in any given set of n turns, the most likely total will be 3n. 10 average turns would get to 30.
So if the player who goes first chooses 1, then the sum of the next 10 turns are most likely to be 30, and the overall total of the first 11 turns is most likely to be 31, the winning number. Since the first player gets to take the odd numbered moves, then he would be the one to take the 11th move, and he would win.
So the best first choice is 1.

Jon P.
02/26/15