Ah ok. I misunderstood the goal of the game. I thought it was to get more than other players, not get the most you can.
Certainly though, without communication a la the Prisoner's Dilemma, a winning solution would be to grab all the nuts as fast as possible. You won't get as many as you possibly can by playing it safe, but without knowing that OTHERS won't grab all the nuts, that's the best scenario.
Eh, it's counter-productive if you know the other people aren't going to take them all first. It's extremely productive if you don't know. Getting ten nuts instead of farming/harvesting for 50 or so is pretty counter-productive... but getting NO nuts because the other guy harvested them all the first cycle is devastating.

