Other me would already know that symmetry fights never result in anything other than a stalmate, therefore I would not need to fight me in a phsyical fight, as I would instead challenge me to a battle of wits that neither of us could win. The other me would know he cannot win, and would thus be forced to fight me anyway. Going on the offensive would then put him in a disadvantage, as I know Ju-Jitsu, which is almost completely based on defence, with little openly offensive moves.
Other me would then know that if he attacks first, I will defed, and likely win, and we would instead settle the dispute with a nice game of chess. After that I cannot make a plan for, becuase the other me would already know it and would counter it, so it's better to just make it up as we go.