Since who ever goes first (say "A") has the same chance of killing the other ("B")... that is 1/6...

"A" might as well go first.. to increase the chance... and hope "B" gets killed... and "B" will never have the chance to strike back.

If "B" survives.... then it is back to square one.

So, who ever goes first have higher success rate.

Does this make sense??