Haha it would be quite a haven to find a place where life, for once, doesn't seem to get the better of us all, eh?!
I see what you mean that by playing first or second you may have a better chance of winning, and it would certainly make sense to play both ways if you truly must know who is better, but I stay with my original stance that it does not affect the game. That comes off a bit screwy so let me try to explain what I mean agin, if I can't say it right, then I admit I'm less than Plato, and we can all move along merrily anyhow...
Completely theoretically, since not realistically possible in complex games, If two players of equally high experience and logical skill start a game of chess then it may be likely that white will win more of the time... But the game would be played exactly the same way if the two players flip-flop sides. That is not a matter of luck per-se, it is a matter of purely incidental statistics. I'm tip-toeing here, admittedly, but what luck is to me in a game is when a "good" decision is made, it can turn out for the worse! If going first were luck, then I argue that sometimes it should turn out for the worse, but in our scenario it never can. White is always the better.
Luck is like you're describing that 40K 1 dice roll wins scenario. If you make a good decision and decide to fire you "ultra-death-laser-destroy" cannon at some evil blob monster, let's call it a good decision because 5 out of 6 of the nodes lead to victory, and only 1 does not, and let's say that 5/6 is the best chance possible for winning the game given all other moves and nodes available.... But you roll a 1, and your "ultra-death-laser-destroyer" blows itself to pieces! GOOD SHOW! You just lost, to luck.
You may have a better chance to win going first, but it's not luck. (Tip-toeing in my Jordan's....)