woodbine

Apologies in advance for the basic question.

I took the chain off my old MTB for a quick degrease and clean. It's the type where you push the pin out with a removal tool. Now, am I best in putting the chain back on to run the same way as it was? Or, would it be better to put the chain on the other way around?

My thinking is that the forces and wear will be in different parts of the links and rollers if I put it on the other way. I'm presuming this would equalise wear and make the chain last longer. Or, as the chain is well used (but not worn), is it best running the way it always has, as it is bedded in this way, and will be happier?