More on competitive sports and other games

I wonder how psychologically feasible it would be to generally engage in competitive sports or other games with one's intention being that the one's competitor win against as strong an opposition as possible. This is not all that difficult to achieve when competing with one's child: one may want the child to beat one, and to beat one when one is playing at one's best. The psychological difficulty is that one's intention that one's competitor win may well weaken one's playing. If one could play excellently with such an intention, wouldn't it be a laudable way to play?

To be as strong an opposition as possible, it would help to have the intention to win. I wonder if it would be possible to have two clearly logically incompatible ends at the same time: (a) that my competitor win against as strong an opposition as possible and (b) that I win. This isn't as problematic as intending p and not p at the same time. Maybe you can't do that, because any action that furthers not p impedes p. But actions that promote (b) can promote (a) by making the opposition as strong as possible, and vice versa. So it might be that incompatible ends like (a) and (b) can be both held together, though it is uncomfortable to do so.