Why would one fight to begin with?

If one fights for food because of famine, trust me, losing won’t hurt his ego, it will just means he will go hungry, and now he has a bigger problem than a hurt ego.

If one fights because he’s offended, his ego is already hurt. Same if one fights for revenge.

If one fights to figure out who’s stronger, well, apparently this is an important enough question for him if he’s willing to risk his physical well-being to validate his superior strength. Isn’t that obvious?

If one fights purely for fun, it cannot matter if one wins or loses, otherwise it’s not purely for fun. His ego won’t be hurt.