From the point of view of kamma, the only real score in contests of injury or competition consists of more bad kamma points for both sides. So, in forgiving the other side, you’re basically promising yourself to forego any opportunity to add to the score.

 "One expression of goodwill [mettā] that’s always an appropriate gift is the gift of forgiveness. In one of the standard phrases for goodwill — “May all beings be free from animosity” — the Pali word for animosity, vera, is the opposite of forgiveness. It’s the vengeful animosity that wants to get back at someone for perceived wrongs. So when we wish that others be free from vera, we’re saying two things: “May all beings receive forgiveness for their wrong actions,” and “May all beings forgive others who have wronged them.”

When you forgive others, you’re not saying that you’re going to love them — or that you’re even going to forget the wrong that they did. You’re simply saying that you won’t try to get back at them.

When you forgive someone who’s wronged you, it doesn’t erase that person’s kamma in having done wrong. This is why some people think that forgiveness has no place in the karmic universe of the Buddha’s teachings. But that’s not so. Forgiveness may not be able to undo old bad kamma, but by erasing any thoughts of vera, it can prevent new bad kamma from being done.

The Dhammapada, a popular collection of early Buddhist poems, speaks of vera in two contexts. The first is when someone has injured you, and you’d like to inflict some injury back. The second is when you’ve lost a contest — in the Buddha’s time, this referred primarily to military battles, but now it could be extended to any competition where loss entails harm, whether real or only perceived — and you want to get even. As when Brazil loses to Argentina in soccer.

In both contexts — injury and competition — forgiveness is what puts an end to vera. You resolve not to settle the score, even if society grants you the right to do so, because you realize that, from the point of view of kamma, the only real score in contests like this consists of more bad kamma points for both sides. So, in forgiving the other side, you’re basically promising yourself to forego any opportunity to add to the score. You have no idea how many lifetimes this particular karmic mud fight has been going back and forth, but you do know that the only way to end it is to stop the vera, and if the end doesn’t first start with you, it may never arrive.

Forgiveness is a stance you may have to make unilaterally, within yourself, but there is the possibility that the other side will be inspired by your example to stop slinging mud as well. That way, both sides will benefit. Yet even if the other side doesn’t immediately join in the ceasefire, there will come a time when they lose interest, and that particular back-and-forth will die.

As for the case when you’ve lost out in a competition, the Buddha says that you can find peace and end vera only by putting winning and losing aside. To do this, you start by taking a good look at where you try to find happiness. If you look for it in terms of power or material possessions, there will always be winning and losing. If you gain power or status, for instance, others will have to lose. If others win, you lose.

But if you define happiness in terms of the practice of merit — giving, virtue, and meditation — there’s no need to create losers. Everyone wins. When you give, other people naturally gain what you’ve shared with them; you gain a spacious sense of wealth within and the love and respect of others without. When you’re virtuous, abstaining from harming anyone, you gain freedom from remorse over your actions, while others gain safety. When you meditate, you give less rein to your greed, aversion, and delusion, so that you suffer less from their depredations, and other people are less victimized by their prowling around as well.

Then you further reflect:

"Greater in battle than the man who would conquer a thousand-thousand men, is he who would conquer just one — himself.

Better to conquer yourself than others. When you’ve trained yourself, living in constant self-control, neither a deva nor gandhabba, nor a Mara banded with Brahmas, could turn that triumph back into defeat."  — Dhp 103–105

Other victories can be undone — “settled” scores, in the light of kamma and rebirth, are never really settled — but victory over your own greed, aversion, and delusion is something that lasts. It’s the only victory that creates no vera, so it’s the only victory that’s really safe and secure.

But this isn’t a victory you can hope to attain if you’re still harboring thoughts of vera. So in a world where we’ve all been harmed in one way or another, and where we could always find old scores to avenge if we wanted to, the only way to find a truly safe victory in life is to start with thoughts of forgiveness: that you want to pose no danger to anyone at all, regardless of the wrong they’ve done. This is why forgiveness is not only compatible with the practice of the Buddha’s teachings. It’s a necessary first step.

That’s one important way in which generosity helps in determining on goodwill."

~ Thanissaro Bhikkhu "Sublime Determinations: a Retreat on the Brahmavihāras"