Time for a Championship!

I'm searching for ideas for a ritual, a festival that happens from time to time where the choosen ones are…choosen.

It happens during the Equinox (day and night with equal hours), receiving the name after the season, where warriors from various nations come together to a Olympic like event where the best of the best are blessed with an ancient magic.
The winners of the games aren't guaranteed of receiving this ancient power but they get rewarded with scholarship, money, a banquet or anything they want - provided by the rulers of the land. Those who are blessed are titled Hosts, (because now they host a small part of the power of the cosmos). The choosening happens by acts of any kind of virtue culminating with a selfless soul.

The Equinox Games are actually the last chance one get to become a Host, the most value and honorable position in this society. Must prove you got strength but also brain and heart, trust your instincts and logic, bringing out the best of a being.
What kind of events do you perform?

What if the previous champion tries to kill the new champion after begging for their life?

If this is supposed to be an Olympics-like event, then it should be about who is the best within their field. Strength, casting ability, endurance, dexterity, mental achievement (something like fencing or even chess?), etc.

Also, surrendering to the weakest opponent out of pity should get you in trouble, as that means that the weakling has to get his ass kicked in the next round.

What would the "ancient magic" be? Ultimate power seems redundant, given the fact that you are already considered the best-of-the-best at that point.

" And finally, you have to defeat a champion in a fight to the death. But in the end, the champion begs for you to not kill him. If you agree, you prove you have heart. If you kill him, you are unsuited for the task."

The death part seems a bit extreme, but it does make sense for the contestants not knowing of that "rule". Indeed, the Entity chooses seemly at random, so in the games the true colors can be shown.

" And maybe, throughout the game, you have one chance to surrender. Who ever surrenders to the weakest opponent, someone who has no chance of winning and shouldn't be there, automatically wins."

This is a nice prompt "one chance to surrender" but it looks more like pity instead of mercy, at least in my point of view. Could you explain? @Fangirl616

" What if the previous champion tries to kill the new champion after begging for their life?"
-The previous champion is there to recognize the contestants mercy or resiliance, usually being a Host himself - naturally stronger and powerfull.

"Also, surrendering to the weakest opponent out of pity should get you in trouble, as that means that the weakling has to get his ass kicked in the next round."
-That's true and kinda hilariously pointless

" What would the "ancient magic" be? Ultimate power seems redundant, given the fact that you are already considered the best-of-the-best at that point."

-Ok, so…The ancient magic is an Entity, the Creator of Life, Life itself. It's their god. Usually represented as a tree with many branches each one with a different "fruit". Those fruits - named Jewels - fall from the branch and travel through space like shooting stars and find the Host that show great virtue. It's not ultimate power, it's a Gift, a small portion of power that can only be harvest with a good heart and a soul that fights for what's good. This is part of their religion.
When a Host turns "evil" he can no longer posses the power, so a new Jewel sprouts in the tree again and the cicle continues. That also apply to a Host's death.

Now, the Games are a normal championship, no magic related, but usually is during the events that new Hosts are selected. A lot of people get a little frustrated even if they come in first place.