# Knockout game

#### arcnets

Hi all,
this may seem a bit martial or militaristic, but remember it's just a model for a mathematical process that I'm interested in.

OK. Imagine you have a game (or fight) where 2 teams oppose each other. The exact nature of the game is not important. However, the game has several rounds, and in each round every player faces all the players of the other team as enemies. The result of each round is one player getting knocked out, meaning he has to leave the game. This means, of course, that a team loses when all its players are knocked out, and the other team wins.

OK, easy up to here. But imagine, when the game is over, you want to give a score to each player.

(1) You could say "A player's score is the number of rounds he survived."

(2) But then you think again. Imagine one team has only one strong player. So all the others get knocked out very quickly, but the strong one, on his own, withstands the enemy team for a long time. Surely this must be honored. So let's say "A player's score is the sum of the numbers of active enemies in every round he survived."

(3) Now you might think again, and say: If a player survives against strong enemies, that must be honored more than if he survived against weak enemies. So let's say "A player's score is the sum of scores of active enemies in each round he survived, divided by a proper number to make it consistent."

Now my questions:
1) Is there a solution to this?
2) Can this solution be reached by iteration, as hinted above?

#### Hurkyl

Staff Emeritus
Gold Member
I suggest looking up the details on some other scoring systems, like that of Chess.

The way you describe your game, it's not a team game, all of the competition is done individual, just with groups of players put together to form a logical unit... so the scoring systems from 1 on 1 games would make sense for your purposes.

Hurkyl

#### arcnets

Originally posted by Hurkyl
so the scoring systems from 1 on 1 games would make sense for your purposes.
Yes Hurkyl I agree, but could you please explain what '1 on 1 games' are and how this solves my problem?

#### Pauly Man

This problem could be written up as a problem in game theory. It sounds like it could be a zero sum game too, as a win for player one is a loss for player two, or they could both draw. I suggest looking up some work on game theory, and taking a lok at how it all works, I am not all that familiar with the theory myself.

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