# 4P games should be played 3 times

#1

The main reason for this is that players are not equidistant: you can have at most 3 equidistant points on a plane. It much more likely for a player to be influenced by a neighbouring opponent than by the one diagonally opposed.

So what I’m proposing is that every 4P game is played 3 times (same seed, different positions), with players A,B,C,D placed:

``````AB    AD    AB
CD    CB    DC
``````

Only in this way we would be able to determine a meaningful ranking on the particular map.

#2

But they’re on the surface of a torus, not a plane.

#3

Not really, the surface is a plane with periodic boundary conditions, i.e. homotopic to a torus, not a torus itself.
The metric is globally (not only locally) flat and it is induced by the Manhattan distance, so as I said above I believe you can’t place 4 points equidistant from each other.

#4

This really means 4P shouldn’t be played at all. I think there should at least be a separate competition for 2P and 4P games like singles and doubles in tennis.

#5

A change in rules to randomly pair you with another bot and then you’d have to cooperate instead of compete during the match would be a really cool way to tease out new strategy goals.

#6

You can if you use rotational symmetry instead of reflection symmetry.

#7

This makes sense, but I guess the theory is that if you play enough games, some you will get a really good player next you and others you will get potatoes next to you. With enough games this problem dissolves.

#8

How many is enough? 10,000?