Esoteric thoughts about game history networks

Today I remembered a thought I had a while ago, which is that our game histories resolve into “shapes” or “networks”, in which each game can be thought of as a connection between the two players.

Shapes can be classified as either

  1. Fixed, meaning that their shape and volume is unchanging

  2. Finite, meaning that they can depend on a particular set of key points remaining valid (ie. certain players remaining active). When a finite shape “decays” it becomes fixed.

  3. Infinite, meaning that no particular point (player) is required to remain active for the shape to continue to grow. Infinite shapes can decay to finite shapes.


Suppose our group is defined as bugcat and his opponents. This is a star shape. Let’s call the number of players in the shape N, and the number of links from a player L. For bugcat, L = N - 1; for all other players L = 1. Notice that although the shape can grow as long as bugcat is active, as soon as he becomes inactive the shape becomes fixed.


We can consider another shape, in which every player must have played every other player – ie. L = N - 1 for all players, and call this a polygon. In a polygon, every player in the shape must remain active for new players to enter. It will also become progressively harder for the shape to grow, since the bar to entry increases.


Those are both finite shapes. Now let’s look at infinite ones. The simplest infinite shape is a “path”, like the path of a Shusaku number. New players can attach to the front end of the path, themselves becoming the new key point.

image

We can also consider a variant in which the path is double-ended, expanding in two directions, and advance this idea to any number of the initial connections of the key player (in this diagram, Gia).


A more sophisticated infinite shape is the ring, in which every player has an L of 2. It can be further complicated by demanding that all ring players connect to a player in the centre, making a cartwheel.

Compared to the path, the ring demands two connections to join rather than one; however, there will be more active players in the shape available to be joined to.


Some shapes better define different human relationships. The polygon is a good match for a small Go club. The path is good for, well, a Shusaku path. The star represents one player’s game history, and so on…

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There are apps that analyse your network (e.g. Facebook friends) and display the connections sorting them in groups.

It would be nice to have something similar based on opponents history.

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This is actually a pretty interesting idea, I bet if you graphed this across OGS as a whole you’d end up with a few really big clusters made up of people who play in the same tournaments frequently, with some linkages between the clusters. There’s a bunch of people who play in lots of 19x19 correspondence tournaments, a bunch who play lots of 9x9 correspondence tournaments, and some who play both, for example

Would definitely be cool to have a tool to visualize a graph of frequent opponents for a player, and their opponents and so on, dataset would get large quickly, but that could be handled somewhat by limiting things to a maximum of only a few degrees of separation from the original player, and only using recent games for each player in the graph. Maybe would make sense to use like the last 128 games for the original player the graph is built around, last 64 for players at one degree of separation, last 32 for players at 2 degrees of separation, 16 at 3 degrees, last 8 at 4 degrees, then last 4 games, then last 2 games, or something like that

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I thought about something like this. To make the task smaller you could only count current correspondence games. But it feels there’s little point to this. Imagine we downloaded everything we need, now what?

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So, how are we regulars connected? (no snub meant to anyone not featured, I was getting worn out)

bugcat – S_Alexander – Gia, yebellz, GoKyle, Samraku, Vsotvep – BHydden
bugcat – xhu98 – Mark5000, trohde, Conrad Melville
bugcat – tibbytabby – Sanonius
bugcat – Koba
bugcat – teapoweredrobot

Seems like Alex and xhu are “hubs”.

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Fun idea! I’d be interested to see if anyone comes up with a graphical rep for all OGS.

Also, I realize I should post and reply more so one day I too will become a regular :slight_smile: