impu1se

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My name is John Moore. I'm currently impulse [1k] on KGS and a resident of Charlotte, NC. This page contains mostly my attempts to understand the CGTPath information. Some day I hope to make it actually contain some sense.


CGT Numbers

A game tree can be represented in the following form as nested brackets of possible games:

    G = { Ba, Bb, Bc, etc... | Wa, Wb, Wc, etc... }

Ba, Bb, Bc, etc... are the games that follow after a certain black move has been played. Wa, Wb, Wc, etc... are the games that follow after a certain white move has been made. The representation doesn't make any assumptions about who will be first to move.

Some games can be represented by simple Numbers that can be thought of as the score.

[Diagram]
{ | } = 0  

There are no possible good moves. This game is a number called 0. Making a number of assumptions, the last player who moved won.


[Diagram]
{ 0 | } = 1  

A win for black. { { | } | } = { 0 | } = 1. This game has one move more for black than the 0 game. In the same way { 1 | } = 2, { 2 | } = 3, and so on.


[Diagram]
{ | 0 } = -1  

The opposite of a game with white and black switched is the negative of the original game. -{ A | B } = { -B | -A }. For example: { | -1 } = -2.


[Diagram]
{ 0 | 0 } = *  

Either player can make the last move and win. This is a fuzzy or infinitesimal game.


[Diagram]
Game with options  

This game is { Ba, Bb | Wa, Wb } since either player will has a choice of two moves. Ba and Wb lead to the equivalent game seen before: { 0 | 0 } = *. Bb lead to the game { 0 | } = 1. Wa is slightly more complex: { 0 | } | 0 } = { 1 | 0 }. So the complete game tree is represented by { 1, * | *, { 1 | 0 } }.


References: ZeroInCGTTerms, CombinatorialGameTheory, Numbers, GoInfinitesimals, SurrealNumbers, DisjunctiveSums


impulse: this is a cute seki

impulse: I had some zen but it came out in the shower

impulse: hmm, 7d teaching a 30k. that's like calling in a bomb strike for a 3 yr old on a tricycle


impu1se last edited by impu1se on April 10, 2007 - 06:08
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