Questions I would ask God about the game of Go
I once tried to write a math&#x2F;CS nerd&#x27;s description of the rules of Go. There&#x27;s an XHTML file of the results at <a href="https:&#x2F;&#x2F;pastebin.com&#x2F;Cn7tbv98" rel="nofollow">https:&#x2F;&#x2F;pastebin.com&#x2F;Cn7tbv98</a> if anyone is curious.<p>Below is a text version:<p>Here is an attempt to describe the rules of Go precisely. This is actually for a generalization of Go that I call MANGO, which stands for MAth Nerd Go<p>Equipment<p>To play Mango, you need the following:<p>• A countable set, I.<p>• A set, C, whose members are subsets of I, each of which contains exactly two members of I.<p>• Three subsets of I, called E, B, and W, such that their union is I, and the intersections of any pair of them is empty.<p>• A real-valued function F, whose domain is I.<p>• A function, T, whose range is {0,1}, that is defined on the real numbers.<p>Definitions<p>• If P is a finite subset of C, and n is a member of I, then the INDEX of n in P is the number of elements of P that contain n.<p>• A finite subset, P, of C is called a PATH if the following conditions are met:<p>1. Each element of I has an index in P of 0, 1, or 2.<p>2. There are exactly two elements of I whose index in P is 1.<p>• An element of I whose index in a path is 1 is called an ENDPOINT of the path.<p>• An element of I whose index in a path is 2 is called an INTERIOR point of the path.<p>• Let S be one of the sets B or W. Let s be a member of S. Let L be the set of all members, e, of E, such that there is a path whose endpoints are s and e, and whose interior points are all in S or E. Let z be the sum over L of F. Then s is ALIVE if T(z) = 1.<p>• The ordered triple (E,B,W) is called the CONFIGURATION.<p>Playing<p>The players must first obtain a Mango set. This consists of agreeing to the sets I, C, E, B, and W, and the functions F and T.<p>The players must agree to an initial score for each player.<p>The players than decide who shall have the first turn. Players alternate turns.<p>On a players turn, that player may do one of two things:<p>• The player may PASS. It then becomes the other players turn.<p>• The player may make a LEGAL MOVE.<p>Note that a player <i>MUST</i> either pass or play a legal move. If there is no legal move, the player is forced to pass.<p>A MOVE consists of performing several actions. In the following, if it is Black&#x27;s turn we will use the symbol M to refer to the set B and the symbol H to refer to the set set W. If it is White&#x27;s turn, M will be W and H will be B. Here are the actions that are taken by a player on that players turn:<p>• A member, n, of E is selected.<p>• n is removed from E and added to M.<p>• All members of H that are not alive at the end of the above step are removed from H and placed in E.<p>• All members of M that are not alive at the end of the previous step are removed from M and placed in E.<p>A move is a LEGAL MOVE if the configuration, (E,B,W), produced by the move is new.<p>The game ends when two consecutive turns are passes.<p>Scoring<p>Each player uses the following procedure to compute his score. We will use the symbol M to refer to B if the player is Black, and to refer to W if the player is White.<p>We use the symbol H to refer I-(E union M).<p>The player starts with the initial score agreed upon at the start of the game.<p>For each m in M, the player receives F(m) points.<p>A player receives F(n) points for each member, n, of E for which the following conditions both hold:<p>• There exists a path with n as one endpoint and the other endpoint in M, and which contains no members of H as interior points.<p>• All paths that contain n as one endpoint and a member of H as the other endpoint contain a member of M as an interior point.<p>The player with the most points wins.<p>Example<p>To play ordinary 19x19 Go, with a 5.5 point Komi, the players might agree to the following:<p>• I = { (x,y) | x and y are integers in [1,19] }<p>• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }<p>• B = W = {}<p>• E = I<p>• The initial scores are 0 for Black, 5.5 for White.<p>• It is Blacks turn.<p>• F((x,y)) = 1<p>• T(z) = int((z+360)&#x2F;361)<p>To play a Go-like game on an infinite board, the players might agree to this:<p>• I = { (x,y) | x and y are integers }<p>• C = { {(x,y),(u,v)} | (x,y) and (u,v) are in I, (x-u)^2+(y-v)^2 = 1 }<p>• B = W = {}<p>• E = I<p>• Initial scores are Black:0, White:0.<p>• It is Black to move.<p>• F((x,y)) = exp(-x^2-y^2)<p>• T(z) = 1 if z &gt; 1&#x2F;1000, otherwise T(z) = 0