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/*
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* Copyright (C) 1999 Rob Crittenden (rcrit@greyoak.com)
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* Copyright (C) 1999,2000 Ross Combs (rocombs@cs.nmsu.edu)
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* Copyright (C) 1999,2000 D.Moreaux (vapula@linuxbe.org)
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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*/
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#include "common/setup_before.h"
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#include <math.h>
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#ifdef HAVE_STRING_H
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# include <string.h>
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#else
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# ifdef HAVE_STRINGS_H
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# include <strings.h>
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# endif
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#endif
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#include "account.h"
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#include "account_wrap.h"
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#include "common/eventlog.h"
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#include "game.h"
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#include "common/tag.h"
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#include "ladder.h"
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#include "ladder_calc.h"
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#include "common/xalloc.h"
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#include "common/setup_after.h"
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static double probability(unsigned int a, unsigned int b) ;
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static int coefficient(t_account * account, t_clienttag clienttag, t_ladder_id id);
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static double two_player(unsigned int *rating);
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static double three_player(unsigned int *rating);
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static double four_player(unsigned int *rating);
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static double five_player(unsigned int *rating);
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static double five_f1(int a, int b, int c, int d, int e) ;
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static double five_f2(int a, int b, int c) ;
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static double six_player(unsigned int *rating);
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static double six_f1(int a, int b, int c, int d, int e, int f) ;
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static double six_f2(int a, int b, int c, int d, int e, int f) ;
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static double six_f3(int a, int b, int c, int d) ;
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static double seven_player(unsigned int *rating);
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static double seven_f1(int a, int b, int c, int d, int e, int f, int g) ;
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static double seven_f2(int a, int b, int c, int d, int e, int f, int g) ;
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static double eight_player(unsigned int *rating);
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static double eight_f1(int a, int b, int c, int d, int e, int f, int g) ;
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static double eight_f2(int a, int b, int c, int d, int e, int f, int g) ;
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static double eight_f3(int a, int b, int c, int d, int e) ;
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/*
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* Compute probability of winning using the Elo system
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*
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* The formula is:
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*
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* D = rating(player a) - rating(player b)
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*
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* 1
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* Pwin(D) = ------------------
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* -(D / 400)
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* 1 + 10
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*/
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static double probability(unsigned int a, unsigned int b)
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{
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double i, j;
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i = (((double)a) - ((double)b)) / 400.0;
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j = pow(10.0,-i);
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return (1.0 / (1.0+j));
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}
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/*
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* This is the coefficient k which is meant to enhance the
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* effect of the Elo system where more experienced players
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* will gain fewer points when playing against newbies, and
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* newbies will gain massive points if they win against an
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* experienced player. It also helps stabilize a player's
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* rating after they have played 30 games or so.
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*
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* K=50 for new players
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* K=30 for players who have played 30 or more ladder games
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* K=20 for players who have attained a rating of 2400 or higher
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*/
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static int coefficient(t_account * account, t_clienttag clienttag, t_ladder_id id)
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{
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int const total_ladder_games=account_get_ladder_wins(account,clienttag,id) +
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account_get_ladder_losses(account,clienttag,id) +
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account_get_ladder_disconnects(account,clienttag,id);
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if (total_ladder_games < 30)
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return 50;
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if (account_get_ladder_rating(account,clienttag,id) < 2400)
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return 30;
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return 20;
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}
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/*
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* The Elo system only handles 2 players, these functions extend
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* the calculation to different numbers of players as if they were
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* in a tournament. It turns out the math for this is really ugly,
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* so we have hardcoded the equations for every number of players.
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*/
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static double two_player(unsigned int *rating)
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{
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unsigned int a,b;
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double ab;
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a = rating[0];
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b = rating[1];
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ab = probability(a,b);
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return ab;
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}
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static double three_player(unsigned int *rating)
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{
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unsigned int a,b,c;
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double ab,ac,bc,cb;
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a = rating[0];
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b = rating[1];
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c = rating[2];
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ab = probability(a,b);
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ac = probability(a,c);
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bc = probability(b,c);
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cb = 1.0 - bc;
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return (2*(ab*ac)+(bc*ab)+(cb*ac))/3;
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}
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static double four_player(unsigned int *rating)
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{
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unsigned int a,b,c,d;
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double ab,ac,ad,bc,bd,cb,cd,db,dc;
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a = rating[0];
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b = rating[1];
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c = rating[2];
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d = rating[3];
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ab = probability(a,b);
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ac = probability(a,c);
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ad = probability(a,d);
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bc = probability(b,c);
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bd = probability(b,d);
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cd = probability(c,d);
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cb = 1.0 - bc;
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db = 1.0 - bd;
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dc = 1.0 - cd;
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return (ab*ac*(cd+bd)+ac*ad*(db+cb)+ab*ad*(dc+bc))/3;
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}
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/* [Denis MOREAUX <vapula@linuxbe.org>, 10 Apr 2000]
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*
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* C D E A D E The winner may be in the
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* A B C E B C A E 2 players or the 3 players
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* A C B A group. In either case, a
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* A A second player must be choosen
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* to be either the one playing
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* against A in the 2-players subtree or being the winner
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* of the 2-player subtree if A is in the 3-players subtree.
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*/
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static double five_player(unsigned int *rating)
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{
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unsigned int a,b,c,d,e;
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a = rating[0];
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b = rating[1];
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c = rating[2];
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d = rating[3];
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e = rating[4];
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return (five_f1(a,b,c,d,e)+five_f1(a,c,d,e,b)+
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five_f1(a,d,e,b,c)+five_f1(a,e,b,c,d))/30;
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}
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/* [Denis MOREAUX <vapula@linuxbe.org>, 10 Apr 2000
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*
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* Two cases to treat : AB-CDE and BC-ADE.
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* in both cases, A win against B.
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* In the first case, A win over the winner of a 3-players game
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* (3 possible winners).
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* In the second case, B win over one of the three other and A is in
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* the 3-players game.
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*/
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static double five_f1(int a, int b, int c, int d, int e)
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{
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double ab,ac,ad,ae,bc,bd,be;
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ab = probability(a,b);
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ac = probability(a,c);
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ad = probability(a,d);
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ae = probability(a,e);
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bc = probability(b,c);
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bd = probability(b,d);
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be = probability(b,e);
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return ab*(ac*five_f2(c,d,e)+ad*five_f2(d,e,c)+ae*five_f2(e,c,d)+
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bc*five_f2(a,d,e)+bd*five_f2(a,c,e)+be*five_f2(a,c,d));
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}
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static double five_f2(int a, int b, int c)
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{
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double ab,ac,bc,cb;
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ab = probability(a,b);
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ac = probability(a,c);
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bc = probability(b,c);
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cb = 1.0 - bc;
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return (2*(ab*ac)+bc*ab+cb*ac);
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}
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static double six_player(unsigned int *rating)
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{
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unsigned int a,b,c,d,e,f;
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a = rating[0];
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b = rating[1];
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c = rating[2];
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d = rating[3];
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e = rating[4];
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f = rating[5];
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/* A B C D
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* A C E F
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* A E
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* A
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*/
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return (six_f1(a,b,c,d,e,f)+ /* A is in group of 4 */
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six_f1(a,b,c,e,d,f)+
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six_f1(a,b,e,d,c,f)+
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six_f1(a,e,c,d,b,f)+
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six_f1(a,b,c,f,d,e)+
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six_f1(a,b,f,d,c,e)+
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six_f1(a,f,c,d,b,e)+
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six_f1(a,e,f,b,c,d)+
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six_f1(a,e,f,c,b,d)+
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six_f1(a,e,f,d,b,c)+
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six_f2(a,b,c,d,e,f)+ /* A is in group of 2 */
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six_f2(a,c,b,d,e,f)+
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six_f2(a,d,b,c,e,f)+
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six_f2(a,e,b,c,d,f)+
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six_f2(a,f,b,c,d,e))/45;
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}
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/* ABCD = group of 4, EF = group of 2, A must win */
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/* D.Moreaux, 10 Apr 2000: changed double to int for the parameters */
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static double six_f1(int a, int b, int c, int d, int e, int f)
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{
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double ab,ac,ad,bc,bd,cb,cd,db,dc,ef,fe,ae,af;
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ab = probability(a,b);
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ac = probability(a,c);
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ad = probability(a,d);
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ae = probability(a,e);
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af = probability(a,f);
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bc = probability(b,c);
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bd = probability(b,d);
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cd = probability(c,d);
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ef = probability(e,f);
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cb = 1.0 - bc;
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db = 1.0 - bd;
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dc = 1.0 - cd;
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fe = 1.0 - ef;
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return (ab*ac*(cd+bd)+ac*ad*(db+cb)+ab*ad*(dc+bc))*(ef*ae+fe*af);
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}
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/* AB is group of 2, CDEF is group of 4, A must win */
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static double six_f2(int a, int b, int c, int d, int e, int f)
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{
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double ab,ac,ad,ae,af;
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ab = probability(a,b);
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ac = probability(a,c);
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ad = probability(a,d);
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ae = probability(a,e);
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af = probability(a,f);
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return (six_f3(c,d,e,f)*ab*ac+
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six_f3(d,c,e,f)*ab*ad+
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six_f3(e,c,d,f)*ab*ae+
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six_f3(f,c,d,e)*ab*af);
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}
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/* ABCD is group of 4, A win */
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static double six_f3(int a, int b, int c, int d)
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{
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double ab,ac,ad,bc,bd,cb,cd,db,dc;
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ab = probability(a,b);
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ac = probability(a,c);
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ad = probability(a,d);
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bc = probability(b,c);
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bd = probability(b,d);
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cd = probability(c,d);
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cb = 1.0 - bc;
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db = 1.0 - bd;
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dc = 1.0 - cd;
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return (ab*ac*(cd+bd)+ac*ad*(db+cb)+ab*ad*(dc+bc));
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}
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static double seven_player(unsigned int *rating)
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{
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unsigned int a,b,c,d,e,f,g;
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a = rating[0];
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b = rating[1];
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c = rating[2];
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d = rating[3];
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e = rating[4];
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f = rating[5];
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g = rating[6];
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return (seven_f1(a,b,c,d,e,f,g)+seven_f1(a,c,b,d,e,f,g)+
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seven_f1(a,d,c,b,e,f,g)+seven_f1(a,e,c,d,b,f,g)+
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seven_f1(a,f,c,d,e,b,g)+seven_f1(a,g,c,d,e,f,b))/45;
|
| 357 |
}
|
| 358 |
|
| 359 |
static double seven_f1(int a, int b, int c, int d, int e, int f, int g)
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| 360 |
{
|
| 361 |
|
| 362 |
return seven_f2(a,b,c,d,e,f,g)+seven_f2(a,b,d,c,e,f,g)+
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| 363 |
seven_f2(a,b,e,d,c,f,g)+seven_f2(a,b,f,d,e,c,g)+
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| 364 |
seven_f2(a,b,g,d,e,f,c);
|
| 365 |
}
|
| 366 |
|
| 367 |
static double seven_f2(int a, int b, int c, int d, int e, int f, int g)
|
| 368 |
{
|
| 369 |
double ab,ac,ad,ae,af,ag,bc,bd,be,bf,bg,cd,ce,cf,cg;
|
| 370 |
double de,df,dg,ed,ef,eg,fd,fe,fg,gd,ge,gf;
|
| 371 |
ab = probability(a,b);
|
| 372 |
ac = probability(a,c);
|
| 373 |
ad = probability(a,d);
|
| 374 |
ae = probability(a,e);
|
| 375 |
af = probability(a,f);
|
| 376 |
ag = probability(a,g);
|
| 377 |
bc = probability(b,c);
|
| 378 |
bd = probability(b,d);
|
| 379 |
be = probability(b,e);
|
| 380 |
bf = probability(b,f);
|
| 381 |
bg = probability(b,g);
|
| 382 |
cd = probability(c,d);
|
| 383 |
ce = probability(c,e);
|
| 384 |
cf = probability(c,f);
|
| 385 |
cg = probability(c,g);
|
| 386 |
de = probability(d,e);
|
| 387 |
df = probability(d,f);
|
| 388 |
dg = probability(d,g);
|
| 389 |
ef = probability(e,f);
|
| 390 |
eg = probability(e,g);
|
| 391 |
fg = probability(f,g);
|
| 392 |
ed = 1.0 - de;
|
| 393 |
fd = 1.0 - df;
|
| 394 |
gd = 1.0 - dg;
|
| 395 |
fe = 1.0 - ef;
|
| 396 |
ge = 1.0 - eg;
|
| 397 |
gf = 1.0 - fg;
|
| 398 |
|
| 399 |
return
|
| 400 |
ab*(
|
| 401 |
(ac+bc)*
|
| 402 |
(ad*(de*df*(fg+eg)+df*dg*(ge+fe)+de*dg*(gf+ef))+ /* 4:d win */
|
| 403 |
ae*(ed*ef*(fg+dg)+ef*eg*(gd+fd)+ed*eg*(gf+df))+ /* 4:e win */
|
| 404 |
af*(fe*fd*(dg+eg)+fd*fg*(ge+de)+fe*fg*(gd+ed))+ /* 4:f win */
|
| 405 |
ag*(ge*gf*(fd+ed)+gf*gd*(de+fe)+ge*gd*(df+ef)))+ /* 4:g win */
|
| 406 |
bc*
|
| 407 |
((bd+cd)*(ae*af*(fg+eg)+af*ag*(ge+fe)+ae*ag*(gf+ef))+ /* 3:d */
|
| 408 |
(be+ce)*(ad*af*(fg+dg)+af*ag*(ad+ad)+ad*ag*(gf+df))+ /* 3:e */
|
| 409 |
(bf+cf)*(ae*ad*(dg+eg)+ad*ag*(ge+de)+ae*ag*(gd+ed))+ /* 3:f */
|
| 410 |
(bg+cg)*(ae*af*(fd+ed)+af*ad*(de+fe)+ae*ad*(df+ef)))); /* 3:g */
|
| 411 |
|
| 412 |
}
|
| 413 |
|
| 414 |
static double eight_player(unsigned int *rating)
|
| 415 |
{
|
| 416 |
unsigned int a,b,c,d,e,f,g,h;
|
| 417 |
double ab,ac,ad,ae,af,ag,ah;
|
| 418 |
|
| 419 |
a = rating[0];
|
| 420 |
b = rating[1];
|
| 421 |
c = rating[2];
|
| 422 |
d = rating[3];
|
| 423 |
e = rating[4];
|
| 424 |
f = rating[5];
|
| 425 |
g = rating[6];
|
| 426 |
h = rating[7];
|
| 427 |
|
| 428 |
ab = probability(a,b);
|
| 429 |
ac = probability(a,c);
|
| 430 |
ad = probability(a,d);
|
| 431 |
ae = probability(a,e);
|
| 432 |
af = probability(a,f);
|
| 433 |
ag = probability(a,g);
|
| 434 |
ah = probability(a,h);
|
| 435 |
|
| 436 |
/* First against A may be one from seven */
|
| 437 |
|
| 438 |
return (eight_f1(a,c,d,e,f,g,h)*ab+
|
| 439 |
eight_f1(a,b,d,e,f,g,h)*ac+
|
| 440 |
eight_f1(a,b,c,e,f,g,h)*ad+
|
| 441 |
eight_f1(a,b,c,d,f,g,h)*ae+
|
| 442 |
eight_f1(a,b,c,d,e,g,h)*af+
|
| 443 |
eight_f1(a,b,c,d,e,f,h)*ag+
|
| 444 |
eight_f1(a,b,c,d,e,f,g)*ah)/315;
|
| 445 |
|
| 446 |
}
|
| 447 |
|
| 448 |
|
| 449 |
static double eight_f1(int a, int b, int c, int d, int e, int f, int g)
|
| 450 |
{
|
| 451 |
/* The winner of the second group, who'll then play against A, may be one
|
| 452 |
from six possible players */
|
| 453 |
|
| 454 |
return eight_f2(a,b,c,d,e,f,g)+
|
| 455 |
eight_f2(a,c,b,d,e,f,g)+
|
| 456 |
eight_f2(a,d,b,c,e,f,g)+
|
| 457 |
eight_f2(a,e,b,c,d,f,g)+
|
| 458 |
eight_f2(a,f,b,c,d,e,g)+
|
| 459 |
eight_f2(a,g,b,c,d,e,f);
|
| 460 |
}
|
| 461 |
|
| 462 |
static double eight_f2(int a, int b, int c, int d, int e, int f, int g)
|
| 463 |
{
|
| 464 |
double ab,bc,bd,be,bf,bg;
|
| 465 |
|
| 466 |
ab = probability(a,b);
|
| 467 |
bc = probability(b,c);
|
| 468 |
bd = probability(b,d);
|
| 469 |
be = probability(b,e);
|
| 470 |
bf = probability(b,f);
|
| 471 |
bg = probability(b,g);
|
| 472 |
|
| 473 |
/* There are 5 player who may play against the 3rd. The third (b) will win
|
| 474 |
over them and lose against a */
|
| 475 |
|
| 476 |
return ab*(eight_f3(a,d,e,f,g)*bc+
|
| 477 |
eight_f3(a,c,e,f,g)*bd+
|
| 478 |
eight_f3(a,c,d,f,g)*be+
|
| 479 |
eight_f3(a,c,d,e,g)*bf+
|
| 480 |
eight_f3(a,c,d,e,f)*bg);
|
| 481 |
|
| 482 |
}
|
| 483 |
|
| 484 |
/* D.Moreaux, 10 Apr 2000: changed double to int for the parameters */
|
| 485 |
|
| 486 |
static double eight_f3(int a, int b, int c, int d, int e)
|
| 487 |
{
|
| 488 |
double ab,ac,ad,ae,bc,bd,be,cb,cd,ce,db,dc,de,eb,ec,ed;
|
| 489 |
|
| 490 |
ab = probability(a,b);
|
| 491 |
ac = probability(a,c);
|
| 492 |
ad = probability(a,d);
|
| 493 |
ae = probability(a,e);
|
| 494 |
bc = probability(b,c);
|
| 495 |
bd = probability(b,d);
|
| 496 |
be = probability(b,e);
|
| 497 |
cd = probability(c,d);
|
| 498 |
ce = probability(c,e);
|
| 499 |
de = probability(d,e);
|
| 500 |
cb = 1.0 - bc;
|
| 501 |
db = 1.0 - bd;
|
| 502 |
dc = 1.0 - cd;
|
| 503 |
eb = 1.0 - be;
|
| 504 |
ec = 1.0 - ce;
|
| 505 |
ed = 1.0 - de;
|
| 506 |
|
| 507 |
/* expansion then factorisation (this function is called 210 times)
|
| 508 |
* gain 4 func_call
|
| 509 |
* 24 *
|
| 510 |
* 30 probability
|
| 511 |
*/
|
| 512 |
return (bc*de+be*dc)*((ab-ad)*bd+ad)+
|
| 513 |
(bd*ce+be*cd)*((ab-ac)*bc+ac)+
|
| 514 |
(cb*de+db*ce)*((ac-ad)*cd+ad)+
|
| 515 |
(cd*eb+cb*ed)*((ac-ae)*ce+ae)+
|
| 516 |
(dc*eb+db*ec)*((ad-ae)*de+ae)+
|
| 517 |
(bd*ec+bc*ed)*((ae-ab)*eb+ab);
|
| 518 |
}
|
| 519 |
|
| 520 |
/* Determine changes in ratings due to game results. */
|
| 521 |
extern int ladder_calc_info(t_clienttag clienttag, t_ladder_id id, unsigned int count, t_account * * players, t_game_result * results, t_ladder_info * info)
|
| 522 |
{
|
| 523 |
unsigned int curr;
|
| 524 |
unsigned int *rating;
|
| 525 |
unsigned int *sorted;
|
| 526 |
|
| 527 |
if (!players)
|
| 528 |
{
|
| 529 |
eventlog(eventlog_level_error,__FUNCTION__,"got NULL players");
|
| 530 |
return -1;
|
| 531 |
}
|
| 532 |
if (!results)
|
| 533 |
{
|
| 534 |
eventlog(eventlog_level_error,__FUNCTION__,"got NULL results");
|
| 535 |
return -1;
|
| 536 |
}
|
| 537 |
if (!clienttag)
|
| 538 |
{
|
| 539 |
eventlog(eventlog_level_error,__FUNCTION__,"got bad clienttag");
|
| 540 |
return -1;
|
| 541 |
}
|
| 542 |
if (!info)
|
| 543 |
{
|
| 544 |
eventlog(eventlog_level_error,__FUNCTION__,"got NULL info");
|
| 545 |
return -1;
|
| 546 |
}
|
| 547 |
|
| 548 |
rating = xmalloc(sizeof(unsigned int)*count);
|
| 549 |
sorted = xmalloc(sizeof(unsigned int)*count);
|
| 550 |
|
| 551 |
for (curr=0; curr<count; curr++)
|
| 552 |
rating[curr] = account_get_ladder_rating(players[curr],clienttag,id);
|
| 553 |
|
| 554 |
for (curr=0; curr<count; curr++)
|
| 555 |
{
|
| 556 |
double k;
|
| 557 |
double prob;
|
| 558 |
double delta;
|
| 559 |
t_game_result myresult;
|
| 560 |
unsigned int opponent_count;
|
| 561 |
unsigned int team_members;
|
| 562 |
|
| 563 |
k = coefficient(players[curr],clienttag,id);
|
| 564 |
opponent_count = 0;
|
| 565 |
myresult = results[curr];
|
| 566 |
|
| 567 |
{
|
| 568 |
unsigned int i,j;
|
| 569 |
|
| 570 |
/* Put the current user into slot 0, his opponents into other slots
|
| 571 |
order is not important for the other players */
|
| 572 |
for (i=0,j=1; i<count; i++)
|
| 573 |
if (i==curr)
|
| 574 |
sorted[0] = rating[i];
|
| 575 |
else
|
| 576 |
{
|
| 577 |
if (results[i]!=myresult)
|
| 578 |
{
|
| 579 |
sorted[j++] = rating[i];
|
| 580 |
opponent_count++;
|
| 581 |
}
|
| 582 |
}
|
| 583 |
}
|
| 584 |
|
| 585 |
team_members = count - opponent_count;
|
| 586 |
|
| 587 |
switch (opponent_count)
|
| 588 |
{
|
| 589 |
case 1:
|
| 590 |
prob = two_player(sorted);
|
| 591 |
break;
|
| 592 |
case 2:
|
| 593 |
prob = three_player(sorted);
|
| 594 |
break;
|
| 595 |
case 3:
|
| 596 |
prob = four_player(sorted);
|
| 597 |
break;
|
| 598 |
case 4:
|
| 599 |
prob = five_player(sorted);
|
| 600 |
break;
|
| 601 |
case 5:
|
| 602 |
prob = six_player(sorted);
|
| 603 |
break;
|
| 604 |
case 6:
|
| 605 |
prob = seven_player(sorted);
|
| 606 |
break;
|
| 607 |
case 7:
|
| 608 |
prob = eight_player(sorted);
|
| 609 |
break;
|
| 610 |
default:
|
| 611 |
eventlog(eventlog_level_error,__FUNCTION__,"sorry, unsupported number of ladder opponents (%u)",opponent_count);
|
| 612 |
xfree((void *)rating);
|
| 613 |
xfree((void *)sorted);
|
| 614 |
return -1;
|
| 615 |
}
|
| 616 |
|
| 617 |
if (results[curr]==game_result_win)
|
| 618 |
delta = fabs(k * (1.0 - prob) / team_members); /* better the chance of winning -> fewer points added */
|
| 619 |
else
|
| 620 |
delta = -fabs(k * prob); /* better the chance of winning -> more points subtracted */
|
| 621 |
|
| 622 |
eventlog(eventlog_level_debug,__FUNCTION__,"computed probability=%g, k=%g, deltar=%+g",prob,k,delta);
|
| 623 |
|
| 624 |
info[curr].prob = prob;
|
| 625 |
info[curr].k = (unsigned int)k;
|
| 626 |
info[curr].adj = (int)delta;
|
| 627 |
info[curr].oldrating = rating[curr];
|
| 628 |
info[curr].oldrank = account_get_ladder_rank(players[curr],clienttag,id);
|
| 629 |
}
|
| 630 |
|
| 631 |
xfree((void *)rating);
|
| 632 |
xfree((void *)sorted);
|
| 633 |
|
| 634 |
return 0;
|
| 635 |
}
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