ODDS GAMES

 

Giving odds (giving a handicap) was popularly used in chess games of the 18th and 19th centuries, when chess was often played for money stakes, in order to induce weaker players to play for wagers.  Odds games are often used in modern times to equalize the playing field against strong computer programs.  Odds games compensate for the difference in skill between two players and thus enable a weaker player to have a chance of winning against a stronger one.

 

There are many kinds of such handicaps:

 

1. Material odds

2. Extra moves (i.e., the weaker player can play the first two or more moves at the beginning of the game)

3. Extra time for moving within the time control

4. Weighting of results (such as "draw odds," the counting of a draw as a loss for the odds-giver)

5. Physical restrictions (such as blindfold games)

6. Special conditions (such as requiring the odds-giver to achieve victory in a particular way)

 

Various permutations of these are also possible.

 

The possibility of Camelot odds games was first mentioned by WCF member Pete Maller.

 

Using handicap #6, the stronger player could be disallowed from winning by castling two of his pieces (that is, he could be forced to capture all of his opponent's pieces in order to win).  Or the weaker player could be allowed to win by only castling one of his pieces.  Or the stronger player could be prohibited from using a Knight's Charge.  There are many possibilities.

 

Handicap #1 would of course be the most common type of Camelot odds game.  Following is a table of all material odds giving choices.  It makes use of the current Knight-Man Valuation formula:

 

N = 1 + (X - 1) ln(P) / ln(14)

 

Where: The value of a Man is 1.0000, N is the value of a Knight, P is the total number of uncastled friendly pieces, and X is the user-defined value of N when P equals 14 (at the start of the game).  You can learn more about the Knight-Man Valuation formula here.

 

For this table, X was set at 2.2500.

 

                   
  ODDS
RECEIVING
SIDE
KNIGHTS
ODDS
RECEIVING
SIDE
MEN
TOTAL
ODDS
RECEIVING
SIDE
STRENGTH
(MAN=1)
ODDS
GIVING
SIDE
KNIGHTS
ODDS
GIVING
SIDE
MEN
TOTAL
ODDS
GIVING
SIDE
STRENGTH
(MAN=1)
ODDS
RECEIVING
SIDE
ADVANTAGE
(MAN=1)
COMMENT  
  4 6 14.36251435 2 10 14.35397183 0.00854251 Two Knights for four Men  
  4 8 16.70794367 3 10 16.64469539 0.06324828 One Knight for two Men  
  1 10 12.13577263 4 4 11.93974303 0.19602961 Six Men for three Knights  
  0 10 10.00000000 4 2 9.39469599 0.60530401 Eight Men for four Knights  
  4 3 10.68675232 0 10 10.00000000 0.68675232 Four Knights for seven Men  
  4 5 13.16289664 1 10 12.13577263 1.02712401 Three Knights for five Men  
  3 10 16.64469539 4 7 15.54309053 1.10160486 Three Men for one Knight  
  4 10 19.00000000 4 9 17.85959386 1.14040614 One Man  
  4 7 15.54309053 2 10 14.35397183 1.18911870 Two Knights for three Men  
  2 10 14.35397183 4 5 13.16289664 1.19107520 Five Men for two Knights  
  4 9 17.85959386 3 10 16.64469539 1.21489846 The Exchange: one Knight for one Man  
  1 10 12.13577263 4 3 10.68675232 1.44902031 Seven Men for three Knights  
  4 4 11.93974303 0 10 10.00000000 1.93974303 Four Knights for six Men  
  0 10 10.00000000 4 1 8.04926667 1.95073333 Nine Men for four Knights  
  4 6 14.36251435 1 10 12.13577263 2.22674172 Three Knights for four Men  
  3 10 16.64469539 4 6 14.36251435 2.28218105 Four Men for one Knight  
  4 10 19.00000000 4 8 16.70794367 2.29205633 Two Men  
  4 8 16.70794367 2 10 14.35397183 2.35397183 Two Knights for two Men  
  4 10 19.00000000 3 10 16.64469539 2.35530461 One Knight  
  2 10 14.35397183 4 4 11.93974303 2.41422881    
  1 10 12.13577263 4 2 9.39469599 2.74107664    
  4 5 13.16289664 0 10 10.00000000 3.16289664    
  0 10 10.00000000 4 0 6.62649535 3.37350465    
  4 7 15.54309053 1 10 12.13577263 3.40731790    
  4 10 19.00000000 4 7 15.54309053 3.45690947    
  4 10 19.00000000 3 9 15.53095775 3.46904225    
  3 10 16.64469539 4 5 13.16289664 3.48179875    
  4 9 17.85959386 2 10 14.35397183 3.50562202    
  2 10 14.35397183 4 3 10.68675232 3.66721951    
  1 10 12.13577263 4 1 8.04926667 4.08650596    
  4 6 14.36251435 0 10 10.00000000 4.36251435    
  4 8 16.70794367 1 10 12.13577263 4.57217104    
  4 10 19.00000000 3 8 14.40731790 4.59268210    
  4 10 19.00000000 4 6 14.36251435 4.63748565    
  4 10 19.00000000 2 10 14.35397183 4.64602817    
  3 10 16.64469539 4 4 11.93974303 4.70495237    
  2 10 14.35397183 4 2 9.39469599 4.95927584    
  1 10 12.13577263 4 0 6.62649535 5.50927728    
  4 7 15.54309053 0 10 10.00000000 5.54309053    
  4 9 17.85959386 1 10 12.13577263 5.72382122    
  4 10 19.00000000 3 7 13.27188576 5.72811424    
  4 10 19.00000000 2 9 13.27154527 5.72845473    
  4 10 19.00000000 4 5 13.16289664 5.83710336    
  3 10 16.64469539 4 3 10.68675232 5.95794307    
  2 10 14.35397183 4 1 8.04926667 6.30470516    
  4 8 16.70794367 0 10 10.00000000 6.70794367    
  4 10 19.00000000 2 8 12.18125717 6.81874283    
  4 10 19.00000000 1 10 12.13577263 6.86422737    
  4 10 19.00000000 3 6 12.12217248 6.87782752    
  4 10 19.00000000 4 4 11.93974303 7.06025697    
  3 10 16.64469539 4 2 9.39469599 7.24999940    
  2 10 14.35397183 4 0 6.62649535 7.72747648    
  4 9 17.85959386 0 10 10.00000000 7.85959386    
  4 10 19.00000000 1 9 11.09062859 7.90937141    
  4 10 19.00000000 2 7 11.08144832 7.91855168    
  4 10 19.00000000 3 5 10.95480727 8.04519273    
  4 10 19.00000000 4 3 10.68675232 8.31324768    
  3 10 16.64469539 4 1 8.04926667 8.59542872    
  4 10 19.00000000 1 8 10.04072416 8.95927584    
  4 10 19.00000000 0 10 10.00000000 9.00000000    
  4 10 19.00000000 2 6 9.96987151 9.03012849    
  4 10 19.00000000 3 4 9.76506424 9.23493576    
  4 10 19.00000000 4 2 9.39469599 9.60530401    
  4 10 19.00000000 0 9 9.00000000 10.00000000    
  4 10 19.00000000 1 7 8.98493576 10.01506424    
  3 10 16.64469539 4 0 6.62649535 10.01820004    
  4 10 19.00000000 2 5 8.84337616 10.15662384    
  4 10 19.00000000 3 3 8.54602200 10.45397800    
  4 10 19.00000000 4 1 8.04926667 10.95073333    
  4 10 19.00000000 0 8 8.00000000 11.00000000    
  4 10 19.00000000 1 6 7.92168808 11.07831192    
  4 10 19.00000000 2 4 7.69734800 11.30265200    
  4 10 19.00000000 3 2 7.28695000 11.71305000    
  4 10 19.00000000 0 7 7.00000000 12.00000000    
  4 10 19.00000000 1 5 6.84867400 12.15132600    
  4 10 19.00000000 4 0 6.62649535 12.37350465    
  4 10 19.00000000 2 3 6.52463334 12.47536666    
  4 10 19.00000000 0 6 6.00000000 13.00000000    
  4 10 19.00000000 3 1 5.96987151 13.03012849    
  4 10 19.00000000 1 4 5.76231667 13.23768333    
  4 10 19.00000000 2 2 5.31324768 13.68675232    
  4 10 19.00000000 0 5 5.00000000 14.00000000    
  4 10 19.00000000 1 3 4.65662384 14.34337616    
  4 10 19.00000000 3 0 4.56108624 14.43891376    
  4 10 19.00000000 2 1 4.04072416 14.95927584    
  4 10 19.00000000 0 4 4.00000000 15.00000000    
  4 10 19.00000000 1 2 3.52036208 15.47963792    
  4 10 19.00000000 0 3 3.00000000 16.00000000    
  4 10 19.00000000 2 0 2.65662384 16.34337616    
  4 10 19.00000000 1 1 2.32831192 16.67168808    
  4 10 19.00000000 0 2 2.00000000 17.00000000    
  4 10 19.00000000 0 1 1.00000000 18.00000000    
  4 10 19.00000000 1 0 1.00000000 18.00000000