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