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Namik, some very intelligent and constructive ideas. I'd like to see these ideas further elaborated and expanded upon (and more applications and examples). Great beginning for very important and intriguing discussion.
This all needs elaboration. It is too cryptic to make heads or tails of.
How does one figure out the first number in the equation, the pieces influence?
Total Pieces influence on the centre of the empty board ( White or Black only, if they are symmetrical) without King and pawns = f.exp.(Orthodox Chess) - Knight = 2x8, Bishop = 2x13, Rook = 2x18, Q =27 ,Total = 97. Empty squares in the beginning of the game = 32. Then for Orthodox Chess S = 97/32 =3.03.
This does not determine whether a game is good or bad, only that it is different from another. And I know that the argument will be made that the Mad Queen variant could represent a standard by which to evaluate other games. But that is merely establishing a arbitrary baseline for comparison and doesn't determine whether the games being compared are good or bad. It could be argued that a game with very weak and very few pieces located on a very large field might represent a negative. But this evaluation would not take into account the in-game rules, such as Shogi drops. The only claim that could be made is that this formula is able to generate a given value for a game. The application of this value would probably be best in conjunction with other considerations of the evaluated game. I would be curious to see evaluation of Shogi and Xiang Qi in addition to the Mad Queen variant. Since these three might epitomize the best in Chess, their quantification and comparison may render some interesting methods by which to evaluate other games. Though these games may resist proper comparison since each have unique aspects.
Of course, this method doesn`t show us which game is better. All Chess variants are good enought. It is just for comparison analyses. If somebody like to play Orthodox Chess then he can choose something similar (pieces density, pieces influence and so on) with using this method.
Even if the game generates a value, using this formula, which is close to or even exactly like that of the Mad Queen variant, it would not necessarily mean that the game is in any way similar. The only thing that this formula would note is a ratio between the piece power/density and field size. This value is really of little use without further considerations. I once advocated that the difference in the piece-types, or the potential exchange ratios, might have an influence in the game. A game which is populated with pieces of similar value offer little chance for advantage during play. While a game with a large variety of piece-types would offer a greater opportunity for advantage during play. Even this would not be the only consideration when evaluating a game. There was a old thread which covered this particular subject. Does anyone know its title and how to access it? Never mind, I found it: http://www.chessvariants.org/index/listcomments.php?limitby=75&subjectid=Game+Design
That previous discussion discusses some other interesting ratios and comparisons. Perhaps Namik would be interested in adding them to this essay and we could continue here where that discussion left off.
Some of the points made here may echo points I made in my article On Designing Good Chess Variants.
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