[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Single Comment Geometric sequence of Chess Games. Chess variants as large as you want.[All Comments] [Add Comment or Rating]George Duke wrote on 2010-08-06 UTCHow many Bishops? Black's generalization of Karakus is a kind of power series, exponential, because he can as well use 3x3 next after or skipping 2x2, which expands each space just from 1 to 4 pieces/spaces. [Reference is to Quadd Shogi Chess and to Giant Chess.] In 3x3 there are nine Queens where there was one, and so on. With all squares three-by-threes, an 8x8 board becomes 24^2, 576 squares. They are like Frolov's moving palace nine-space, out of one or as if one; but in pure Black each of the nine has the same residual piece-type without variation. That is the methodology of Karakus and the Black twosome, incidentally specified by that Xiangqi-size restricted area having 3 its specific instance. Missoum's approach here differs still in growing boards. 'N=3' is the first nontrivial case, where we find ourselves today; or as Missoum writes, ''The reader may have found extensive literature about the 8x8 chess game.'' Some systems characterize by period-doubling towards Chaos abruptly, but Chaos(or Chess) can prove manageable mathematically. Let's say the play is rather on a Missoum board n=8. You want to know how many Bishops you have. There is the formula used in the first (2005) of these three comments, taken from Missoum's text, arriving at 126 Bishops with n=8. (The example is Missoum's late in the article.) Why? Knowing the number of Bishops and full piece disposition allow interim values to be calculated, settled on, and adjusted player and computer. As for Knights, closely following or duplicating Bishop in numbers, notice Missoum's method of extending their reach with longer leap-lengths available by board sizes emerged. Sustainable growth; where governments fail we succeed.