Knightf7mate: You see, it all has to do with promotion. Each time you promote a pawn, a whole new realm of nearly infinite possibilities exist. And when you consider 8 possible promotions of pawns into 6 possible pieces on each side, the number of possible moves overwhelms even a countably infinite chess computer. He went on with excitement in his voice. I learned that there are gambits that only a few humans have glimpsed. He showed me game by Naka with 8 knights on the board. See what I mean?
There are possibilities with this game that are beyond the horizon of even countably infinite computers.
Slowly, my game improved and I eked out a few draws here and there as I honed these new skills. Finally, I won my first game and now I can even beat Djahb-doo every now and then.
You mean he is better at chess than you? Who is he? I asked.
You haven’t figured it out? He is the first Grand Master, a first class Wizard of a chess player. It was he who invented this game long ago in India. Caisa came to him one night in a dream. She said humanity will kill itself one day if they don’t stop playing these stupid games of life and death. The next day he presented his king with the rules of chess. His only mistake was that he asked in return for a doubling of wheat on each square as payment. The king, not capable of seeing that many moves ahead agreed. When the king eventually learned that his kingdom would be bankrupt, he called the Wizard to account. When the Wizard said yes, he knew his request would surpass all the king’s wealth the king told him he truly made a bad move, one of ego and pride. He was banished from the kingdom and when he passed on, Caisa took him in.
Bha-bee, I said, isn’t there a mistake here? You told me that 6 pieces can be promoted. Aren’t there only rook, knight, bishop and queen that can be promoted?
Bha-be said, those are the rules you play by now, but they are not the rules as first relayed by Caisa.
In Her original conception, pawns may be promoted into all six pieces, even a King. The pieces may be placed anywhere on the board (except a pawn promoted to the 8th rank is considered an offer of a draw, which may be refused). If a pawn is promoted to a King, the current King is removed from the board and a new King may be placed anywhere else on the board except into check. Finally, the pieces on the back rank may be placed in any order by either side in this order: R, N, B, B, N, R, Q, K.
Wow I said. Those were the original rules?
Yes, Bha-be said, along with some rules about clocks which we are still only beginning to understand. Though I didn’t know it at the time, it was Caisa who inspired me to randomize the pieces and add increments of time to the clock.
When you put all those rules together, Caisa assured me that the number of possible positions exceeds Aleph Null, the first countably infinite number. Only she knows if it’s greater than Aleph Null and Aleph One. Sometimes I wonder if that number is 64 raised to the Aleph Null. Once I thought I saw Caisa and Djahb-doo playing on a 10x10 board.
I could only sit in silence as I contemplated this new realm of chess.
When at last my mind returned to the here and now, I asked Bha-be what lay in his future?
He said, my destiny was to continue to play my entire life span of 64 years. I did fulfil Caisa’s desire to expand the rules, for which she is grateful. Eventually, I am destined to eventually play Karpov, Kasparov, Anand, Kramnik, Carlsen, Nakamura, Karjakin, Caruana, and many, many others. Oh my dance card is nowhere near full.
Every generation, Caisa has a round robin of 64 players, each the winner of a round robin of 64 players, themselves the winner of a round robin of 64 players. It does keep me up late at night, discovering new variations and replaying prior games.
I asked him if there was a database of all games previously played.
He said there was a limited edition available. You are familiar with Knuth’s up arrow notation?
Yes, I said. It’s an exponention process of 2 raised a power of itself. 2 ! 4 means 2x2x2x2. 2!!4 means 2 to the 16th which is 65,536.
How much is 2 ! 8, he asked.
256, I said.
Very good he said. In that notation, the index of games listed in the limited edition is 2 !!!! !!!! 8. Nobody has been able to give the number the actual pages in the book. Only Caisa knows.
He showed me his watch, a gift from Caisa. It had 8 large numerals with 8 smaller marks within each octal.
Time for you to go. Very pleased to meet you. Send my love to everyone you meet. And remember - e4 is still best by test, even up here.
Finito