List of discussion boards
You are not allowed to post messages to this board. Minimum level of membership required for posting on this board is Brain Pawn.
Today I was curious to know "how big" this game is when compared to chess. I decided to start by counting the number of positions where there is a definite loss.
There are 100 squares on the board, and when 92 are occupied, it must mean white has lost since black made the last move.
How many positions like that are there?
Well there are 100!/92!8! ways to have 92 arrows shot, and 8!/4!4! ways for white to occupy the remaining 8 empty squares, and 4!/4! ways for black to fill in the last 4 squares for each of these positions.
100!/92!8! =
100x99x98x97x96x95x94x93/8x7x6x5x4x3x2 =
186,087,894,300
8!/4!4! = 140
4!/4! = 1
So the total is:
26,052,305,202,000
Over 26 trillion ways to lose if you have filled every square on the board.
(hide) If you need to find an older message from the selected user, click on his Profile and use the "show this user messages" link at the page top. (konec) (show all tips)