Corr. There are 20 possible first moves in chess.
A lot more first moves than go.
#32, what? o_O
There are literally hundreds of possible first moves in Go.
There are literally hundreds of possible first moves in Go.
If a move means one white, one black, there are 361x360 = 129,960 first moves in Go. Compared to 400 chess moves.
Another interesting number is the possible configurations. A close estimation is that there are 10^170 possible legal board configurations in Go. This is approximately 10^50 x the number of possible chess games! I repeat, there are more possible Go figurations than there are possible games in chess. The number of possible games in Go is an open question.
Another interesting number is the possible configurations. A close estimation is that there are 10^170 possible legal board configurations in Go. This is approximately 10^50 x the number of possible chess games! I repeat, there are more possible Go figurations than there are possible games in chess. The number of possible games in Go is an open question.
#33 I was thinking of othello. Go definitely looks difficult. I have only played Othello.
Interestingly , To calculate the possible moves in go one has to consider the symmetry of the board, since all four corner's are symmetric , the first play in go probably has 19x19/4 possible moves.
#36
Yes, but I think there is more symmetry than that. The number of possible half-moves, i.e. black's move, is: 55. Those 55 symmetrically unique points break down in the following way. 1 point, tengen, is totally unique. 9 + 9 points, from tengen to the corner, and from tengen to the side, can each be found in 4 places on the board, and the remaining 36 points forming a triangle occur in 8 places on the board when symmetry is taken into account.
I haven't checked this thourougly but I count the number of possible first moves as:
1*54 (tengen + white's move) + 9*188 (the 9 points along along the line from tengen to the side +white's move, I count 188 unique white moves because of mirror symmetry) +9*188 (analogous reasoning, this time the 9 points from tengen to the corner) + 36 * 360 (the remaining triangle points + white's move of which there are 360 unique points) = 54 + 18*188 + 36*360=16398 unique first moves. This cuts down the number of unique first moves to about 12.6% of the initial number given. This is reasonable because of the "8-symmetry", the four symmetry lines of the plane divides the Go board into roughly 8 regions). However googling these numbers is disconcerting, since it turns up nothing. If I'm wrong, *shrug*. Correct me!
Yes, but I think there is more symmetry than that. The number of possible half-moves, i.e. black's move, is: 55. Those 55 symmetrically unique points break down in the following way. 1 point, tengen, is totally unique. 9 + 9 points, from tengen to the corner, and from tengen to the side, can each be found in 4 places on the board, and the remaining 36 points forming a triangle occur in 8 places on the board when symmetry is taken into account.
I haven't checked this thourougly but I count the number of possible first moves as:
1*54 (tengen + white's move) + 9*188 (the 9 points along along the line from tengen to the side +white's move, I count 188 unique white moves because of mirror symmetry) +9*188 (analogous reasoning, this time the 9 points from tengen to the corner) + 36 * 360 (the remaining triangle points + white's move of which there are 360 unique points) = 54 + 18*188 + 36*360=16398 unique first moves. This cuts down the number of unique first moves to about 12.6% of the initial number given. This is reasonable because of the "8-symmetry", the four symmetry lines of the plane divides the Go board into roughly 8 regions). However googling these numbers is disconcerting, since it turns up nothing. If I'm wrong, *shrug*. Correct me!
intuitively it sounds correct to divide by 8, analogous to what they do in tablebases
that is, for every position (without pawns) there are 7 'identical' positions
that is, for every position (without pawns) there are 7 'identical' positions
Even with the large number of theoretical first moves, within the professional Go world, there are less "reasonable" first moves than chess. Professionals will basically only play 4-4, 3-4, 5-4, or 3-3, and even 3-3 is extremely rare.
This topic has been archived and can no longer be replied to.