When playing a handicap game of h stones, white should be compensated for each of black's handicap stones (excluding the final one). So white gets h - 1 points compensation.
Compensation in even games, (or komi as it is usually known - from the
japanese), may be set to half a point (or zero), using the 'You cut the cake,
I'll choose which piece' rule.
In other words, who plays black is determined randomly. Black plays their first move, then white chooses whether to play as black, or as white.
Ideally, the game should end after both players have played the
same number of moves (including passes). So if white passes first, then
black passes, then white should pass again (because black played first).
In some cases this may result in white losing the game by half a point. In that case the result could be declared drawn.
Superko and board history
A superko rule implies the existence of a board history (even if only in the player's heads). The creation of a board history can be formalised as follows: After a player has moved, this board position goes into that player's board history.
Superko and passing
When a player passes, does that clear the board history? Maybe it should clear the board history only for the player who passes. So only those board positions where the other player just played are kept in someones board history. Somewhere in the 1 by 5 'tree' is a case where the board looks the same but a different person is to move.
Taking account of symmetries, the total number of board configurations can be calculated exactly using Polya Enumeration. Its about 3361/8. exact number
The number possible if colour toggling is dreamt of, can be bounded using similar methods. exact numbers do you want to know more?
Superko and symmetry
Is playing a move and rotating the board 180 degrees a way of avoiding superko restrictions? Some small board 'solutions' (1x5?) do not take this question into account.
eg. --x-- -> -ox-- -> x-x-- -> x-xo- -> x-x-x -?> -ox-x
notion from deep within puzzling discussion
The explanation of the rules may be more entertaining than the game itself
A deeply perverted attempt at the categorisation of balanced forms