About superko:
Specifically, there is the so-called positional superko rule, in which case it is the position which cannot be repeated, or the situational superko rule, in which case it is not just the position, but also the situation (i.e. the player to play) which cannot be repeated.
In the A/B/C ko example above, under the situational superko rule, it is you who would break the rule if you captured A again, after one cycle. Under the positional superko rule, it would be your opponent who breaks the rule when capturing A (halfway through the cycle).
Eh, something is wrong here. -- RobertJasiek
Some Ko-rules allow one repetition, but not more.
The superko rule also has other implications; normally the board position repeats after a few moves (in the above example, after six moves). However, the sequences of moves, which produce the same board position, can be large and involve captures by both sides. As long as both parties are unwilling to play another line of play (they both consider the play which leads to the 'superko' optimal) then the superko situation will arise.
It should be noted that, under current Japanese rules, situations which would be prohibited by a superko rule will lead to a no-result (not jigo), and not to a loss for the player who plays the move.
(Actually, under Japanese rules the no-result is pronounced only upon agreement by the players. --Bob Myers)
However, the positions are very rare. I have never seen one in real life. When they do occur, they are normally talked about a lot - because they are so rare. If either player is leading enough to discard a group here then the game may be continued. Otherwise, if the winner is determined by who kills here, they have to fight three ko. Black captures at a, White at b, Black at c and then White has to capture at a if rules allow a return to the initial position.
-- HolIgor
For more information about the various rulesets in general and ko rules in particular, take a look at Robert Jasiek's homepage
-- Morten Pahle
Uhhh.... Just to let you guys know... 'b' isn't a ko... If white plays at b, it captures that whole black group. -God Ginrai
Bill: Err. White would win the triple ko, that's all.
Later: Somebody altered the diagram caption to say that Black was to play. That is not necessary. It is still a triple ko, regardless of who has the move. The same is true for a simple, direct ko. One player with the move can win the ko, the other player can take the ko.
We could even be in the middle of a superko fight. White might have taken the triple ko, capturing a stone at a, and Black might have just played a ko threat.