# Cycle

Keywords: Ko

A cycle is a move sequence that starts and ends at the same position. If at the end of the cycle it is the same player's turn as at the start, it is also a situational cycle (repeats the same situation). If cycles are allowed without restrictions on them, it is possible for a game to go on indefinitely.

Although it is easy to play cycles if both player cooperate in creating them, such cycles are not interesting, because it will be to the benefit of one of the players to break the cycle and play elsewhere. More interesting is to consider those cycles that can be forced by one player. Such cycles would allow a player that is behind to prevent a loss by forcing the game to go on indefinitely.

Such cycles are rare, and the only one that is seen regularly in actual play is the basic ko. repeating the position in a basic ko is prohibited under all rule sets.

Longer cycles, such as triple ko, eternal life or round-robin ko are not prohibited by all rule sets. This is probably because they are so rare that they were never considered. In rule sets that allow them, a game in which they occur is usually declared "no result", which is sometimes ruled as jigo (tie), and sometimes replayed.

We can classify cycles by the number of moves that are played before the position repeats. Shorter cycles are more common than longer cycles, and cycles with an even number of moves are far more common than those with an odd number of moves. If multiple cycles occur on the board simultaneously, they may affect each other, and combine to form a larger cycle (triple ko is an example of this).

# One move cycle

The 1 move cycle is mostly a theoretical construct. In most rule sets it is impossible to play a one move cycle.

Single stone suicide

A single stone suicide constitutes a one move cycle. This can only occur in rule sets that allow suicide (but do not use positional superko) and is completely pointless even then, unless one wishes to pass without the other being allowed to end the game immediately.

# Two move cycle

The two move cycle is the most common cycle, as this is the basic ko.

Basic ko

The basic ko, prohibited under all rule sets, repeats the position after two moves. Cycles that are longer than this are usually called long cycles

# Three move cycle

Send two, return one

The sending two, returning one sequence is an example of a three move cycle. Under territory scoring rules, this sequence constitutes a loss for white, as white has give two prisoners to black's one. Under area scoring, it does not constitute such a loss, but still loses sente

If positional superko is used, is prohibited. This might, in exceptional circumstance, lead to counter-intuitive results

Under rules that use area scoring, but that do not prevent long cycles, this pattern would allow the white player to force the game to go on indefinitely, unless the black player is willing to take a local loss (in the above case, by ignoring and allowing white to capture, turning the seki into a live white group and losing black 6 points). Under territory scoring rules, this is not the case, as each repetition of the cycle gains black points. Black can then play through the cycle a few times until he has gained enough points to compensate for the local loss.

# Four move cycle

Eternal Life

The sequence known as eternal life constitutes a four move cycle.

If either positional or situational superko is used, is prohibited in the above sequence. Under basic ko rules, this cycle could repeat indefinitely.

# Five move cycle

Send three, return two

This sequence, known as sending three, returning two, shows a five move cycle. As with all cycles that have an odd number of moves, this sequence loses sente. Unlike the sending two, returning one scenario however, is mandatory for black as the only way to avoid losing his group.

Under positional superko rules, is prohibited.

# Six move cycle

Triple ko

This basic triple ko example shows a six move cycle (actually a combination of three 2-move cycles) Under superko rules, is prohibited.

Eternal ko is also a six move cycle.

# Eight move cycle

Round robin ko

The round robin ko constitutes an eight move cycle.

The quadruple ko is also an eight move cycle.

# Ten move cycle

Triple ko stones cycle

The triple ko stones cycle (not the same as triple ko) constitutes a ten move cycle. Mentioned at http://home.snafu.de/jasiek/ko.pdf.

Shimada's ko also constitutes a ten move cycle. Mentioned at http://www.britgo.org/rules/molasses.html and http://harryfearnley.com/go/shimada/intro.html.

Round robin ko (an eight move cycle) and Molasses ko (an eight move sequence, but not a cycle in itself) can both be made into ten move cycles by combining them with basic kos.