All known forced Go cycles are impossible with this rule. The nature of the rule itself suggests that forced cycles are either impossible or astronomically rarer than they are in Go when the superko rule is not used. Ko fights proceed in a similar way to those of Go, with the difference that captures and moves answered by captures aren't valid ko threats. On the other hand, snapbacks are not possible. Under the unrefined rule, it is necessary to make a ko threat before any consecutive capture occurs.
If a play causes a board position to be repeated, the game will end in a draw. If forced cycles are indeed impossible, this will require cooperation between the players, which shouldn't occur in actual play.
Luis Bolaños Mures designed Stoical Go in September, 2012. The game is available to play with the Zillions of Games program. All odd-sized boards from 7x7 to 19x19 are implemented, as well as the option to use neutral blocking pieces to change the shape of the board.
Looking for features present in all known forced Go cyclical sequences and then banning moves with one of those features is one of several ways to produce Go-related games without forced cycles. Albeit impractical, the minimally restrictive game produced by this method would consider all those features at once and only forbid those moves that don't negate any of them.
A sample list of such features follows. As new types of cycles are found, the list may be reduced.
This list could also be useful, albeit rarely, to identify potential cycles in the course of a game.
- At least one series of two consecutive captures (one by each player) occurs. This is the feature used in Stoical Go.
- At least once a capture by one player is immediately followed by an enemy placement inside one of the player's territories. A territory is defined in its strict sense, i.e. a maximal set of orthogonally adjacent empty points only constitutes a territory of one color if no point in it is orthogonally adjacent to a stone of the opposite color.
- No move results in the capture of more than four stones.
- No capturing group is bigger than four stones. A capturing group is the group of a capturing placement (not the other groups that take part in a capture).
- No capturing domain is bigger than four stones. A capturing domain is the domain of a capturing group. A domain of one color is a maximal set of orthogonally adjacent points that are not occupied by stones of the opposite color.
- No move results in the capture of more than one group.
- No snapbacks occur. A snapback is defined as a capture of a single stone by extending an already existing group followed by the capture of said capturing group by placing a stone on the just vacated point, provided that said stone can't be immediately captured again.
- No individual captures with the features of the first or second capture in a snapback occur.
- At least one "strict disturbing capture" occurs. A strict disturbing capture is defined as a capture of exactly one enemy group in such a way that a) more than one friendly group is adjacent to the area vacated by the capture, and b) all liberties of the capturing group are part of the area vacated by the capture. Note that strict disturbing captures are topologically equivalent to those affected by the basic ko rule.
- At least one "disturbing capture" is immediately answered by the opponent with another. A disturbing capture is either loose or strict. A loose disturbing capture is the same as a strict disturbing capture except that a) the capturing group is made of exactly one stone and has exactly one liberty before any removals, and b) said liberty is part of an empty area that isn't adjacent to any other friendly stones. An empty area is a maximal set of orthogonally adjacent empty points.
- No captures other than "disturbing captures" occur.
- All captured groups are "open lines". An open line is a set of stones such that none of them is adjacent to more than two other stones in the set and at least one of them is adjacent to less than two other stones in the set.
- All capturing groups and all capturing domains are open lines. A capturing group, again, is the group of a capturing placement.
- At the moment a stone is placed (before any removals), the domain it belongs to is always an open line. This is true for capturing as well as non-capturing placements.
The defining rule of a minimally restrictive soft finite game that considered all these features could be formulated as follows:
You can't make a disturbing capture of less than five stones with a capturing domain smaller than five stones immediately after a disturbing capture of less than five stones with a capturing domain smaller than five stones made by your opponent, unless a) both are loose disturbing captures, b) in at least one of them either the capturing domain or the captured group is not an open line, or c) at least one of the two captures has the features of the first or second capture in a snapback.
(For a future revision: expand definition of disturbing captures to include mention of sizes and open lines, and possibly include only basic features on the list and leave definition of disturbing captures for the summation rule.)
tapir: You are aware that you will have many "right to capture" fights? Even snapbacks are impossible in your variant.
luigi87: Not that many, but yes, often a player will have to use a ko threat in a given sequence to earn the right to capture back. The same happens with snapbacks as well. This feature adds a global positional factor to the evaluation of local fights, which needn't be a bad thing. As for snapbacks, they can be explicitly allowed without reintroducing forced cycles into the game.
luigi87: Eternal life is not possible in Stoical Go. in the entry's example sequence is an immediate re-capture.
Sandra: [Cooperative cycle (not a forced cycle):]
Slarty: It's still (technically) needed to know what happens if a repeating position is played, to define the game. It could be a source of a little confusion though I think the page is clear. (would imagine borrowing chess's threefold repetition = draw in a very thorough description). Anyway, the game should be pretty good. It's difficult to make it the same as Go (in under ten words, at least) - because there can be snapbacks of any size.
A funny variant idea (doesn't need its own page) is to forbid the last player who captured (or the one with the most prisoners) from capturing again. It's sort of like the doubling die mechanic in backgammon.
luigi87: Yes, it reminds me of a set of bizarre finite Go variants that I discussed a while ago on Life In 19x19. In the most basic one, once a player makes a capture for the first time, that player can’t create any more groups for the rest of the game. It creates an intriguing build up of tension prior to the point when one of the players decides to make a capture. As for repetitions, you're right. I've just added a rule to handle them.
luigi87: Eternal life and round robin ko are possible under that rule. This variant is a little similar to one variant related to simultaneouness I was thinking about, that was this: White cant move to a place that had an piece on previous turn and cant capture an piece that was included on previous turn or that make an group with a piece added on previous turn. Game end after 2 consecutive passes if the last pass was a white one, or 3 passes (white pass will still be the last one.