Forum for Force (Mathematics)
Definition of "play-force"? [#1606]
I find these definitions difficult to understand. The definition of "force" makes sense to me, but the others are unclear.
Let's begin with "play-force". The currently proposed definition is: A player can play-force something if he can force the something so that until then he makes only plays. The construction "...so that until then..." confuses me.
My best guess is that what is meant is:
Player X can play-force condition C if (1) he can force C; and (2) a strategy exists for forcing C in which player X does not pass.
Is this correct?
If something already exists on the board, is it correct to say that (vacuously) either player can play-force (or just force) that something?
Xela, I like your definition:
In my understanding "play-force" is flowery wishy-washy for the verb "force".
As the "play-force" happens is explained by "force" 5 words later, which happens during a game anyway ,
the "play" seems indeed to indicate the absence of PASSES.
However, if PASSES are part of the game, then PLAYing comprises PASSes,
which renders the invented word unsuitable for the intention.
Perhaps "NoPASS-force-play" ?
Please accept that my terminology relies on the definition "A move is either a (board-)play or a pass." and that it does not rely on informal phrases like "playing". You can throw-in informality with the purpose to confuse us but this does not question my definitions but rather one should question why you do not want to distinguish between informal language and formal language.
BTW, informal language speaks of "approach move" because the term is older than the rules experts' agreement in about 1997 to use "A move is either a (board-)play or a pass." whenever possible. To keep confusion small, I use "approach play" because it is always a "play" and never a "pass" that is used for approach.
Similarly, you should start using informal phrases like "moving" instead of "playing" when you mean "making plays or passes".
It is:
Player X can play-force condition C if
- (1) he can force C using a strategy S,
- (2) T1 is the initial moment,
- (3) Tc is the first moment when X has achieved C,
- (4) from T1 to Tc, X makes only plays.
If plays and passes are the only move types, then (4) implies that, from T1 to Tc, X does not make any pass.
Note that the opponent may make passes though.
If something already exists on the board, then it depends on the precise details of the definition of "force" whether the player can play-force the something. Here I have referred to the ![[ext]](images/extlink.gif)
Japanese 2003 Rules / version 35a. Let us find out:
- "force" uses "if there is at least one hypothetical-strategy of his".
- A player's "hypothetical-strategy" is "a set of one or more than one left-parts of hypothetical-sequences".
- A "left-part" of a hypothetical-sequence is "either the whole hypothetical-sequence or a part that consists of one or more than one successive hypothetical-moves of it and starts with its first hypothetical-move."
- So a left-part consists of at least one (hypothetical-)move.
- So a (hypothetical-)strategy implies at least one move.
- So force relies on making at least one move.
- So play-force relies on making at least one play.
- So if something already exists on the board, then neither player can play-force it.
Thanks for your comments. This is my first serious attempt at studying formal rules, and I hope to understand these definitions soon! However, it is not yet clear to me.
Are you assuming that moment Tc is distinct from T1? If we admit the possibility that Tc=T1, then I don't see how your definition differs from the one I posted above. On the other hand, if Tc=T1 is forbidden, this needs to be explicitly stated.
"If something already exists on the board, then neither player can play-force it"--can we discuss with reference to two examples?
![[Diagram]](diagrams/33/040796d5a41da202194648e67303b699.png)
![[Diagram]](diagrams/51/09ac08a33f3c884a23170d7614704e01.png)
T1 cannot equal Tc because "force" requires at least one move (as I have explained above).
Your example 1: yes.
Your example 2: A two-eye-formation does not exist on the board. Two-eye-formation is defined, e.g., here or here or here as
A two-eye-formation is a set of one or several strings of the same player and exactly two empty intersections so that each of the strings is adjacent to each of the two intersections, none of the strings is adjacent to another empty intersection, and each of the two intersections is adjacent only to the strings.
Thank you for your patient answers! After thinking about your comments, and looking more carefully at the Japanese 2003 rules, it is now starting to make sense to me.
I think a lot of the potential for confusion stems from the fact that words such as "pass", "move", "force" and "strategy" are used here in formal ways that may differ subtly from some people's intuition. Perhaps it is worth adding a sentence or two to the beginning of the main page to make this clear.
Considering the fact that a "strategy" is necessarily non-empty (this was not initially clear to me), it still seems to me that the two definitions of "play-force" given so far in this forum are equivalent. Would you consider replacing the definition on the main page with either of these formulations?
The X and C definition is slightly different from the original definition, at least I fear this might be the case. (I lack time to explain this though.) Also the original as such should not be hidden. Rather than replacing it, you might add the other definition as an alternative.
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