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Subject: Is it possible to have a pure abstract strategy game where no side is favored and it doesn't draw? rss

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Russ Williams
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docreason wrote:
Gipf Series was an example of what I was talking about. The idea is changing the environment of the game, by what is not present, by playing a subgame to see if such a change gets added. Rather than argue over whether or not a new piece coming into game is considered a new rule, let's make the change an actual change to the rules during play, that wasn't in the game originally. Such a rules change happens by playing a subgame to win the right to do so. In this case, is it possible doing this to end up with a game where neither side has a theoretical advantage and also there are no draws?

In short, theoretically, it it possible to have a pure abstract strategy game where no side has an advantage, and also no draws, in the cases where the rule set is infinite and not finite?

OK, so you're talking about playing a subgame for the right to really change the rules, not just playing a subgame which has a well-defined effect already defined in the existing rules?

That's rather an open-ended "brain-stormy" idea which needs to be more clearly specified.

What kind of rule changes are permitted? Does the game have well-defined rules about what possible rule changes are (like in Fluxx), so that it is still a well-defined "meta"-system? I.e. the "active rules" in Fluxx change during the game as Rule cards get played and removed, but in a sense that is just twiddling data in a pre-defined unambiguous way defined by the "real" fundamental game rules, which do not change.

Or are the possible rule changes undefined and open-ended? If so, then can I start a subgame for the right to change the rules to include a new rule that "If I win a subgame, then I immediately win the entire main game"? Or even to introduce a new rule that "The player named Russ immediately wins"?
 
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russ wrote:
OK, so you're talking about playing a subgame for the right to really change the rules, not just playing a subgame which has a well-defined effect already defined in the existing rules?

That's rather an open-ended "brain-stormy" idea which needs to be more clearly specified.
You may be talking about Lemma
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mrraow wrote:
russ wrote:
OK, so you're talking about playing a subgame for the right to really change the rules, not just playing a subgame which has a well-defined effect already defined in the existing rules?

That's rather an open-ended "brain-stormy" idea which needs to be more clearly specified.
You may be talking about Lemma
That Lemma sounds like an interesting game which might the sort of thing that Richard is getting at in a way.

It makes me ponder: the proposed new rule should surely depend only on the game state itself and not on external factors (analogous to the "Spock Rule" in Zendo). I.e. surely the following would not be valid proposed new rules (right?) :

* "Only a player with a beautiful face may place a red piece."

* "A red piece can only be played if the player has not yet coughed during the game."

* "A red piece can only be played if the radio is playing a commercial."

Or I guess such rules would be allowed in the "wacky party game" version of the game and not in the "serious abstract strategy game" version of Lemma?


Also the proposed new rule, even if depending purely on the game state, must surely be well-defined and objectively verifiable. E.g. what about rules like:

* "If the current number of red pieces is N, then a red piece can only be played if the (googol+N)th decimal digit of pi equals 0." (Well-defined and verifiable in principle, but not in practice.

* "A red piece can only be played if the Riemann Hypothesis is true." (Presumably well-defined but a difficult question whose answer unknown so far.)

* "A red piece can only be played if the next piece played after it is blue." (Hmm, is this a legitimate rule or a "time travel paradox" sort of thing? I have no idea...)


If we imagine that the proposed new rules must conform to some obvious "common sense" type objective and practical computability restrictions, such a game might be viewable as similar to Fluxx, but simply with an infinite number of "cards" or "boolean flags" marking which of the (infinitely many possible) rules are "in effect". I.e. imagine an infinite set of rules R like:
1. A red piece can be only be played if the current total number of red pieces is even
2. A red piece can be only be played if the current total number of red pieces is odd
3. A red piece can be only be played if the current total number of red pieces is greater than 10
...
Then there is a well-defined function f from Powerset(R) (the set of all subsets of R) x R - > {valid, invalid} defining for every possible set of rules which might be simultaneously in effect and for every possible proposed new rule whether or not it is valid.

Viewed through that lens, it's formally not a game where the rules are being changed, but a game where you're simply marking additional rules as being in effect. Only informally is it a game where the rules are being changed.

Mere semantics? I dunno. It boils down to whether you view the concrete rules like "A red piece can be played" as fundamental game rules or as "mere data".

A bit like how in some programming languages, programs are themselves simply data which can be manipulated and interpreted.

All this mathematical philosophizing aside, the original question remains whether such a game could somehow favor no side if it were drawless. My hunch is that theoretically that is impossible, exactly because of the reasoning that in effect these new rules can simply be viewed as manipulating the game state, if we consider the game state to include a boolean vector of which rules (out of the set of all possible rules) are in effect.

E.g. if we look at the "simple example" of Fluxx and imagine some combinatorial variant instead of the standard random variant of Fluxx: people would informally say that "the rules are constantly changing" in combinatorial Fluxx, yet any combinatorial version would clearly still be combinatorial and thus (by the known elementary theorem of combinatorial game theory) favor one player (if draws are not possible).

If we generalize to an infinite rule set, I see no reason to assume that result would change. Indeed combinatorial game theory already deals with games with infinitely many possible states and transitions; there are various examples of such games in Winning Ways. I could be overlooking something, but I don't believe that the basic theorem about some player or side being favored presupposes that the set of possible game states or successor states is finite.
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That's a most careful answer to a most careless question.
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russ wrote:
All this mathematical philosophizing aside, the original question remains whether such a game could somehow favor no side if it were drawless. My hunch is that theoretically that is impossible, exactly because of the reasoning that in effect these new rules can simply be viewed as manipulating the game state, if we consider the game state to include a boolean vector of which rules (out of the set of all possible rules) are in effect.
If the game is finite, and has no draws then clearly you can work back from the end states to show that the game favours one player or the other; however, there are other no-win states other than a draw:
- loops
- infinite, non-repeating games

In either of these cases, the game may not be biased. An infinite ruleset would seem to allow for the possibility of at least one of these outcomes.

It might also be possible to argue for the inclusion of finite games which will not end before the heat-death of the universe; but this is a practical restriction, not a theoretical one
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Well, considering one of the ideals for an abstract strategy game would be one that didn't favor a side, but also didn't draw. So, while with normal conditions this isn't possible, the question becomes one of what can be done to get much closer to it, in both a practical and theoretical way. That is, without imperfect information or other forms of luck.
 
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docreason wrote:
Well, considering one of the ideals for an abstract strategy game would be one that didn't favor a side, but also didn't draw. So, while with normal conditions this isn't possible, the question becomes one of what can be done to get much closer to it, in both a practical and theoretical way. That is, without imperfect information or other forms of luck.

But it is possible...

See post above yours, or my post in this thread.
Re: Is it possible to have a pure abstract strategy game where no side is favored and it doesn't draw?

The L-game doesn't draw. It has loops in game positions. It doesn't end until one of the players makes a mistake and opens a winning line of play for the other.

 
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mrraow wrote:
An infinite ruleset would seem to allow for the possibility of at least one of these outcomes.
Not necessarily. The game tree could be infinitely bushy (wide branching) but finitely deep, for example. Or have no maximum length for branches, but nonetheless every branch is finite. There are various examples of such games in Winning Ways.

More formally, you could view it as that the successor relation between game states ("from state X you can go to state Y") merely needs to be well-founded (there is no infinite chain "X goes to Y goes to ..."), which is perfectly possible with an infinite number of states.

Whether an infinite ruleset allows infinitely long state chains or not depends on the details of the infinite ruleset... which still has not been fleshed out in any concrete way.
 
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herace wrote:
docreason wrote:
Well, considering one of the ideals for an abstract strategy game would be one that didn't favor a side, but also didn't draw. So, while with normal conditions this isn't possible, the question becomes one of what can be done to get much closer to it, in both a practical and theoretical way. That is, without imperfect information or other forms of luck.

But it is possible...

See post above yours, or my post in this thread.
Re: Is it possible to have a pure abstract strategy game where no side is favored and it doesn't draw?

The L-game doesn't draw. It has loops in game positions. It doesn't end until one of the players makes a mistake and opens a winning line of play for the other.
Huh? If it permits loops in game positions, then it has draws.
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russ wrote:
Huh? If it permits loops in game positions, then it has draws.
According to whose definition of a game?

Look at the rules for the L-Game or Achi. No ties since even if the game position is repeated, the game continues.

A repeated position isn't permissible for a combinatorial game, but it is allowed for an abstract strategy game.
 
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herace wrote:
russ wrote:
Huh? If it permits loops in game positions, then it has draws.
According to whose definition of a game?

Look at the rules for the L-Game or Achi. No ties since even if the game position is repeated, the game continues.

A repeated position isn't permissible for a combinatorial game, but it is allowed for an abstract strategy game.

I'm confused; you seem to be saying that if a game loops forever, then it's not a draw...? To me, that's obviously a draw. The game is drawn out forever and no one wins.

(I don't believe that the term "draw" necessarily implies termination; but it certainly implies that there is no winner. I tend to follow Conway's convention in Winning Ways (page 14) and distinguish between a "tie" (the game terminates and there's no winner) and a "draw" (the game does not terminate and so of course there's no winner), since it seems a useful distinction. In casual gamer speech, "draw" seems used to cover both of those situations, in my observation.)


EDITED TO ADD: And there are certainly plenty of examples of trivially easy cycles in some positions in some games, where neither player will make a mistake and lose, but instead both players prefer to keep cycling and draw instead of ending the game and lose. So it's not necessarily true that some player will inevitably make a mistake and break any cycle.
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While I see the value of the discussion in a theoretical sense, I wonder about its importance in a practical sense. All players can avoid mistakes at some times, and some players make mistakes at all times, but there aren't any players who can avoid mistakes at all times.

In particular, players that engage in a new strategy game usually make mistakes all the time. In a theoretical context there's no 'scope' for a mistake: it leads you from a won to a lost position. Our tendency to apply scope (i.e. 'big' mistakes) is based on our limited perspective. So is applying 'scope' to the advantage one or the other side is thought to have in a strategy game. But we're blessed with that limited perspective, though it may seem a curse in any particular game, because otherwise the concept of playing games would cease to exist.

So if I say that the 'scope' of the mistakes that beginners make in a strategy game, usually greatly outweighs the 'advantage' of one side, then I'm obviously lying the truth. The point being: why bother about creating the 'ideal' game if one's capabilities will fail to do it justice. Trying to exploit the advantage in a majority of the existing games is hard enough, especially if a balancing mechanism is provided. We don't need 'ideal' games, we need good games.

P.S. I copied this from rga, it's a game called "No-where" and the author asks the very same question about this particular game: is it a win for the first player, or the second, or is it a draw.
No-where
 
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I will say this issue matters, because I can say, as a rule, under these normal conditions, the day an abstract strategy game is born, it has an expiration date with it. And with the likes of checkers, and even chess, as a game catches on, it will develop a community that will wear it out, resulting it getting stale. On the highest levels of chess, for example, the first dozen moves have been played out.
 
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russ wrote:
I'm confused; you seem to be saying that if a game loops forever, then it's not a draw...? To me, that's obviously a draw. The game is drawn out forever and no one wins.

As I tried to point out in my first post in this thread, it depends on how you define a "pure abstract strategy game." To me the definition does not forbid repeats in the piece positions.

If you want to make finite games out of L-Game or Achi, then you could play with a time clock like that which is used for chess games. So you could win when your opponent runs out of time.

docreason wrote:
I will say this issue matters, because I can say, as a rule, under these normal conditions, the day an abstract strategy game is born, it has an expiration date with it. And with the likes of checkers, and even chess, as a game catches on, it will develop a community that will wear it out, resulting it getting stale. On the highest levels of chess, for example, the first dozen moves have been played out.

I accept your conclusion about the possibility of a game getting stale, but there are multiple reasons for that. The game isn't interesting to play, no mental challenge after having learned the game play, knowing that a computer can play perfectly and a human can't. So there are many reasons for a game being stale and not holding the interest of a critical mass of players.

Probably few of us play Tic-Tac-Toe or Checkers now, but I'd bet that almost all know the games and have played in the past.

 
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herace wrote:
russ wrote:
I'm confused; you seem to be saying that if a game loops forever, then it's not a draw...? To me, that's obviously a draw. The game is drawn out forever and no one wins.

As I tried to point out in my first post in this thread, it depends on how you define a "pure abstract strategy game." To me the definition does not forbid repeats in the piece positions.
And I'm agreeing to consider such a game to be a "pure abstract strategy game", but I'm pointing out that if the game never terminates, then surely that means that no one wins. (We agree that no one wins a game which never terminates, right?) And "no one wins" certainly implies "draw" to me.

(To be clear, there are is also another way that "no one wins" can happen, i.e. game termination with neither player achieving a victory condition. This is commonly also called a "draw", though I prefer calling it a "tie" as Conway suggests, to distinguish the 2 cases of "no one wins".)
 
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docreason wrote:
I will say this issue matters, because I can say, as a rule, under these normal conditions, the day an abstract strategy game is born, it has an expiration date with it.
Even though every game has a mathematical solution in principle, I see no reason to assume that every game's "expiration date" is within several centuries or even within the lifespan of humanity as a species, though.
 
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russ wrote:
docreason wrote:
I will say this issue matters, because I can say, as a rule, under these normal conditions, the day an abstract strategy game is born, it has an expiration date with it.
Even though every game has a mathematical solution in principle, I see no reason to assume that every game's "expiration date" is within several centuries or even within the lifespan of humanity as a species, though.
This may be a matter of context. In our day and age it is very hard to predict what the evolution of game programming might have in store. A century from now, we may have populated Mars or depopulated the Earth.

It also depends on the game. A game like Draughts may well have appeared 'inexhaustible' a century ago. Yet it took about that very century to do it. Programs have played a minor role in that, it just so happened that top players no longer had the means to fool other top players, and the exceptionally large margin of draws provided a safety net for both sides at all times. Chess might go the same way, though in that case it probably takes humans and programs to do it.

Go will always be a great game between humans, and draws can easily be excluded by including a half point in the komi value. Humanly speaking the game borders on inexhaustible, but Go might fall victim to advances in game programming.

It is impossible to exhaust a game like Mu, but humans might eventually not be able to beat programs, because less than perfect ones will yet be able to outcalculate them, if not nowadays, then certainly in the foreseeable future.

Humans need good games for humans. If a game offers a fair resistance against being programmed, that's all the better. But if a game grows, so will the programming efforts, and none are safe anymore. For programmers it's open season.
 
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To be clear, I'm not asserting that some games will definitely never be cracked (either in the sense of become too drawish or broken for humans playing them, or even in the sense of being solved by computer) before humanity disappears.

I'm just saying that I see no basis for stating with certainty that all games definitely will be cracked.

It seems to me that we simply have insufficient information to know or even to usefully predict.


But insofar as I can uncertainly predict, I have a hard time believing that a game like Go would ever become stale and drawish like checkers when played between humans, even if it becomes technically solved by computer. If I had to bet, I'd say that Go does not have an "expiration date" in the practical sense (i.e. for human players). The technical kind of "expiration date" (i.e. for computers) seems not very relevant to me as a human player, no more than a marathon runner is bothered that a car can drive 26 miles faster than a human can run it.
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russ wrote:
We agree that no one wins a game which never terminates, right? And "no one wins" certainly implies "draw" to me.
I'm going to split hairs. This isn't really defensible unless a consistent and complete set of definitions has been defined to analyze games. Here goes....

There is no rule in either the L-Game or Achi which allows the game to terminate before a winning position is achieved. So these game can't end in a "draw."

Yes, a given game position can evaluate as a draw since neither player should win.

russ wrote:
To be clear, there are is also another way that "no one wins" can happen, i.e. game termination with neither player achieving a victory condition. This is commonly also called a "draw", though I prefer calling it a "tie" as Conway suggests, to distinguish the 2 cases of "no one wins".

Defining draw (intermediate evaluation of a game position) and tie (evaluation of game which has terminated) in such a manner makes a nice distinction. Obviously these two definitions would confuse the masses unless the definitions were explicitly stated and used consistently.
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herace wrote:
russ wrote:
I'm confused; you seem to be saying that if a game loops forever, then it's not a draw...? To me, that's obviously a draw. The game is drawn out forever and no one wins.

As I tried to point out in my first post in this thread, it depends on how you define a "pure abstract strategy game." To me the definition does not forbid repeats in the piece positions.

If you want to make finite games out of L-Game or Achi, then you could play with a time clock like that which is used for chess games. So you could win when your opponent runs out of time.

I accept your conclusion about the possibility of a game getting stale, but there are multiple reasons for that. The game isn't interesting to play, no mental challenge after having learned the game play, knowing that a computer can play perfectly and a human can't. So there are many reasons for a game being stale and not holding the interest of a critical mass of players.

Probably few of us play Tic-Tac-Toe or Checkers now, but I'd bet that almost all know the games and have played in the past.

Well, what you mention here ended up being a possible path to coming up with a concept someone was looking at. They were looking at having a real-time game, where you did strategy, but not dexterity based. The idea of getting in moves and having your opponent run out of time, as a win condition, could be something interesting. Say, the idea is to strategically implement tactics that will cause your opponent to lose, if they are careless, or run out of time if they wait too long. This is not an optimally pure abstract strategy game, but could be a new genre of strategy games at least.

Idea is to have a rich enough environment as to not have it boring though. I am now inspired to come up with something.
 
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Did a quick serach, and found two geeklists about a timer. Both seem forgotten.

Games That Include A Countdown Timer

what games benefit most from a timer? help!

-------
edit - third geeklist
Playing at the Speed of Strategy >> Games That Really Need a Timer


 
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docreason wrote:
They were looking at having a real-time game, where you did strategy, but not dexterity based. The idea of getting in moves and having your opponent run out of time, as a win condition, could be something interesting.
TAMSK
 
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mrraow wrote:
docreason wrote:
They were looking at having a real-time game, where you did strategy, but not dexterity based. The idea of getting in moves and having your opponent run out of time, as a win condition, could be something interesting.
TAMSK

That may actually be the only game that does. I was wondering if others can be done, specifically designed around time constraints, which don't have each piece as a timer element. The gotcha with Tamsk is that the pieces were fiddly in nature, and the game cost too much to make. It is part of the reason why it got yanked from the Gipf series.
 
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docreason wrote:
Idea is to have a rich enough environment as to not have it boring though. I am now inspired to come up with something.
Mephisto may not be quite what you mean, but it is a perfect information abstract for any number of players (preferably beer infested nerds) and it uses a sand timer.

complete rules
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christianF wrote:
docreason wrote:
Idea is to have a rich enough environment as to not have it boring though. I am now inspired to come up with something.
Mephisto may not be quite what you mean, but it is a perfect information abstract for any number of players (preferably beer infested nerds) and it uses a sand timer.

complete rules

That looks like it is akin to Ricochet Robots in that you race to figure out a puzzle. I am curious if it is possible to do a game with offense and defense, where you modify the environment and pieces to block someone, rather than race to be first to solve it.
 
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