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Subject: Done to Depth rss

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Nathan James
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A discussion that began with the World Chess Championsip eventually brought up this statement on depth:

CoreyClark wrote:
nhjelmberg wrote:
CoreyClark wrote:
nhjelmberg wrote:
Isn't art a better analogy than programming language? Just like people still admire old art, they keep returning to old games in spite of the many new games they can choose from. In my opinion, we can't design better games until we understand the concept of "fun".

No, that's the thing, its not a better analogy. I've spent a great deal of argumentation on disabusing people of this notion. People seem to think abstract game design isn't objective just because nobody dies, nor is seriously injured, by playing a bad game.

Care to elaborate? I'm genuinely interested in the challenge of finding objective game criteria.

The keyword is "depth". excepting the more nebulous issue of what constitutes "poor clarity", depth is the most reliable measure of a game's worth. Personally I don't find the "local/global" paradigm to be the best at defining depth. The argument I like to make is that in-essence Othello is a more strategic game than Hex, while not practically being deeper. I measure depth not on a local vs global scale but rather by the amount of proportional action that is taken against a preceding move. Othello is a game with more heuristic layers than Hex has. Othello is not a deeper game than Hex simply because of the narrowness of its decision tree. But in Othello the best move doesn't often directly confront the previous move, whereas in Hex the opportunity to tenuki is a rarity. At any rate, I find this definition for depth to be most useful. If a good move often doesn't directly answer the preceding move/s, then you have a mostly strategic game on your hands, if a good move is always a vital response to the preceding move, then your game is mostly tactical.
 
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Nathan James
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This is my attempt to build a definition of depth from first principles.

NJames wrote:
Every game has a complete game tree, which is the totality of the game. This is what the game is as opposed to what it may seem to be. We could describe the tree as being wide, i.e., having many options at a given point, or deep, i.e., progressing for many plies before resolution. Because we generally invent and play games that are too large for direct analysis of the complete game tree, we normally discuss games based on how we must approach them, which is by applying clever heuristics.

We must keep careful distinction between what we might call analytical depth, which would be searching through the plies of the tree, and strategic or conceptual depth, which would be found in games that permit increasing levels of cleverness. Every game has analytical depth exactly equivalent to its game tree. We often note that analytical depth is not sufficient to produce the other kind of depth.

The depth we care about is the experience of exploring a game through a series of evolving concepts or heuristics. Conceptual depth is entirely a matter of playing games in the absence of a game tree that permits our direct inspection. It is an artifact of how a finite mind interacts with an overwhelmingly large game tree.

In order for a player to experience conceptual depth in a game, the game must submit to a series of increasingly difficult insights. We can probably identify some things as necessary for conceptual depth, and also some things that will probably signal conceptual depth, but I doubt we can ever guarantee conceptual depth. As proof of the last point, I note that there is always the possibility of discovering an insight that breaks the game. Since it is human-attainable insight that matters, even solving a game by supercomputer wouldn't permit a guarantee.
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NJames wrote:
Every game has a complete game tree, which is the totality of the game. This is what the game is as opposed to what it may seem to be. We could describe the tree as being wide, i.e., having many options at a given point, or deep, i.e., progressing for many plies before resolution. Because we generally invent and play games that are too large for direct analysis of the complete game tree, we normally discuss games based on how we must approach them, which is by applying clever heuristics.

We must keep careful distinction between what we might call analytical depth, which would be searching through the plies of the tree, and strategic or conceptual depth, which would be found in games that permit increasing levels of cleverness. Every game has analytical depth exactly equivalent to its game tree. We often note that analytical depth is not sufficient to produce the other kind of depth.

The depth we care about is the experience of exploring a game through a series of evolving concepts or heuristics. Conceptual depth is entirely a matter of playing games in the absence of a game tree that permits our direct inspection. It is an artifact of how a finite mind interacts with an overwhelmingly large game tree.

In order for a player to experience conceptual depth in a game, the game must submit to a series of increasingly difficult insights. We can probably identify some things as necessary for conceptual depth, and also some things that will probably signal conceptual depth, but I doubt we can ever guarantee conceptual depth. As proof of the last point, I note that there is always the possibility of discovering an insight that breaks the game. Since it is human-attainable insight that matters, even solving a game by supercomputer wouldn't permit a guarantee.

I have a different perspective of depth separate from the game-tree complexity. While a deep game usually (possibly universally) has a large game-tree/state-space complexity/branching factor, this does not mean a large tree is contingent on depth. For example "n x n" Tic Tac Toe can be hugely complex, but still relatively simple. Or for a less popular opinion, 59x59 Connect6 is to me relatively shallow for what it is. The appearance is a huge board with limitless potential, but I find it rather superficial in that the game works because of the huge canvas rather than being enhanced by it. For comparison, a 13x13 game of Go is a fraction of the size of 9 go-board Connect6 but there are concepts of life and death, territory counting, nets, ladders, etc just as much as in 19x19 or 9x9.

Therefore, I think depth arrives from how the components interact with one another. A Chess variant where each piece is split into right moving and left moving versions would have double the pieces, and therefore double the "content" but would be less deep than normal Chess because they can interact with less of the pieces. Another example could be creating a Chess variant where Pawns could move backwards. I personally believe this would be deeper than modern chess, but that's just me. Slither as well is incredibly deep because of the way the stones are placed/moved allows them to always change their relationship with other stones and therefore increase component interactivity.
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Joe Joyce
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Grin, I'm happy to follow your lead, and crib from myself from that World Chess Championship thread.

joejoyce wrote:
I like the idea of 'depth' better than 'clarity' but will argue for 'width' as another measure...
Yes, I'm talking about multi-move abstracts here. There are some, and there will be more. And multi-move games can/do have depth in each individual turn, or 'width', which is merely depth turned on its side. I also think a game with width as well as depth will more likely exhibit not just emergence, but stronger emergence, because there are far more interactions in such a game.

CoreyClark wrote:
... I measure depth not on a local vs global scale but rather by the amount of proportional action that is taken against a preceding move... If a good move often doesn't directly answer the preceding move/s, then you have a mostly strategic game on your hands, if a good move is always a vital response to the preceding move, then your game is mostly tactical.
I like the basic idea a lot. In explicitly looking at the position and intention of a move, you can see a range of move types, from the purely tactical 'I attack your piece here with my piece(s) next to it' all the way to 'later I want this now empty area, so will move this piece over here, which isn't doing anything important right now, into the area to occupy and protect it.' By counting how many* of the different types there are, we get a measure of how much leisure the player has to pursue future goals, or how desperately the player is enmeshed in the immediate struggle for survival. Go seems beautifully suited to this type of analysis. You should be able to tell a lot when comparing such ratios for different players of the same game.
*Not getting into the "is it tactics or strategy?" discussion here other than to say wargamers have to deal with the same question, and they've evolved at least 4 categories: tactical, operational, strategic, and grand tactical.

The following is in reply to the initial quote in this thread.
joejoyce wrote:
I see clarity as understandable, even (sometimes) desirable as a game feature in 1 move/turn games. But even there, many games are opaque, Arimaa being a fine example of that in my estimation. And this totally neglects multi-move games. Take double Go: the 2 stones dropped each turn may respond directly to one board situation, respond directly to 2 different situations, go toward 1 strategic goal, go to 2 strategic goals, or respond to an immediate threat and further a strategic plan. Isn't that more depth right there?

In a seriously multi-move game, you can pursue a whole range of tactical, operational, and strategic options. To me, that has to allow more depth in general, granting the very likely existence of exceptions. And that raises hell with the concept of clarity. Once you get past a (very) few moves/turn, players won't necessarily even know what the end of their turn will be even after they've started making moves that turn, much less be able to gauge the reply with any real sense of accuracy.

But there will be obvious victory conditions: kill these specific pieces, occupy those places, utterly destroy the opponent's forces, all being simple and direct and easy to understand. That's an important kind of clarity, even if you don't have the slightest idea how to go about it. There are other kinds of clarity. In a war of even attrition, the larger force wins. You will have in-game goals and principles that will allow/help you to see the forest while in the trees, give you a compass for right action and right direction. This is, in essence, all the clarity there is in a chess game, taken as a whole. Yes, you can see several moves into the future but how well, and that's for one piece. In a massively multi-move game, you might see several moves *wide*, across space in the same time/turn, rather than several moves across time into the future in the same (board) space. What are the essential differences? Other than in one instance you are projecting alternating 'you, opponent' moves, and in the other, you're projecting several 'you' moves? How much clarity, and of what kinds, do you want? ;)
To expand on clarity, and what depth does to it, consider that the clarity of chess mmm, say instead, a simple 1 move/player-turn abstract, is very granular. Every piece, piece type, position, board geometry... is important and the good players will see all or most of the (key) relationships, and be able to project several turns into the future with very good confidence. In a significantly larger, more complex (and multi-move) game, you lose the granularity, and have to go on general principles. You can't calculate future game states in advance, there are too many options for each player. Your clarity has become statistical. The good players will still know what to do, but they won't be relying on memorized patterns a la chess and Go, but relying on both memory of similar situations and the general and specific principles abstracted from the statistics.
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Nathan James
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Impartial games preclude strategic depth by an interesting mechanism. They do not permit players to develop advantages of varying degree. Each position is either 100% won or 100% lost, with any inaccuracy in a won position immediately forfeiting all advantage. Now there is the possibility of applying some clever pattern recognition to a game like misere Nim, but there are never degrees of advantage. Consequently all that is left is analysis rather than strategy.

...

Questions:

Is the cleverness used to assess a misere Nim position a strategy in any meaningful sense?

If a similar type of cleverness was not perfectly accurate, would it qualify as strategic thinking?
 
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Nathan James
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Cortez527 wrote:


I have a different perspective of depth separate from the game-tree complexity. While a deep game usually (possibly universally) has a large game-tree/state-space complexity/branching factor, this does not mean a large tree is contingent on depth. For example "n x n" Tic Tac Toe can be hugely complex, but still relatively simple. Or for a less popular opinion, 59x59 Connect6 is to me relatively shallow for what it is. The appearance is a huge board with limitless potential, but I find it rather superficial in that the game works because of the huge canvas rather than being enhanced by it. For comparison, a 13x13 game of Go is a fraction of the size of 9 go-board Connect6 but there are concepts of life and death, territory counting, nets, ladders, etc just as much as in 19x19 or 9x9.

Therefore, I think depth arrives from how the components interact with one another. A Chess variant where each piece is split into right moving and left moving versions would have double the pieces, and therefore double the "content" but would be less deep than normal Chess because they can interact with less of the pieces. Another example could be creating a Chess variant where Pawns could move backwards. I personally believe this would be deeper than modern chess, but that's just me. Slither as well is incredibly deep because of the way the stones are placed/moved allows them to always change their relationship with other stones and therefore increase component interactivity.

The game tree is the first approximation of the depth we might find in a game. A game has depth not greater than it's game tree, and almost certainly less. Part of identifying a deep game is recognizing what allows a player to ignore large parts of the tree.

I think what you're noting here is that if all the interactions are local, a large board doesn't increase depth. That is certainly true. Ideally, we would look for a game with fractal-like qualities. Where the interactions scale up, and up, and up.
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NJames wrote:


The game tree is the first approximation of the depth we might find in a game. A game has depth not greater than it's game tree, and almost certainly less. Part of identifying a deep game is recognizing what allows a player to ignore large parts of the tree.

I think what you're noting here is that if all the interactions are local, a large board doesn't increase depth. That is certainly true. Ideally, we would look for a game with fractal-like qualities. Where the interactions scale up, and up, and up.

The global vs local fractal relationship is really the crux of it. Ranging chess pieces are a tremendous source of depth because they not only cover much of the board at any one time, they can do things like pin, skewer, and cross wider distances to attack from opposite sides. They exhibit global influence compared to more localized pawns. In Go, stones combine with their neighbors, so while they only occupy a single intersection and care about liberties on only 4 sides, they can be global through the total combination of stones through liberty sharing.

I think some of the question of depth lies in the separation between Strategy vs Tactics. Strategy is usually defined as the high level notion of a plan (e.g. attack left side), while tactics are the specifics (place stone on intersection (4,4) ). However in the context of board games, I will expand tactics one level further and define it as the "algorithmic sequence of moves to achieve the goal". In a sense, it treats the game moves as orders of steps the same way speed Rubik's cube solvers use movement patterns.

So in Go my strategy could be "protect top left corner", while the tactic is "place stone at (4,4), expect response at (5,4), then play (4,3)". So a game needs to be strategic enough to have a variety of general approaches to victory, while tactical enough to make the movement sequence important.
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Nathan James
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CoreyClark wrote:
If a good move often doesn't directly answer the preceding move/s, then you have a mostly strategic game on your hands, if a good move is always a vital response to the preceding move, then your game is mostly tactical.
Playing non-answering moves would seem to be possible because the players are building different advantages for themselves, no? I mean, the moves could be nonsense, but barring that, I envision each player building a different kind of advantage or else in a different part of the board. The payoff comes when the two advantages clash and we find out which was decisive.
 
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christian freeling
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I'm a bit surprised that relative permanency hasn't entered the equation yet. The pawn structure in Chess for instance allows sub-goals of a relative permanency to emerge, in part because pawns themselves have permanency in their forwards progress.
Now imagine Chess without pawns. Or Dragonfly, where pawns gradually disappear. Aren't these games (presuming the first one is one) more 'tactical'.
It's just a thought, I don't claim it says anything in general about 'depth'. But sub-goals with some permanency are one of the things that allow Chess players to plan deeply.
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I wonder if permanency is a different kind of depth, closer related to "cost benefit analysis" and long term planning as compared to identifying the best move for that exact moment. Pawns with their inability to travel backwards means that if it's the ideal move to capture on the left diagonal, then that means they can't occupy that space to slow down bishops in future turns. Of course that illustrates another question, are there different kinds of depth?
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christian freeling
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Cortez527 wrote:
I wonder if permanency is a different kind of depth, closer related to "cost benefit analysis" and long term planning as compared to identifying the best move for that exact moment. Pawns with their inability to travel backwards means that if it's the ideal move to capture on the left diagonal, then that means they can't occupy that space to slow down bishops in future turns. Of course that illustrates another question, are there different kinds of depth?
If always identifying the best move were humanly possible we wouldn't have to play anymore. We're condemned to heuristics and increasingly to AI (if aspiring to world dominance). So I'm not sure what there is to 'compare'.

Permanency as such doesn't show up in the tree, you have to look at the game. A weird notion here is that Corey sees some things opposite of my view. I think Hex allows deep planning because it is all permanency. Othello to me is more tactical because for long stretches there's no permanency at all. It starts radiating from the corners, the explicitly permanent spots.

If a game allows relatively permanent sub-goals to emerge, then the mind can use them as stepping stones to the ultimate goal and frame plans. Nick might have some thoughts on that. My point is, I suppose, that the game is not the tree.
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christianF wrote:

If always identifying the best move were humanly possible we wouldn't have to play anymore. We're condemned to heuristics and increasingly to AI (if aspiring to world dominance). So I'm not sure what there is to 'compare'.

Permanency as such doesn't show up in the tree, you have to look at the game. A weird notion here is that Corey sees some things opposite of my view. I think Hex allows deep planning because it is all permanency. Othello to me is more tactical because for long stretches there's no permanency at all. It starts radiating from the corners, the explicitly permanent spots.

If a game allows relatively permanent sub-goals to emerge, then the mind can use them as stepping stones to the ultimate goal and frame plans. Nick might have some thoughts on that. My point is, I suppose, that the game is not the tree.

To tie it back to Nathan's focus on the game tree, the counter to being too heuristic could be having many paths to victory. In a way, his position (as I understand it) fits in with this because a particular movement may not set the trajectory explicitly towards victory or defeat. Instead the branches could be wide enough that (outside the endgame) there are many ways to still profit or recover from strong moves played against you.

Assuming I'm interpreting him correctly.
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Nathan James
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christianF wrote:
Permanency as such doesn't show up in the tree, you have to look at the game. ... My point is, I suppose, that the game is not the tree.
This is a mistake. The complete game tree shows every position and the moves that transition between them. When there is no way back to a previous position, the tree will show that with one-way arrows.

ChristianF wrote:
But sub-goals with some permanency are one of the things that allow Chess players to plan deeply.
Here I think you are using deep to mean a number of plies, which would be what I've been calling analytical depth. Analytical and conceptual depth are certainly not exclusive, but neither are they interchangeable. We will run into trouble if we equivocate.

Or do you mean that permanence supports conceptual depth in terms of plans like "press forward on the left side" as opposed to explicitly analyzed lines of play?
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christian freeling
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NJames wrote:
christianF wrote:
Permanency as such doesn't show up in the tree, you have to look at the game. ... My point is, I suppose, that the game is not the tree.
This is a mistake. The complete game tree shows every position and the moves that transition between them. When there is no way back to a previous position, the tree will show that with one-way arrows.
Long ago and far away I made a complete tree of MiniMancala. That was fun. But where analitical depth is more the domain of AI, humans are concerned with conceptual depth.

NJames wrote:
ChristianF wrote:
But sub-goals with some permanency are one of the things that allow Chess players to plan deeply.
Here I think you are using deep to mean a number of plies, which would be what I've been calling analytical depth. Analytical and conceptual depth are certainly not exclusive, but neither are they interchangeable. We will run into trouble if we equivocate.

Or do you mean that permanence supports conceptual depth in terms of plans like "press forward on the left side" as opposed to explicitly analyzed lines of play?
Yes, I mean it as an almost necessary means to support conceptual depth. It's too late now to consider whether it's sufficient. That feels tricky. I'll think about it. Meanwhile keep posting, it's a nice angle.
 
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christianF wrote:
NJames wrote:
christianF wrote:
Permanency as such doesn't show up in the tree, you have to look at the game. ... My point is, I suppose, that the game is not the tree.
This is a mistake. The complete game tree shows every position and the moves that transition between them. When there is no way back to a previous position, the tree will show that with one-way arrows.
Long ago and far away I made a complete tree of MiniMancala. That was fun. But where analitical depth is more the domain of AI, humans are concerned with conceptual depth.
This is why the game is not the tree. To rephrase, the game is the engagement of human perceptual faculties, with the tree, as the tree is represented visually (you could represent a deep game in binary and it would cease to be deep and instead would be utterly incomprehensible. This also points to another important implication: the depth of a game is limited not only by the tree and what's in it, but also in how that tree can be represented visually. If it can be represented in a way that allows the visual system to process it well, that makes a gigantic difference)
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NJames wrote:
christianF wrote:
Permanency as such doesn't show up in the tree, you have to look at the game. ... My point is, I suppose, that the game is not the tree.
This is a mistake. The complete game tree shows every position and the moves that transition between them. When there is no way back to a previous position, the tree will show that with one-way arrows...
The game tree is not the game. The game is the particular path through the game tree you and your opponent take. So each individual game is a point of view of the game/game tree. And each one is very much a unique viewpoint. We even say the game is good or bad based on our views about how it played, and no one (worthwhile) game encompasses the entire game tree. I would also argue here the entire game tree is art/craft/genius invention, depending on your point of view, of a pocket intellectual universe, or at least a boxed one, small enough to be carried between games, a.k.a.: unique journeys in that universe. You are not your family tree. Nit picked. ;)

I like the point about arrows representing a discontinuity, like captures, in the game tree. But the shape of the tree can get complex. If you have a mechanism for removing pieces during the game and also a mechanism for replacing pieces during that game, you've created a looping mechanism, which will at least sometimes allow the exact same instantaneous board state to occur in 2 or more different places in the tree, with very different surroundings. In this case you need path trajectory information as well as complete instantaneous board state information to understand why the specific immediately following board states are there or aren't there, but somewhere else in the game tree. Again, the conclusion seems to me to be that a game is a specific path through some part of the game tree. And that's why chess players almost never care about draws except in championship events. Most players don't have the skill to get to that part of the game tree where high-level games draw almost every game. We are perfectly happy winning and losing mostly, rather than drawing.

************EDIT:
Crud! And Congrats! You beat me to it, Nick. That's what I get for stopping for dinner and some US news and politics.
 
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So I went to bed thinking about examples of deep games that don't have some form of permanency emerging during play that allows players to have a framework of sorts to give direction to their thoughts. I could think of none, so I'll put it before the forum. Anyone?

Meanwhile permanency maybe isn't the right word for something that may turn out to be temporary. 'Permanent' doesn't suggest any gradation, but in this context we have gradation.

Abolute permanency is featured in pure placement games without movement or capture. Or in a pawn's forward progress. Or in a pawn's promotion. That doesn't mean the pawn or the piece to which it is promoted cannot disappear. They are not necessarily 'permanent' themselves. You find the same absolute permanency in forward progress and promotion in Draughts, or in live groups in Go.

There's also relative permanency. You see it a lot in Chess, White can for instance place a knight on d6 covered by a pawn on e5 because black's pawns are past the square. The knight won't stay there for the rest of the game, but for the immediate future it has a nice spot.

Othello is all flipflop in the beginning but once the corners are reached, permanency gradually enters. Imagine Othello on an endless board, now there a game without any permanency! Only, it isn't a game.

I could go on a while, but I think the question at the beginning is a good one: can anyone imagine an abstract strategy game without some form of permanency?

P.S.
Maybe I should add that permanency is imo. a necessary condition for conceptual depth. I don't think it's sufficient, but certainly necessary. I don't want to give the impression of pushing things off topic.
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christianF wrote:
I could go on a while, but I think the question at the beginning is a good one: can anyone imagine an abstract strategy game without some form of permanency?
If you change the question to "can anyone imagine a good abstract strategy game without some form of permanency?" then I bet you're right that there aren't any.

But there are some abstract strategy games (which seem not very good) with no permanency, in which players move neutral pieces around until one player achieves some winning configuration of those neutral pieces.
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Nathan James
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It seems we need to define "the game," although, I think I defined my own use of it a few posts back.

milomilo122 wrote:
To rephrase, the game is the engagement of human perceptual faculties, with the tree, as the tree is represented visually
I suppose this means that no two people have ever played the same game, since their faculties certainly do not engage the, uh, game in the same way.

Does the game not exist unless someone is currently playing it? May we not usefully speak of playing the same game on an iPhone as we play on a table?

I agree that the representation is important, but I'm not sure about the need for the redefinition.

joejoyce wrote:
The game tree is not the game. The game is the particular path through the game tree you and your opponent take.
This is what I would normally refer to as "a game of Chess" as opposed to "the game of Chess."

I wonder if there is a technical term for a single instance of playing the game. We could invent one if we need it badly enough.
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russ wrote:
christianF wrote:
I could go on a while, but I think the question at the beginning is a good one: can anyone imagine an abstract strategy game without some form of permanency?
If you change the question to "can anyone imagine a good abstract strategy game without some form of permanency?" then I bet you're right that there aren't any.

But there are some abstract strategy games (which seem not very good) with no permanency, in which players move neutral pieces around until one player achieves some winning configuration of those neutral pieces.
The L-game springs to mind.

Here's a difference between Pente and Hexade (placement + capture). Both are capricious with little permanency. But Pente has a capture cut-off so there's added permanency because the number of captures is relevant. Maybe the example isn't, but in view of a possible new angle to depth I thought I'd throw it in.
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christian freeling
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NJames wrote:
Does the game not exist unless someone is currently playing it?
I've on occasion argued that it may exist before even conceived. But let's leave philosophy out of it.
 
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NJames wrote:
It seems we need to define "the game," although, I think I defined my own use of it a few posts back.

milomilo122 wrote:
To rephrase, the game is the engagement of human perceptual faculties, with the tree, as the tree is represented visually
I suppose this means that no two people have ever played the same game, since their faculties certainly do not engage the, uh, game in the same way.
Can you repeat or rephrase your definition of "the game"? I'm not sure what we're discussing here. Is Nick's definition what you mean? Do you mean the hypothetical case of 'playing' a game with access to the complete tree? So that your strategy could be more 'analytical' in that you can actually follow lines up and down as actual positions?
In that case I have a few more questions.
 
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Nicholas Hjelmberg
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christianF wrote:
russ wrote:
christianF wrote:
I could go on a while, but I think the question at the beginning is a good one: can anyone imagine an abstract strategy game without some form of permanency?
If you change the question to "can anyone imagine a good abstract strategy game without some form of permanency?" then I bet you're right that there aren't any.

But there are some abstract strategy games (which seem not very good) with no permanency, in which players move neutral pieces around until one player achieves some winning configuration of those neutral pieces.
The L-game springs to mind.

Here's a difference between Pente and Hexade (placement + capture). Both are capricious with little permanency. But Pente has a capture cut-off so there's added permanency because the number of captures is relevant. Maybe the example isn't, but in view of a possible new angle to depth I thought I'd throw it in.

An interesting and important angle. Would Go become a deeper game if you added rules for moving stones? Its decision tree would expand but would anyone equal that to depth? Permanency (or is inertia a better term?) should definitely be included in a discussion about depth.
 
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christian freeling
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nhjelmberg wrote:
An interesting and important angle. Would Go become a deeper game if you added rules for moving stones? Its decision tree would expand but would anyone equal that to depth? Permanency (or is inertia a better term?) should definitely be included in a discussion about depth.
Joe can tell you more about that, here's a thread.

To clarify the Pente/Hexade example, captured stones in Hexade mean fiddlestick while in Pente they are a permanent addition to the score and thus to the road to victory.
 
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christianF wrote:
nhjelmberg wrote:
An interesting and important angle. Would Go become a deeper game if you added rules for moving stones? Its decision tree would expand but would anyone equal that to depth? Permanency (or is inertia a better term?) should definitely be included in a discussion about depth.
Joe can tell you more about that, here's a thread.

To clarify the Pente/Hexade example, captured stones in Hexade mean fiddlestick while in Pente they are a permanent addition to the score and thus to the road to victory.

There goes my idea of a Go variant into the trash but thanks for the link. Back to idea of a Chess variant then.
 
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