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Subject: Done to Depth rss

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Cameron Browne
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NJames wrote:
The model proposed in the paper doesn't reference the refinement of the strategy at all, it is only concerned with how the strategy functions when given a certain amount of computational resources.
Yes, even one of the papers' authors disagrees with the emphasis on the objective measurement of computational resources in the paper! It seems pointless to remove the human player experience from the game.

So my reading of that diagram might be different to what the main author intended, but it coincidentally captures what I think is the essence of strategic potential beautifully.

Regards,
Cameron
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Cameron Browne
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Nestor's Omega is a very concrete example of the importance of strategies to human players, and also possibly the linear accumulation of strategies.

Omega: Each turn, the current player places a piece of each colour. The winner is the player with the highest score, given by the product of the group sizes of their colour. For example, White is winning in the following game with 1x2x2x3x4 = 48 pts.



Note how mentally taxing it is just to calculate the score for each player! It takes seconds, leaving no time to plan ahead. Add to that the high branching factor (61x60x59x58 = 12,524,520 possibilities for the opening turn) then players ended up just making random moves and seeing what happened. Not very satisfying.

Players initially did not like this game and it seemed destined for the scrap heap. Then Greg Schmidt implemented it for his Axiom AI* and noticed a pattern: the player with more groups and smaller groups than their opponent usually won. Further, the player whose average group size was closer to 3 usually won. We've subsequently found various mathematical proofs that 3 is the optimal element size for maximising the product of a partition.

This led to a very simple strategy that players could grasp: Make your groups as close to size 3 as possible. The game suddenly became human-comprehensible and playable; strategic clarity. Rather than spending their entire mental budget doing trivial calculations, players could now focus on strategic planning. Much more fun!

The next strategy learnt is the obvious corollary: Make enemy groups as different from size 3 as possible. This has profound implications for the game. It means that a good strategy is to connect enemy groups together to make them larger than 3, while trying to block your own groups from being connected together by opponents.

Omega suddenly became both a connection game (for enemy groups) and an anti-connection game (for friendly groups), which then opened up a whole slew of further connection-based strategies to be learnt.

Regards,
Cameron

* The Axiom AI used Monte Carlo tree search with strictly random playouts. The ease with which this simple algorithm can stumble upon and reveal such key strategies - with nothing more sophisticated than random playouts - makes me optimistic regarding the automated detection of strategic potential.
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Cameron Browne
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One issue I have with the "strategy ladder" diagram is that it implies that strategies accumulate from less powerful to more powerful as you learn the game.

But I wonder if it's the other way around. The Omega example above shows a game-changing strategy (make groups of 3) being learnt first, followed by more subtle strategies (connection-based) being learnt subsequently.

Similarly, in Chess I would say that avoiding doubled pawns is a less important strategy in general than keeping your queen alive... but it's keeping the queen alive that players will learn first!

Perhaps we should instead be looking for the accumulation of increasingly subtle and sophisticated strategies that build on the coarser more obvious ones. More advanced strategies need not be more powerful in themselves, it is their accumulated effect building on previous learnt strategies that is important.

As long as there is more to be learnt about a game, it remains interesting.

Regards,
Cameron
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Richard Moxham
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camb wrote:
One issue I have with the "strategy ladder" diagram is that it implies that strategies accumulate from less powerful to more powerful as you learn the game.

But I wonder if it's the other way around. The Omega example above shows a game-changing strategy (make groups of 3) being learnt first, followed by more subtle strategies (connection-based) being learnt subsequently.

Similarly, in Chess I would say that avoiding doubled pawns is a less important strategy than keeping your queen alive; but it's keeping the queen alive that players will learn first!

Perhaps we should instead be looking for the accumulation of increasingly subtle and sophisticated strategies that build on the coarser more obvious ones. More advanced strategies need not be more powerful in themselves, it is their accumulated effect building on previous learnt strategies that is important.

As long as there is more to be learnt about a game, it remains interesting.

Regards,
Cameron
I was interested to read this, because it looks as if the point of view expressed here is closely in line with what has always seemed to me to be the case: namely that the sequence of systematic strategy-learning works backwards from 'first principles' (in the sense of 'the first principles to have come to light'). Indeed, I'd go so far as to say that this is almost bound to be the process. Ultimate aims are always likely to be conspicuous (even self-evident), but the search for staging-posts is trickier - and logically dependent, if the quest is to be systematic, since route-planning is hard to envisage in the absence of a destination!

So the word advanced is itself unhelpful, because potentially misleading. And (if I may say so), I guess the same might be true of your "building on" .

 
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camb wrote:
One issue I have with the "strategy ladder" diagram is that it implies that strategies accumulate from less powerful to more powerful as you learn the game.
I understood that diagram less literally. I.e. surely the individual dots don't really represent concrete independent little nuggets like the first dot means "protect your queen", the second dot means "avoid doubling pawns", etc, which are learned in some strict order, do they?

In reality improving at a game is clearly not such a linear progression of learning one concrete self-contained strategic maxim after another in sequence. Different people learn them in different orders; different people learn them at different speeds; and the distinctions between "different" strategic insights can be blurry in the first place.

So I supposed the dots represent more abstractly that you occasionally get some new kind of new aha-insight or conceptual breakthrough (but not necessarily one specific insight necessarily corresponding to that exact position on the x-axis), and helps you play better.

And so the problem with the too-easy game is that only a small number of aha-insights suffice before the game is too easy (and those insights come quickly), and the problem with the too-hard game is that it takes too frustratingly long before you get any clue about strategy.
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Cameron Browne
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mocko wrote:
And (if I may say so), I guess the same might be true of your "building on" .
True! There's no reason that more subtle strategies need be dependent on existing ones.

And I like the fact that you mention working backwards. For a long time I've wanted to look into developing an AI that uses a form of retrograde analysis to learn strategies useful in the end game (where things are more certain and more easily measured) then work backwards to find sub-goals that lead to those... then work backwards to find sub-goals that lead to those... etc.

Never got around to it.

Regards,
Cameron
 
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russ wrote:
I understood that diagram less literally. I.e. surely the individual dots don't really represent concrete independent little nuggets like the first dot means "protect your queen", the second dot means "avoid doubling pawns", etc, which are learned in some strict order, do they?
From the paper:
Quote:
Each dot represents a complete, fully- defined algorithmic strategy for playing a particular game represented by each path. Each dot is the best strategy that can be achieved at that level of computational resources.
I agree that this is too literal. Instead, each curve should be seen as a trajectory of competence or knowledge about the game, and each dot as a milestone learnt along the way.

russ wrote:
different people learn them at different speeds
For example, someone playing Chess in a train as opposed to someone playing it in an airplane...

Regards,
Cameron
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camb wrote:
russ wrote:
different people learn them at different speeds
For example, someone playing Chess in a train as opposed to someone playing it in an airplane...
Ha!

So astronauts playing Chess in the space station, for example, would learn much faster than us stuck on earth.
 
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christian freeling
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russ wrote:
camb wrote:
russ wrote:
different people learn them at different speeds
For example, someone playing Chess in a train as opposed to someone playing it in an airplane...
Ha!

So astronauts playing Chess in the space station, for example, would learn much faster than us stuck on earth.
Yes, but doesn't time move slower for them?
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christianF wrote:
russ wrote:
camb wrote:
russ wrote:
different people learn them at different speeds
For example, someone playing Chess in a train as opposed to someone playing it in an airplane...
Ha!

So astronauts playing Chess in the space station, for example, would learn much faster than us stuck on earth.
Yes, but doesn't time move slower for them?
Life is a series of trade-offs...
 
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milomilo122 wrote:
milomilo122 wrote:

Christian (or anyone else with considered opinions on this subject):

How about Manifest Chesstiny? Is that a good or bad solution? I haven't given it much thought but it feels like it could be an improvement over Fischer Random, as a tournament game.
And a related question: would Manifest Chesstiny be even better if the stones were done away with entirely, so that the turn rule became:

Quote:
On your turn, place any off-board piece onto any empty space on your back row, if possible, and then move any one of your Chess pieces on the board as normal.
Hi Nick I had an afterthought. I realised rather late that there's another difference (next to not being able to capture a non-existing stone): You could in principle keep entering on the same square. I'm not sure about the extent of the consequences, but then I thought: Why not use the pawns for that very purpose?

So you put them on the first row and give them the option to move one, two or maybe even three squares on their first move (requiring a modified e.p. because you can't really do without, not without altering the whole pawn interaction).
The rule now may be:
Quote:
On your turn you may either move a piece (pawn) or you may move a pawn of the first row and place a piece on the vacated square.
Of course pawns on the first row might be captured, and in that case you lose both the pawn and a piece, because you cannot enter on the square anymore.
Idea?

P.S. There are details to be addressed of course but if we can't work them out, who can?
P.P.S. Don't answer that, I can think of a lot who can.
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camb wrote:
Players initially did not like this game and it seemed destined for the scrap heap. Then Greg Schmidt implemented it for his Axiom AI* and noticed a pattern: the player with more groups and smaller groups than their opponent usually won. Further, the player whose average group size was closer to 3 usually won. We've subsequently found various mathematical proofs that 3 is the optimal element size for maximising the product of a partition.

This led to a very simple strategy that players could grasp: Make your groups as close to size 3 as possible. The game suddenly became human-comprehensible and playable; strategic clarity. Rather than spending their entire mental budget doing trivial calculations, players could now focus on strategic planning. Much more fun!

The next strategy learnt is the obvious corollary: Make enemy groups as different from size 3 as possible. This has profound implications for the game. It means that a good strategy is to connect enemy groups together to make them larger than 3, while trying to block your own groups from being connected together by opponents.

Omega suddenly became both a connection game (for enemy groups) and an anti-connection game (for friendly groups), which then opened up a whole slew of further connection-based strategies to be learnt.
I have experienced these phenomena in a slightly more straightforward game called Multiplicity (early 2013 but alas, not in the database yet). It's two-player and each having their own colour, but the behaviour is the same. It can be played at mindsports but I doubt it ever has been. I use to call it a 'reverse connection game' and it reveals a similar ideal group size. Maybe you should have a look at it if you find the behavioural consequences of its goal interesting.
 
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Nathan James
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christianF wrote:
NJames wrote:
christianF wrote:

That may be debatable. In China XiangQi became the game of the masses although Go had been around for a long time already, but had been confined to the upper class. I'm not sure why it became more popular than Go once it had arrived, because I assume that Go material wasn't harder to get by than Chess pieces. But maybe I'm wrong about that.
Chess is more conceptually accessible. When you begin playing Chess, you can't help but think of narratives. The narratives give the mind something to build strategic ideas out of. Of course, the ideas you will have first are garbage, but you will have them, and very quickly.
Good point to discuss in your Done to Depth thread: What, if any, is the relationship between conceptual accessibility and conceptual depth?
Good idea, Christian.

Instead of building strategic ideas out of narratives, I think I should have said, that the same elements we build narratives from are also easy to build strategies with.

And we can bring in the just mentioned idea of protecting the Queen in Chess as an example. What sort of effort is required to learn that the Queen is very important? Basically, zero. Contrast that with the squares on an Othello board, or worse yet the intersections on a Go board.

As strategy get more refined, the advantages the players are working with become smaller and smaller. Eventually weaker players can't even see the tiny successes that the strongest players are playing for. The possible advantages in Chess are positively HUGE, which allows even the very dull to play meaningful games.
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Nathan James
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camb wrote:

* The Axiom AI used Monte Carlo tree search with strictly random playouts. The ease with which this simple algorithm can stumble upon and reveal such key strategies - with nothing more sophisticated than random playouts - makes me optimistic regarding the automated detection of strategic potential.
Intriguing!

Do I understand correctly that it was the human who noticed the pattern, and not a self-modifying algorithm?
 
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christianF wrote:
I have experienced these phenomena in a slightly more straightforward game called Multiplicity (early 2013 but alas, not in the database yet). It's two-player and each having their own colour, but the behaviour is the same. It can be played at mindsports but I doubt it ever has been. I use to call it a 'reverse connection game' and it reveals a similar ideal group size. Maybe you should have a look at it if you find the behavioural consequences of its goal interesting.

I feel compelled to mention that this was the last(?) in a string of similar games (from oldest to newest): Product Wars/Mind Ninja - Pattern 14, Produto/Product Hex, Omega, Alpha, Multiplicity.

Omega and Multiplicity are the only ones where you multiply all your groups together, but I wonder if the other games also have this 'reverse connection' thing going? I haven't played them, so I can't tell.
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NJames wrote:
Instead of building strategic ideas out of narratives, I think I should have said, that the same elements we build narratives from are also easy to build strategies with.
I don't think it's all that important which. The idea with the most fruitful and far-reaching implications is simply (simply!) that games with differentiated pieces conduce to narrative.

I've seen it argued that an individual Go encounter is no less inherently memorable than its Chess equivalent. The reasoning (if such it may be called) seems to be that there are Go players who can recall entire games in perfect detail - occasionally with the additional assertion that there's an essential difference in something called The Eastern Mind. Knowing almost nothing about Go, and roughly the same about cognitive psychology, I'd venture to suggest that this is flapdoodle. It seems pretty unlikely that a majority of people anywhere find the relative disposition of undifferentiated things as easy to remember as that of things with stand-out features. Homo landmarkicus.

A key part of the memorable is differentiation, and a key part of accessibility is being memorable.
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michamund wrote:
christianF wrote:
I have experienced these phenomena in a slightly more straightforward game called Multiplicity (early 2013 but alas, not in the database yet). It's two-player and each having their own colour, but the behaviour is the same. It can be played at mindsports but I doubt it ever has been. I use to call it a 'reverse connection game' and it reveals a similar ideal group size. Maybe you should have a look at it if you find the behavioural consequences of its goal interesting.

I feel compelled to mention that this was the last(?) in a string of similar games (from oldest to newest): Product Wars/Mind Ninja - Pattern 14, Produto/Product Hex, Omega, Alpha, Multiplicity.

Omega and Multiplicity are the only ones where you multiply all your groups together, but I wonder if the other games also have this 'reverse connection' thing going? I haven't played them, so I can't tell.
I haven't played Omega and I haven't played Multiplicity all that often (contrary to Omega you need an applet for keeping the score), but the 'reverse connection' behaviour is quite obvious. Or at least it was to me because 'seeing it' was what made me invent the game.
 
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Cameron Browne
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NJames wrote:
Do I understand correctly that it was the human who noticed the pattern, and not a self-modifying algorithm?
That's right. It still requires a human observer to recognise and interpret the insight.

One thing seriously lacking in all AI research over its almost 70 years is the aspect of explanation. We are still using "black box" approaches that can learn good solutions for complex problems, without providing any clue as to the underlying functions that produce those results.

AlphaGo and AlphaZero are classic examples; brilliant results, but the only clue as to the superhuman strategies they emulate is to observe them in action and hope to notice patterns in play.

In the current work I mentioned, we're looking at learning simple piece arrangements that emulate particular strategies. This approach could have a number of benefits:
1. Improve AI play (by biasing MCTS playouts).
2. Indicate good/bad strategies (maybe allowing estimation of strategic potential).
3. Easy transfer to other contexts.
4. Allow explanation of learnt strategies in human-comprehensible terms.

Here's a paper that outlines the basic idea (http://cambolbro.com/temp/strategic-features-anon.pdf). It's just been submitted and is under review so is anonymised.

Regards,
Anonymous
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mocko wrote:
NJames wrote:
Instead of building strategic ideas out of narratives, I think I should have said, that the same elements we build narratives from are also easy to build strategies with.
I don't think it's all that important which. The idea with the most fruitful and far-reaching implications is simply (simply!) that games with differentiated pieces conduce to narrative.

I've seen it argued that an individual Go encounter is no less inherently memorable than its Chess equivalent.
Nathan's idea may be considered 'conceptual accessibility', the implication being that Chess scores higher than Go, a view to which I agree.

Now if Chess' popularity is in part due to it, then I think it's worth noting that 'conceptual accessibility' and 'conceptual depth' are not the same thing. Go may well be argued to have a comparable depth, for instance, but not the same accessibility. But obviously both are quite crucial for the human mind.
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christianF wrote:

Now if Chess' popularity is in part due to it, then I think it's worth noting that 'conceptual accessibility' and 'conceptual depth' are not the same thing. But obviously both are quite crucial.
I'd love to hear more people weigh in on this. I've gone back and forth on this point, although I believe in this thread I have maintained that accessibility is a necessary component of depth. It is the "not too hard" quality.

What is more useful, to say that we want depth and accessibility, it to say that accessibility is necessary for depth?
 
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NJames wrote:
christianF wrote:

Now if Chess' popularity is in part due to it, then I think it's worth noting that 'conceptual accessibility' and 'conceptual depth' are not the same thing. But obviously both are quite crucial.
I'd love to hear more people weigh in on this. I've gone back and forth on this point, although I believe in this thread I have maintained that accessibility is a necessary component of depth. It is the "not too hard" quality.

What is more useful, to say that we want depth and accessibility, it to say that accessibility is necessary for depth?
Well, accessibility helps you to get to depth in the first place, so in that perspective it may be considered necessary.
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christianF wrote:
NJames wrote:
christianF wrote:

Now if Chess' popularity is in part due to it, then I think it's worth noting that 'conceptual accessibility' and 'conceptual depth' are not the same thing. But obviously both are quite crucial.
I'd love to hear more people weigh in on this. I've gone back and forth on this point, although I believe in this thread I have maintained that accessibility is a necessary component of depth. It is the "not too hard" quality.

What is more useful, to say that we want depth and accessibility, it to say that accessibility is necessary for depth?
Well, accessibility helps you to get to depth in the first place, so in that perspective it may be considered necessary.
Indeed. Depth that you can't access stands a good chance of leaving you cold.

 
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Cameron Browne
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NJames wrote:
What is more useful, to say that we want depth and accessibility, it to say that accessibility is necessary for depth?
Hang on, is what you call "accessibility" the same as clarity? Robert Abbott covered this years ago in "Under the Strategy Tree":

Quote:
The apparent depth of a game does not depend on how far you can travel down the strategy tree of the game. It instead depends on how far you can see down the strategy tree. And how far you can see depends on the clarity of the game.
Regards,
Cameron
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I don't think accessibility equals clarity, no. As far I as I can tell, clarity indicates an ease in reading several plies ahead.

When I think of how accessible simple strategic ideas are in Chess I think about how readily the mind appreciates the idea of "protect the king," "get the queen into action quickly," "attack on the left," etc. The mind naturally conceives of interesting terms, like outpost, blockade, fortress, while playing the game. Even if you wanted to, you couldn't play a game of Chess without forming strategic ideas. They may not be very good, but that isn't the point.

In contrast, you could much more easily play Go and never think anything more than "this is weird." Narrative metaphors can be applied, but they come less readily. The whole character of the game is more alien.

Chess provides lots of "affordances" (to borrow a term that may not quite fit) for strategy.
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camb wrote:
NJames wrote:
The model proposed in the paper doesn't reference the refinement of the strategy at all, it is only concerned with how the strategy functions when given a certain amount of computational resources.
Yes, even one of the papers' authors disagrees with the emphasis on the objective measurement of computational resources in the paper! It seems pointless to remove the human player experience from the game.

So my reading of that diagram might be different to what the main author intended, but it coincidentally captures what I think is the essence of strategic potential beautifully.

Regards,
Cameron

Does this mean that we are further away from the premise that abstract game design is objective, one of the starting points of this thread? I agree that the human experience is important but I can't see how it can be objectively measured.
 
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