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Subject: One of the best connection games out there rss

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Billy McBoatface
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As a fan of abstracts, you would think I like connection games, but many of them leave me cold. I'm not sure why games like hex, Y, etc., feel dull to me, but they do.

But Slither is an exception. It's rules are almost as simple as hex, so let's get them out of the way:

* Each player takes a color. One player tries to connect the left and right edges, the other player tries to connect the top and bottom edges.
* Each turn you must add a piece to the board (which is a grid). Then you may shift one of your pieces by one space either orthogonally or diagonally.
* At the end of your turn, you must not have two pieces that are diagonally connected. For example:

. . . . . . . . . . . . O O O .
. O . . . O O . . O # # O . O .
. . O . . . O . . . O . O O . .
. . . . . . . . . . . . . . . .
White can't This is White can't This is illegal
play this OK do this either also!


There we go, the whole rules.

What makes this better than other connection games? I think that it's a combination of being able to move your pieces, and the "no diagonal" rule. Moving your pieces keeps the board from feeling too static, and the diagonal rule means that your pieces might not always be good - sometimes having a piece in a certain place is a liability, because it makes it illegal to a piece where you really want it!

Slither has very high clarity (to borrow Robert Abbott's term), so if you focus on a situation you can plan ahead for many moves. But you have to be careful, one little missed move possibility and all your calculations are wrong! Finding the sequence that lets your pieces play efficiently while leaving your opponent's pieces in a tangled mess that can't do anything useful without running into the no-diagonals rule is the key to winning.

If you have a go board then you already have the equipment for this game. Heck, if you have a checkers board and enough pieces then you can try out a small game. Give it a try, it's a great game.
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wmshub wrote:
Slither has very high clarity (to borrow Robert Abbott's term), so if you focus on a situation you can plan ahead for many moves.

Thank you for the review. However, the comment above is the one that most baffles me. I have played Slither a number of times, but didn't find it to be a paragon of clarity. If anything the double moves combined with the sheer number of possibilities seemed rather opaque. Can you please clarify?
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tckoppang wrote:
wmshub wrote:
Slither has very high clarity (to borrow Robert Abbott's term), so if you focus on a situation you can plan ahead for many moves.

Thank you for the review. However, the comment above is the one that most baffles me. I have played Slither a number of times, but didn't find it to be a paragon of clarity. If anything the double moves combined with the sheer number of possibilities seemed rather opaque. Can you please clarify?
I'd put slither's clarity below Hex, because of the movement. But I'd put it above chess (where a queen move can change the whole board), and above something like reversi/othello (where, again, a single move can change the effects of everything else). I'd put it more around go or checkers. So, I guess you could be right "very high clarity" was probably wrong, that would be a game like hex, but I still would call it high clarity.
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wmshub wrote:
tckoppang wrote:
wmshub wrote:
Slither has very high clarity (to borrow Robert Abbott's term), so if you focus on a situation you can plan ahead for many moves.

Thank you for the review. However, the comment above is the one that most baffles me. I have played Slither a number of times, but didn't find it to be a paragon of clarity. If anything the double moves combined with the sheer number of possibilities seemed rather opaque. Can you please clarify?
I'd put slither's clarity below Hex, because of the movement. But I'd put it above chess (where a queen move can change the whole board), and above something like reversi/othello (where, again, a single move can change the effects of everything else). I'd put it more around go or checkers. So, I guess you could be right "very high clarity" was probably wrong, that would be a game like hex, but I still would call it high clarity.


Relatedly, I've found that over time, I've learned to play good, strategic moves, without calculating. This sort of "over the lookahead horizon" play is evidence of at least some discoverable clarity.
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can someone elaborate on what "clarity" means? I have seen this term before, didnt understand it then, and am somewhat skeptical of its value.

I do like Slither; Ive played it just a few times but there is definitely something there.
 
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Russ Williams
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sundaysilence wrote:
can someone elaborate on what "clarity" means? I have seen this term before, didnt understand it then, and am somewhat skeptical of its value.

It's often used as in this article:
http://www.thegamesjournal.com/articles/DefiningtheAbstract....
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sundaysilence wrote:
can someone elaborate on what "clarity" means? I have seen this term before, didnt understand it then, and am somewhat skeptical of its value.

I do like Slither; Ive played it just a few times but there is definitely something there.
Clarity is the ability to visualize more easily the effects of a move in a game. A game with higher clarity generally is easier to plan ahead in, because you can keep track in your head of several moves in sequence and see what the end result will be. Games like hex, where each move is very small and simple, tend to have very high clarity. Chess is a lot lower. I first saw the term when Abbott was critiquing his own game, "Ultima"; he decided it wasn't a very good game because the clarity was so low that nobody could read ahead more than a very few moves, negating the opportunity for longer term strategy. I'm not sure whether he invented the "clarity" term or not, but that was the first time I heard it.

Edit: Beaten to it by Russ! And the article he links to has a different definition. I'd go with his. My definition is one I came up with just from seeing it used before. Maybe I did use it wrong it my review here?

Edit #2: I'm not so sure that my definition is wrong. Both Thompson and I refer to Abbott as the source of the term, complaining that Ultima has low clarity; but by Thompson's definition, Ultima has fairly high clarity. Certain pieces in Ultima are significantly better than others, so a clear short-term goal is to capture the good pieces or trade inferior pieces for better ones. But by my definition Ultima does have the low clarity that Abbott complained about; all but the king move like rooks or like queens, and attacks can come in many wildly different manners, making it very hard to keep track of changes in threats as pieces move. Is there a better consensus on the term than just this article?
 
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thanks for the article, havent read it yet.

But arent all games either deterministic or not? in deterministic games, some games have few choices, but then the depth goes to great depths. Whereas game like chess which might have 20 or 30 possible moves, then depth might only be 4 or 5 moves.

But either way, it amounts to the same thing, it still going to work out to X number of choices, some incredible number. And as the number gets too large then it becomes an educated guessing game.

Another way to look at things, take a game like Dvonn or CLans or Nim where every move is limiting the number of choices that are left. In these games, the game is invariable running toward the end. But in chess you can go back and forth, so there are times when there is no foreseeable end to the game. I see a distinction here that makes logical sense to me.

What is interesting about Dvonn or CLans to me, is that at the beginning of the game there are tons of choices, so many that it is impossible to calculate them all, but near thee end of the game the choices are so limited and the decision tree so small that there is nothing you can do to change the outcome. At some pt. then in the middle of the game, there is a sort of climax where at the right moment, the decision tree is able to be studied and you can make an optimum choice. A better player might see it earlier. The advantage to me, is that these games do not drag on unlike chess, which can easily run 20 or 30 moves past the time when the game was already lost.

I see this as a useful distinction among games, but I see "clarity" as a subjective sort of thing.
 
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sundaysilence wrote:
thanks for the article, havent read it yet.

But arent all games either deterministic or not? in deterministic games, some games have few choices, but then the depth goes to great depths. Whereas game like chess which might have 20 or 30 possible moves, then depth might only be 4 or 5 moves.

But either way, it amounts to the same thing, it still going to work out to X number of choices, some incredible number. And as the number gets too large then it becomes an educated guessing game.

But 2 games could have similar branching factor depth and different clarity. It's not simply about the number of decisions/choices. It's about how easy it is assess positions, find good moves, and so on. E.g. in the extreme case, a game could be so unclear that no matter how much time you spend analyzing it, you really have no idea which of your possible moves are better looking than others, and you may as well guess randomly. On the other hand, a game could have a huge number of possible branches yet the best move could be very clear.

Quote:
What is interesting about Dvonn or CLans to me, is that at the beginning of the game there are tons of choices, so many that it is impossible to calculate them all, but near thee end of the game the choices are so limited and the decision tree so small that there is nothing you can do to change the outcome. At some pt. then in the middle of the game, there is a sort of climax where at the right moment, the decision tree is able to be studied and you can make an optimum choice. A better player might see it earlier. The advantage to me, is that these games do not drag on unlike chess, which can easily run 20 or 30 moves past the time when the game was already lost.

I agree; I often like those kinds of games which "wind down" in some sense and come to an inevitable end.

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I see this as a useful distinction among games, but I see "clarity" as a subjective sort of thing.

Certainly there's an element of subjectivity to it! But there's also some element of "empirical objectivity" to it I would say, in the same sense that even though how we perceive various stimuli is subjective, nonetheless it's a safe bet that most people find it unpleasant to have their hand dunked in boiling water. Similarly most people find (e.g.) tic-tac-toe to have higher clarity than chess.
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russ wrote:
It's not simply about the number of decisions/choices. It's about how easy it is assess positions, find good moves, and so on. E.g. in the extreme case, a game could be so unclear that no matter how much time you spend analyzing it, you really have no idea which of your possible moves are better looking than others, and you may as well guess randomly.


this is the part I am having a hard time understanding. Assuming the game is an abstract, where all the information is known to both players, is it just a question of understanding how the game works?


Let me ask a couple questions, for those games that lack clarity:

What is the difference between a game that is complicated and one that lacks clarity?

Do these games get more understandable with more experience?
 
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sundaysilence wrote:
russ wrote:
It's not simply about the number of decisions/choices. It's about how easy it is assess positions, find good moves, and so on. E.g. in the extreme case, a game could be so unclear that no matter how much time you spend analyzing it, you really have no idea which of your possible moves are better looking than others, and you may as well guess randomly.


this is the part I am having a hard time understanding. Assuming the game is an abstract, where all the information is known to both players, is it just a question of understanding how the game works?

From a theoretical standpoint, some games are inherently harder to solve than others. E.g. see
https://en.wikipedia.org/wiki/Game_complexity

From a practical standpoint this is also clearly true. E.g. people have an easier time playing tic-tac-toe than chess.

And it's not just because chess has more possible moves in an average position.

E.g. on average a typical chess position has a couple dozen possible moves. But we can easily create some game where a position has hundreds or millions of possible moves from a given position, but the best move is obvious. E.g. a race game on a large square grid where players start on the south edge and want to be the first to reach the north edge and each turn you can move to any square within distance 100 of your current position. Each turn there are thousands of possible moves you could make, but the clarity of the game is trivially clear: you simply want to move directly north.

Quote:
Let me ask a couple questions, for those games that lack clarity:

What is the difference between a game that is complicated and one that lacks clarity?

Define what you mean by "complicated". Do you mean complicated rules or complicated strategy? (The 2 are independent/orthogonal issues.)

I'll assume you mean strategy. A game with simple strategy is probably very clear. (E.g. tic-tac-toe.) A game with non-obvious strategy has less clarity, but hopefully has SOME clarity because otherwise any move looks as good as any other move to you.

Quote:
Do these games get more understandable with more experience?

For "real world" games, certainly yes. I think we can easily construct "artificial" example games with low or zero clarity which you'll practically never get better at, e.g. games which involve calculation of effectively unpredictable cryptographically secure functions - no experience or intuition will help you know what input string produces a given hash string result from a cryptographically secure hash function, for example. But that's not the sort of "game" which real humans would probably enjoy playing.
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OK I did read the article and am not convinced clarity is anything more than a complex game (abstract games primarily) where the strategy is non intuitive. That is the best I can make of the article.

two things: the one example he gives is Ultimaa. Which I vaguely recall reading about but have never really played. Can anyone give a more common example of an opaque game?

At the end of the bit about CLarity, he brings up that experience is needed. Well that is true of many games and certainly true of games like chess; with more experience one understands more about what is needed to win.

But isnt that the same thing as saying that in abstract game, the strategies are often non intuitive simply because abstract games do not reflect real life? And with experience we will get better at them because we will learn to suppress our reality based leanings and give into the abstract nature.

Here's an example from chess. My ten year old was having trouble with finding the next move; and I suggested one, "But I dont see how that helps me.."

"Right it doesnt win. It can only draw. But sometimes that's the best you can do You have to play for a draw. because anything else just loses."

So its non intuitive, you play for a draw because the abstract nature of the game sets it up that way. To try to win is to lose. Totally non intuitive. But thats the nature of abstract games, they dont relate to real life. The answers are not based on real life.

So isnt opaqueness like that?
 
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sundaysilence wrote:
OK I did read the article and am not convinced clarity is anything more than a complex game (abstract games primarily) where the strategy is non intuitive. That is the best I can make of the article.

"The strategy is non-intuitive" seems a possible way to re-phrase it to some degree.

Othello is sometimes mentioned as not having high clarity. A beginner, used to playing other abstract games, might reasonably feel that intuitively it is good to have more pieces than the opponent during play. Yet that intuition is wrong in many Othello positions. So the strategy is not intuitively obvious.


But note that having intuitive strategy does not mean a game is easy. E.g. in many games, having more pieces in play than the opponent IS generally good. You may easily see that moves A, B, C look clearly good (because they capture an enemy piece) and moves D, E, F look clearly bad (because you'll lose a piece), so there is some clarity there, but you still don't know which of A, B, C is the best move. And deciding that might take lots of careful difficult analysis. So the basic strategy is intuitive (kill enemy pieces and don't let your own get killed) but "the devil is in the details" - it's still not always easy!


Quote:
But isnt that the same thing as saying that in abstract game, the strategies are often non intuitive simply because abstract games do not reflect real life?

I don't think that's true.

1. I'm comfortable with "abstract" reasoning, doing math, etc. It's not inherently unintuitive.

2. Many "real life" problems are even more difficult and intractable than abstract problems, because real life is far messier and more complex than the usually simple minimalist rules of an abstract game. Navigating a complicated government bureaucracy is far worse than figuring out a decent move in a chess game.

(Indeed, the whole point of abstraction in math & science is to make a problem easier to solve. It's too difficult to realistically calculate in detail the motion all the zillions of atoms in the earth rotating around the sun, so we abstract the earth and sun to perfect spheres, which don't really exist in "real life".)

Quote:
Here's an example from chess. My ten year old was having trouble with finding the next move; and I suggested one, "But I dont see how that helps me.."

"Right it doesnt win. It can only draw. But sometimes that's the best you can do You have to play for a draw. because anything else just loses."

So its non intuitive, you play for a draw because the abstract nature of the game sets it up that way. To try to win is to lose. Totally non intuitive. But thats the nature of abstract games, they dont relate to real life. The answers are not based on real life.

Huh? In real life it often happens that you can't get the ideal result you hope for (and trying to "win" will only hurt you), so you have to settle for some kind of compromise. I don't see that as unintuitive or not based on real life at all. Quite the contrary!

A tie result in a game seems very much like deciding to compromise in real life instead of trying to defeat the other person (e.g. in a business deal, a lawsuit, a disagreement in a store, an argument with a friend/spouse, whatever).
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all those situations you quote in the last para. those are economic situations involving a win/win outcome. That's totally different from competitive zero sum situations.

Think of football or baseball or basketball or boxing or anything like that where two players or two teams are in competition why would it be better to play for a draw if it seems like a win is more likely? You dont kick a FG and tie the game if you are on the one yard line with a chance to win. Or at least that's not conventional wisdom.

You act like this is so hard for you to imagine and yet use examples that arent even in the same setting. These economic situations you site, what would a draw be like anyhow? Is a draw even an outcome when you're dealing with more than 2 players?

If you are ahead in a boxing match, you dont try to avoid knocking the guy out. But in chess, when you get ahead by a piece, your primary strategy is to exchange NOT go for the mate. You have to play chess a lot to start to realize this... Because the other guy, who is behind in material, he actually is better placed to attack the king, because well, giving up that material he actually gained a move to spend on that strategy.

Any real life competition, when you feel you are ahead you dont play for a tie. This seems natural to me. THe examples you give seem completely unnatural to competitive games. They are OK for economic examples, but economics must necessarily deal with more than 2 parties for it to make any sense. Usually many parties. Hence a win/win outcome makes sense for multi party games. but not two person zero sum games.

Othello is an interesting example because I have played it and yes it is counter intuitive that flipping more stones is counter productive. But then you study the game and it is more about positioning especially near the corners.

But so what? So that is what it takes to win. its non intuitive from the ordinary sense of scoring, that more is better. But once you figure this out; then you look at the game differently; you look at it from a positioning stand point.

I am not sure that makes the game any more deeper or any more opaque. Its just a different way of looking at things. But the game is still logical and you go step by step in order to analyze it...

I am looking for some qualititative difference that makes the game opaque. All I can come up with so far, is that the strategy is counter intuitive.
 
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russ wrote:
... you still don't know which of A, B, C is the best move. And deciding that might take lots of careful difficult analysis. So the basic strategy is intuitive (kill enemy pieces and don't let your own get killed) but "the devil is in the details" - it's still not always easy!



But we already have "depth" as one variable. The depth of the decision tree or really the volume of it (it could be broad and shallow or it could be narrow and deep). Basically how much we have to factor to make a good move.


That's all you're saying here, it seems to me. Yes certain decisions are difficult. That could very well be related to the depth of the game how complex it is.

But this guy is hypothesizing some other factor "clarity". Well how is clarity or opaqueness different from complexity. That's the base question.

To say that something is the "devil in the details" that doesnt explain what clarity/opaqueness is.

I do agree with you about the real life problems with government, etc. I am not sure that helps us to understand here because we are simply comparing various abstract games. Even if we want to put real life into it, the "opaqueness" I presume would come from human pyschology which is indeed an interesting subject; but I dont think that is what they are getting at with opaqueness.

Otherwise, I would have understood all that before.
 
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sundaysilence wrote:
all those situations you quote in the last para. those are economic situations involving a win/win outcome. That's totally different from competitive zero sum situations.

Huh? Are you disagreeing that there are obvious situations in real life where you need to "cut your losses" instead of going for the win? Plenty of economic (and other) situations do not end in a win-win but more of a tie, or a "compromise" which doesn't really please either party, but which they both prefer to losing.

Quote:
Think of football or baseball or basketball or boxing or anything like that where two players or two teams are in competition why would it be better to play for a draw if it seems like a win is more likely?

That's the big "if". I'm talking about situations where you think that a win is NOT likely. In that case, it's often foolish to go for the win instead of trying to merely minimize your losses. Such situations often arise in real life. It doesn't seem at all counterintuitive or abstract to me. E.g. you know you are in the right about some disagreement with a store about a small defective product, e.g. you bought an apple and it turns out to be bad, you discover the next day, but you know from experience that the store is not going to refund your money, so you don't bother wasting your time trying to go argue about it with them. That's not a win-win situation, that's cutting your losses and avoiding wasting your time because you realize the probability of your winning (getting a refund) is too low to bother with.
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My take on clarity is based on the difference between Chess and Go and probably puts Slither midway. In Go it is fairly easy to visualise the effect of multiple moves, in Chess this is much more difficult task, though obviously made easier by practice. Both games have useful heuristics and methods of paring down the possible moves but it's this easy mind's eye visualisation that differentiates them. For Slither I can fairly easily imagine where strings of pieces go but it was initially quite difficult to visualise the positions in which illegal moves prevent blocking which is so key to the game. so for this reason it kind of sits between the two.
 
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But again this is all coming down to a subjective determination of what is clear to you; and b) relies on a category we have already defined as "depth."

The point about practice helping to see the results also cuts against your point. All skill games get better with practice. Presumably if we all practice as much at each game, the moves of Go, or Chess or Slither would all be equally obvious/non obvious to us...

WHat other conclusion is there? These are, by definition; abstract games where all the information is out there in front of us. it is a question of how far you or I can calculate the decision tree or else come up with some short hand heuristic to make that decision.

What difference does it make if the goal is to capture the king or capture the most territory? How is one any more clearer than the other?
 
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wmshub wrote:
As a fan of abstracts, you would think I like connection games, but many of them leave me cold. I'm not sure why games like hex, Y, etc., feel dull to me, but they do.

But Slither is an exception. It's rules are almost as simple as hex, so let's get them out of the way:

* Each player takes a color. One player tries to connect the left and right edges, the other player tries to connect the top and bottom edges.
* Each turn you must add a piece to the board (which is a grid). Then you may shift one of your pieces by one space either orthogonally or diagonally.
* At the end of your turn, you must not have two pieces that are diagonally connected. For example:

. . . . . . . . . . . . O O O .
. O . . . O O . . O # # O . O .
. . O . . . O . . . O . O O . .
. . . . . . . . . . . . . . . .
White can't This is White can't This is illegal
play this OK do this either also!


There we go, the whole rules.


Why is case 2 above legal but case 4 illegal?
 
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cdunc123 wrote:
wmshub wrote:
As a fan of abstracts, you would think I like connection games, but many of them leave me cold. I'm not sure why games like hex, Y, etc., feel dull to me, but they do.

But Slither is an exception. It's rules are almost as simple as hex, so let's get them out of the way:

* Each player takes a color. One player tries to connect the left and right edges, the other player tries to connect the top and bottom edges.
* Each turn you must add a piece to the board (which is a grid). Then you may shift one of your pieces by one space either orthogonally or diagonally.
* At the end of your turn, you must not have two pieces that are diagonally connected. For example:

. . . . . . . . . . . . O O O .
. O . . . O O . . O # # O . O .
. . O . . . O . . . O . O O . .
. . . . . . . . . . . . . . . .
White can't This is White can't This is illegal
play this OK do this either also!


There we go, the whole rules.


Why is case 2 above legal but case 4 illegal?

The rules say that, at the end of a turn, for any two like-colored, diagonally adjacent stones there must be at least one like-colored stone which is orthogonally adjacent to both. The two center stones in case 4 don't comply with this.
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Quote:
The rules say that, at the end of a turn, for any two like-colored, diagonally adjacent stones there must be at least one like-colored stone which is orthogonally adjacent to both. The two center stones in case 4 don't comply with this.


Thanks.

Am I right to think the game play is better with the current rule, as opposed to an alternative rule such as "diagonals are illegal unless they are part of a single group of stones"? I find that alternative rule more elegant, for what it's worth. But it would allow case 4 above and I'm guessing the game is better with case 4 illegal -- is that right? I have not played Slither yet, so I have no way of knowing.
 
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cdunc123 wrote:
Am I right to think the game play is better with the current rule, as opposed to an alternative rule such as "diagonals are illegal unless they are part of a single group of stones"? I find that alternative rule more elegant, for what it's worth. But it would allow case 4 above and I'm guessing the game is better with case 4 illegal -- is that right? I have not played Slither yet, so I have no way of knowing.

I prefer the current rule because it's simpler to check (both for humans and computers), but otherwise the differences in game play are extremely small.

(The game is drawless either way, as far as I know.)
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