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Subject: Explaining the concept behind Lazo rss

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David Bush
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When I pitched my game Lazo to Jay Tummelson of Rio Grande Games, he told me it was "too hard." Since then I have changed the tile design and the way I present the rules. You can see my latest attempt to explain on the Wiki page for Lazo. You can see the same content from the main Lazo page if you click on More-> Community Wiki, but it doesn't look quite right that way.

I intend to add more introductory puzzles, a section on tactics, and some more advanced puzzles. I would greatly appreciate your feedback. The main thing I want to know is, after reading these rules, would you feel confident that you could play the game straight out of the box? Also is there ANY PART that you still find confusing? I am concerned that I may have started out slowly but then speeded up too much. I need a different perspective to point out the (probably) obvious to me.

Thanks in advance!

EDIT: I should mention that since this post I have modified the beginning of the rules to mention the game object at the start. Stephen's comments were based on the earlier version of the rules.
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Stephen Tavener
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1. You would be better off to start with the high-level stuff (how to win, etc), then fill in the details later. If you start with the detail without giving people a conceptual framework to hang it all off, they are going to find it tough going. The rules explanation actually starts about 3/4 of the way down the page.

2. Some of the text seems irrelevant to play. For instance, "The peg portion is half as thick as the rest of the tile.". It would be more useful in s separate documents explaining how to make a set.

3. "This way of stacking is called a lattice. The lattice extends beyond those spaces which can be occupied by tiles."

This made me scratch my head. Maybe if I had read further to the actual rules; but again, it didn't seem relevant to play at this point.


My mind kind of slid off the rest of the rules at this point, and I stopped reading - sorry
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David Bush
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mrraow wrote:
1. You would be better off to start with the high-level stuff (how to win, etc), then fill in the details later. If you start with the detail without giving people a conceptual framework to hang it all off, they are going to find it tough going. The rules explanation actually starts about 3/4 of the way down the page.

Providing a conceptual framework is exactly what I thought I was doing. How will the reader understand what a hole path is until I explain what the lattice is in the first place?

Quote:
2. Some of the text seems irrelevant to play. For instance, "The peg portion is half as thick as the rest of the tile.". It would be more useful in s separate documents explaining how to make a set.

It is relevant; this disparity in thickness is what creates blocking regions in the lattice.

Quote:
3. "This way of stacking is called a lattice. The lattice extends beyond those spaces which can be occupied by tiles."

This made me scratch my head. Maybe if I had read further to the actual rules; but again, it didn't seem relevant to play at this point.


My mind kind of slid off the rest of the rules at this point, and I stopped reading - sorry :(

Okay, so you didn't read the game object? I lost you before you got that far?
 
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Stephen Tavener
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Quote:
Okay, so you didn't read the game object? I lost you before you got that far?


Sorry

I _will_ try again when my sleep:caffeine ratio is more favourable.
 
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David Bush
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Everything I placed at the start is a lead-up to the game object. If I were to put the game object first, wouldn't someone else tell me "you need to provide a conceptual framework first"? I don't mean to sound petty. I appreciate your feedback. But it seems I'm damned if I do and damned if I don't.

It's important to know the lattice extends beyond the pyramid of cells where tiles may be placed. Sometimes a hole path needs to extend into these unreachable cells in order to pass completely through a loop. So, I thought it would be best to say the lattice extends beyond in all directions.

I guess I just lost your trust during the course of my explanation. It read like I was wandering around at random without regard to whatever this game might be. Would you agree?
 
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Rex Moore
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I think all rules should start off with how you win the game... I guess what many rulesets call the object of the game. Whether it's "most victory points wins" or "first to connect two opposite sides" or "make your opponent exhaust their deck first."

So perhaps, David, it could start like this:

"Lazo is a board game for two players which uses special tiles. The object of the game is to form a lattice path (explained momentarily) with your tiles which makes a loop that goes completely around an opposing path."


I think that alone puts me in a better frame of mind to try to understand the rules. Note that you'll use "(and possibly with the board surface)" and the definition of a hole path later in the rules. I don't think they're necessary right at the top when you're trying to give folks a quick overview.

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David Bush
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Okay, thanks for the tip. I modified the beginning, and I mentioned a little further down that "this disparity in thickness creates blocking regions"

I do appreciate everyone's feedback. If there is a problem in the rules for you, there is almost certainly the same problem for lots of other people.
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Peter S.
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Just read the rules for the game, and I have to agree with the other commenter. Before you even get to the "How to play Lazo" section, having a "What is Lazo?" section that says something like:

Lazo is an abstract, topographical wrestling match where your goal is to "pin" your opponent to the board by forming a "bridge" over a "river" of two or more of their pieces, or to "squeeze" your opponent by forming a 3D loop of your own pieces around a river of theirs.

...would give context to all of the rest of the rules that otherwise would be missing. Also, some of the rules could be simplified quite a bit:

Tiles are adjacent when they are in direct contact, not counting the peg. Thus, two tiles are adjacent either when their corners are touching, or when one tile's corner is resting atop another tile's center.

A series of adjacent tiles of the same color is a "river" or "path" - while Lazo is an abstract game, the flowing and branching nature of the game can be likened to tiny rivers forming during a rainstorm, or game trails winding their way though quiet woods, or the roots of two neighboring trees becoming tangled with each other over time.

New tiles may be played to any vacant space, but must be played such that they are adjacent to another tile of their color or to the board. (It may help to think of the board as one giant tile of both colors, both for placing tiles and for seeing if a loop has been completed.)


This is just what came to mind after an initial reading and some time spent thinking about what the rules are looking to communicate. Also, you may want to move puzzles and examples into a glossary, simply to avoid spreading the core rules of the game over too many pages.
 
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David Bush
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Not trying to nit pick, just trying to follow what you say.

ErsatzDragon wrote:
Just read the rules for the game, and I have to agree with the other commenter. Before you even get to the "How to play Lazo" section, having a "What is Lazo?" section that says something like:

Lazo is an abstract, topographical wrestling match where your goal is to "pin" your opponent to the board by forming a "bridge" over a "river" of two or more of their pieces, or to "squeeze" your opponent by forming a 3D loop of your own pieces around a river of theirs.

So, my brief "Each player tries to make a loop which goes completely around an opposing path" does not provide enough context in your opinion?

Quote:
...would give context to all of the rest of the rules that otherwise would be missing. Also, some of the rules could be simplified quite a bit:

If you believe the rules could be simplified, does that mean they provided you with more than enough information? Do you feel confident, after reading my rules, that you could play the game straight out of the box?

Quote:
[i]Tiles are adjacent when they are in direct contact, not counting the peg. Thus, two tiles are adjacent either when their corners are touching, or when one tile's corner is resting atop another tile's center.

Did you find all my diagrams of the lattice structure superfluous?
Also, "not counting the peg" why not counting the peg? The peg is thinner than the rest of the tile. The bottom surface of the peg does not touch anything. That is why there are blocking regions.

Quote:

This is just what came to mind after an initial reading and some time spent thinking about what the rules are looking to communicate. Also, you may want to move puzzles and examples into a glossary, simply to avoid spreading the core rules of the game over too many pages.

I appreciate your suggestions. How do I do this glossary? It appears to me I have just this one wiki page to edit. Do you personally not need the examples to understand the game?
 
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Peter S.
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twixter wrote:
Not trying to nit pick, just trying to follow what you say.

ErsatzDragon wrote:
Just read the rules for the game, and I have to agree with the other commenter. Before you even get to the "How to play Lazo" section, having a "What is Lazo?" section that says something like:

Lazo is an abstract, topographical wrestling match where your goal is to "pin" your opponent to the board by forming a "bridge" over a "river" of two or more of their pieces, or to "squeeze" your opponent by forming a 3D loop of your own pieces around a river of theirs.

So, my brief "Each player tries to make a loop which goes completely around an opposing path" does not provide enough context in your opinion?

Quote:
...would give context to all of the rest of the rules that otherwise would be missing. Also, some of the rules could be simplified quite a bit:

If you believe the rules could be simplified, does that mean they provided you with more than enough information? Do you feel confident, after reading my rules, that you could play the game straight out of the box?

Quote:
[i]Tiles are adjacent when they are in direct contact, not counting the peg. Thus, two tiles are adjacent either when their corners are touching, or when one tile's corner is resting atop another tile's center.

Did you find all my diagrams of the lattice structure superfluous?
Also, "not counting the peg" why not counting the peg? The peg is thinner than the rest of the tile. The bottom surface of the peg does not touch anything. That is why there are blocking regions.

Quote:

This is just what came to mind after an initial reading and some time spent thinking about what the rules are looking to communicate. Also, you may want to move puzzles and examples into a glossary, simply to avoid spreading the core rules of the game over too many pages.

I appreciate your suggestions. How do I do this glossary? It appears to me I have just this one wiki page to edit. Do you personally not need the examples to understand the game?


It's mostly a case of organization, just moving the parts around so that the core ideas are presented first, the most compact version of the rules is laid out, and then the consequences of those rules are more deeply explored. The diagrams are not superfluous, though they only take on meaning after the text explanations.

(By "not counting the peg" I was meaning the same thing as "The bottom surface of a triangular peg is not adjacent to any tile beneath it." In other words, the peg isn't considered when determining if two tiles are adjacent.)

I should clarify that I when I said that the rules could be simplified, I was meaning the text explanation of the rules, i.e., simpler and more direct phrases could be used to explain the concepts. I wasn't intending to mean that the rules of the game should be substantively altered. Also, I was looking at the "Lazorules" PDF, so forgive me if this is intended to be a Wiki page rather than an instruction manual.

I do think there are many opportunities to "tighten up" the language, though I'm coming from a background in technical writing - if you're not familiar with technical writing, a quick search turned up this presentation: http://web.mit.edu/me-ugoffice/communication/technical-writi...

Really, the sentences I wrote were intended as examples. You can consider them or not at your leisure. And everyone's writing style is different.
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David Bush
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ErsatzDragon wrote:
... Also, I was looking at the "Lazorules" PDF, so forgive me if this is intended to be a Wiki page rather than an instruction manual.

Gah. EVERYTHING I submitted before, the pdf files, the images, ALL of it I intend to delete and replace with a new pdf , new images etc. The ONLY thing I seek comments on is the wiki, which may serve as the framework for a rulebook, but I haven't written it yet.

I would still like to know, if you think the rules could be more concise, does that mean you understand them? Does anyone feel they understand these rules AS PRESENTED IN THE WIKI well enough to play the game? What about the diagram that I use to explain the steps you should take to recognize a 3-D loop, for example. Did anyone get that far? How about the puzzles? Did anyone try them? Or is it just too much to slough through the way it is?

You say you want me to "put the core ideas first." I should first "[lay out] the most compact version of the rules" and then "explore the consequences." Apparently this means you want me to hold off on explaining what a lattice is until I define the game object. Is that right?

But the lattice is not a consequence of the rules. It's the foundation for the rules. It's the framework I need to explain in order for the rules to make sense. How can I tell you to form a lattice path which an opposing path passes completely through until I explain what this lattice is?

Also, I would like to point out, these rules are not very long. Most of the space is taken up with diagrams. Compared to Caylus Magna Carta for example, the number of concepts the gamer is expected to assimilate is much less. But apparently, the concept of an opposing path passing through a loop is so daunting, the readers need me to entice them with an allegorical description that (for example) sounds like a turn-based wrestling match, so they are willing to stay with me to the end. Is this really the case? Or were you referring to the pdf file?

I do appreciate your feedback! This is what I asked for. I just don't follow how changing the order around will make understanding any easier.
 
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John
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twixter wrote:
How about the puzzles? Did anyone try them?

I tried them and got both right. I think I have understood how to win though there are various bits of the rules I'm not sure whether I understood.

Things that confused me - the first mention of "peg" I was looking for a small round peg rather than the 3 hex bit. This wouldn't be an issue if I had the actual pieces in front of me when reading the rules. I found it difficult to work out what I was looking at with the right hand tile in the first picture, the second picture was better.

The mentions of "infinite lattice" and "This lattice does NOT completely fill the three dimensional space it occupies. There are blocking regions located on top of the hexagonal tips of each lattice space, and also below the surface of the peg on the underside. This is important to know when you play the game." I presume the important part here is that the peg part doesn't make the hole it fills your colour? I can't work out what the significance of the blocking regions is - these are the parts of the piles which touch other tiles aren't they?

I found these style of pieces easier to visualise for some reason (perhaps just because these are physical pieces rather than a rendering):



(As an aside I couldn't quickly work out this puzzle - how many moves does it take to win?)
 
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John
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zabdiel wrote:
I think I have understood how to win...


1. By creating a loop which surrounds one or more of you opponent's pieces on the base layer.
2. By creating a bridge from the base layer which goes up over a two connected opposing tiles.

Question - if the bottom right tile here was black instead of white then would this be a win for white?

 
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David Bush
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zabdiel wrote:
The mentions of "infinite lattice" and "This lattice does NOT completely fill the three dimensional space it occupies. There are blocking regions located on top of the hexagonal tips of each lattice space, and also below the surface of the peg on the underside. This is important to know when you play the game." I presume the important part here is that the peg part doesn't make the hole it fills your colour? I can't work out what the significance of the blocking regions is - these are the parts of the piles which touch other tiles aren't they?

I don't understand what "the peg part doesn't make the hole it fills your color" means. The upper surfaces of the tips of the tiles do not touch anything when tiles get stacked on top of them. The bottom surface of each peg does not touch anything. There is a gap because the peg is thinner than the rest of the tile. I call this gap a blocking region. The significance of this gap is shown in the very next image with six yellow tiles and one black tile. There is no vacant space adjacent to the tip of that black tile. This is not a winning loop for yellow. It's very important to understand why this is not a winning loop. Which you seem to understand all right, but not, apparently, what blocking regions have to do with it. (And yes, you're right about the win for yellow if that tile were black.)

I would very much like to know, if you think you could specify it for me, just how I lost you on that point.

Quote:
I found these style of pieces easier to visualise for some reason (perhaps just because these are physical pieces rather than a rendering):



(As an aside I couldn't quickly work out this puzzle - how many moves does it take to win?)

Well no, all these images are POVray generated. That's not a real set; at least, I don't have one. I did make some small Lazo pieces for Shapeways but they were quite expensive, over a dollar each.

Oh, that's a tough one. The shortest solution I could find was nine ply, or white wins on white's fifth move. There are some variations I looked at, when working it out again, that occupy holes that are barely visible in the diagram. But the fact they are there is significant. My email is twixtfanatic atsymbol gmail period com so you could email me if you would like me to send you the solution. Thanks for reminding me that I created these puzzles. I could certainly use them again when I get to the Advanced Puzzles section. Note that "everything is upside down" from this perspective compared to my latest images. But that's the perspective your opponent will see sitting across from you with a physical set.
 
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Peter S.
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I won't be able to reply at length until tomorrow evening (gaming and working, working and gaming cool ), but I see it as only a question of semantics: why use the term "lattice"? What concept does this cover or introduce that isn't covered by simply saying "path"? That's all I'm meaning: a lattice (as you're using the term) will arise naturally, if not automatically, from following the rules for placement regarding adjacency and the rules for victory involving looping or pinning an opponent's tendril. So it may not need its own special term.

Also, the example sentences I drafted aren't intended to be comprehensive of the rules, they were just specific rules that I thought of ways to rephrase; I should have been clear about that in my original post, though in my defense it was getting very late. I could give the language about lattices a second pass to see if anything occurs to me.

(Plus, there's all sorts of vocabulary that could be considered for various things within the game, such as "tendril". )
 
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David Bush
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I changed the wording in the wiki. I added

"The term peg used here refers to this triple hexagon shape."

and

"This disparity in thickness creates gaps in the lattice structure which are called blocking regions."

and later on, next to the diagram of adjacent cells on the layer above, I added

"Note that nothing touches the tips of a tile when other tiles are stacked on top of it."

Maybe this helps clarify the rules a bit.

 
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David Bush
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ErsatzDragon wrote:
I won't be able to reply at length until tomorrow evening (gaming and working, working and gaming :cool: ), but I see it as only a question of semantics: why use the term "lattice"? What concept does this cover or introduce that isn't covered by simply saying "path"? That's all I'm meaning: a lattice (as you're using the term) will arise naturally, if not automatically, from following the rules for placement regarding adjacency and the rules for victory involving looping or pinning an opponent's tendril. So it may not need its own special term.

Maybe I don't need the term lattice. But how else will I explain what a blocking region is? When a player sees a false loop such as this:



how do I make the case that this does not win? IMO if I just say "that black tip is not adjacent to any vacant space" without using the term "blocking region" then the reader may have difficulty understanding. But if the reader can visualize a blocking region sitting in the way, that would seem to make understanding easier.

I appreciate your feedback and I await your longer response.
 
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Peter S.
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Sorry, I didn't get the opportunity to read the wiki page until this evening.

Let me copy the text regarding lattices from the wiki:

Lazo wiki wrote:
The tiles can stack on top of each other like cannonballs.

This way of stacking is called a lattice. The lattice extends beyond those spaces which can be occupied by tiles.

A cell (or space) is an element of this lattice which has the same shape as the tiles. If it is not occupied by a tile, it is a vacant cell.


The way this is phrased implies that "ground level" pieces placed on the board that are not stacked are not part of a lattice, and that "vacant cells" only occur in the lattice and are therefore different than empty spots on the board. Mainly, I think that folks that aren't familiar with the mathematical definition of the term "lattice" will misunderstand it, and likely think it's referring to the stacked pieces rather than the space.

Thus, my question would be, do players need to understand the concept of a lattice to understand 1) that their pieces can stack, 2) that stacked pieces follow a specific pattern, and 2) that looping a lone piece isn't a victory? This is not a rhetorical question: I could see keeping it and actually expanding the explanation, or I could see how it can be explained without using the term.

Similarly, saying that the lattice is "infinite", while true, may give the incorrect impression that the play area is infinite, where the rules of placement confine play to a narrowing cone above (and below) the board.

As before, just to offer an example, if I wanted to keep the term I would introduce it with a layperson's explanation:

Ersatz suggestion wrote:
The tiles can stack on top of each other like cannonballs. Because they follow this strict triangular pattern both on and above the board, the space can be visualized as a lattice within which the pieces will be placed, and through which each player's paths will grow. Each spot within the lattice is a cell; cells can either be vacant or contain a tile.


I don't know whether keeping the term or discarding it would make explaining blocking easier or harder.
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twixter wrote:
Well no, all these images are POVray generated. That's not a real set; at least, I don't have one.

Ok - it's a good generated image then. Maybe changing the lighting/shadows on the images on the Wiki page would make it slightly to tell which pieces were on which level?

twixter wrote:
IMO if I just say "that black tip is not adjacent to any vacant space" without using the term "blocking region" then the reader may have difficulty understanding.


Ok, I'm not sure whether I understand it correctly - if the bottom right tile was black and was surrounded by white tiles then would it be a win for white? I was assume it would but it sounds like it might not be.
 
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David Bush
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zabdiel wrote:
twixter wrote:
Well no, all these images are POVray generated. That's not a real set; at least, I don't have one.

Ok - it's a good generated image then. Maybe changing the lighting/shadows on the images on the Wiki page would make it slightly to tell which pieces were on which level?

It's difficult for me to show a position with POVray images. Maybe you prefer the older design because it was more complicated, and it was easier to make out what pieces were located where. The new simpler shape has edges that seem to disappear in an overhead view. Maybe I don't know POVray so well after all. I increased the radius of the rounded edges for the image below, which helps, but IMO not enough. I intend to replace the puzzles images with flat overhead views.

Quote:
twixter wrote:
IMO if I just say "that black tip is not adjacent to any vacant space" without using the term "blocking region" then the reader may have difficulty understanding.


Ok, I'm not sure whether I understand it correctly - if the bottom right tile was black and was surrounded by white tiles then would it be a win for white? I was assume it would but it sounds like it might not be.

If you have any doubt, then I haven't done my job. Are you referring to this?



Yes, yellow has a winning 3-D loop here. A two-tile bridge over a two-tile river is the standard shape of a 3-D loop.
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ErsatzDragon wrote:
Sorry, I didn't get the opportunity to read the wiki page until this evening. :)

Let me copy the text regarding lattices from the wiki:

Lazo wiki wrote:
The tiles can stack on top of each other like cannonballs.

This way of stacking is called a lattice. The lattice extends beyond those spaces which can be occupied by tiles.

A cell (or space) is an element of this lattice which has the same shape as the tiles. If it is not occupied by a tile, it is a vacant cell.


The way this is phrased implies that "ground level" pieces placed on the board that are not stacked are not part of a lattice, and that "vacant cells" only occur in the lattice and are therefore different than empty spots on the board. Mainly, I think that folks that aren't familiar with the mathematical definition of the term "lattice" will misunderstand it, and likely think it's referring to the stacked pieces rather than the space.

Thus, my question would be, do players need to understand the concept of a lattice to understand 1) that their pieces can stack, 2) that stacked pieces follow a specific pattern, and 2) that looping a lone piece isn't a victory? This is not a rhetorical question: I could see keeping it and actually expanding the explanation, or I could see how it can be explained without using the term.

Similarly, saying that the lattice is "infinite", while true, may give the incorrect impression that the play area is infinite, where the rules of placement confine play to a narrowing cone above (and below) the board.

As before, just to offer an example, if I wanted to keep the term I would introduce it with a layperson's explanation:

Ersatz suggestion wrote:
The tiles can stack on top of each other like cannonballs. Because they follow this strict triangular pattern both on and above the board, the space can be visualized as a lattice within which the pieces will be placed, and through which each player's paths will grow. Each spot within the lattice is a cell; cells can either be vacant or contain a tile.


I don't know whether keeping the term or discarding it would make explaining blocking easier or harder.

This is golden, thank you. This could be just what I need to get through to intelligent people who may not be mathematically inclined.

I don't know for sure if I need the term lattice to show that pieces can stack or not. After all, I show that pieces can stack before I even mention the term. What I believe I do need it for, is to explain what a hole path is, and what it isn't. That "isn't" part means the reader should know what a blocking region is, so looking at a position like this



the reader immediately recognizes black has won with a board surface loop not a 3-D loop, that those yellow tips visible around loops of black are blocked, and there is no hole path that passes though at those points.

I am working on making lots of changes at once. Thanks again for your help. Your suggested re-wording will probably be included in the video I am working on also.
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Florent Becker
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twixter wrote:


the reader immediately recognizes black has won with a board surface loop not a 3-D loop, that those yellow tips visible around loops of black are blocked, and there is no hole path that passes though at those points.


I have the following reformulation in mind, in order to make this distinction more explicit. I'm not sure if it's actually equivalent or not, but it does give the same answers for each of your puzzles, so if it's not right, then probably at least one more example is needed.

First, I would modify your pieces to have some markings showing on every non-tip hex of the pieces. Call these markings "points".

Then, the rules are as follows:

Player take turn placing one tile of theirs, either in a hole on the playing surface, or in the hole created by three tiles arranged in a triangle. The winner is the first to capture at least one of their opponent's points. A point is captured either:
- by encircling it with a visible loop of your tiles,
- or by covering it with a "bridge", i.e. a tile which connects two previously disconnected group of tiles of yours, each touching the table.


It is less elegant now that there are two winning conditions instead of one, but it can be followed by a discussion about the lattice, and how this is really only one win condition.
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David Bush
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galbolle wrote:
twixter wrote:


the reader immediately recognizes black has won with a board surface loop not a 3-D loop, that those yellow tips visible around loops of black are blocked, and there is no hole path that passes though at those points.


I have the following reformulation in mind, in order to make this distinction more explicit. I'm not sure if it's actually equivalent or not, but it does give the same answers for each of your puzzles, so if it's not right, then probably at least one more example is needed.

First, I would modify your pieces to have some markings showing on every non-tip hex of the pieces. Call these markings "points".

Then, the rules are as follows:

Player take turn placing one tile of theirs, either in a hole on the playing surface, or in the hole created by three tiles arranged in a triangle. The winner is the first to capture at least one of their opponent's points. A point is captured either:
- by encircling it with a visible loop of your tiles,
- or by covering it with a "bridge", i.e. a tile which connects two previously disconnected group of tiles of yours, each touching the table.


It is less elegant now that there are two winning conditions instead of one, but it can be followed by a discussion about the lattice, and how this is really only one win condition.

That's a very clever insight, and would be correct if the only type of 3-D loop were an "arch" that used the board to form part of the loop. But consider puzzle 6:

White wins with F6 which covers black points on tiles E7 and G7, as you say, and connects yellow tiles E9 and H6. But in this case, E9 and H6 were already connected by a long chain of yellow tiles. This loop does not use the board surface.

You are right that I should introduce this term "points," probably at the same time I define "tips." I should probably stress that adjacent tiles on adjacent layers touch the underside of a tip to the top surface of a point. I'm not sure if I will physically mark the points or not. I have already placed my order for laser cut pieces to make molds for casting and changing the design would mean money down the drain, so I am motivated to provide extremely logical reasons for not doing that.

I'm grateful for your input!
 
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John
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galbolle wrote:

- by encircling it with a visible loop of your tiles,
- or by covering it with a "bridge", i.e. a tile which connects two previously disconnected group of tiles of yours, each touching the table.

This is roughly how I was thinking of the rules but with a slight modification to the second part. I was certainly thinking of them as loops and bridges or arches. I realised that the two groups didn't need to be disconnected. It seems to me that the rules and winning conditions aren't actually that complex, just the way they are worded currently seems a bit complex.
 
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John
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twixter wrote:
If you have any doubt, then I haven't done my job. Are you referring to this?

Yes, yellow has a winning 3-D loop here.

Ok, I'll have to try to remember what I was thinking here. Ok, I think what I was saying was that would yellow still win in that picture if they had connected the bottom left tile & middle right tile round the bottom & right of black's bottom right tile. I'm sure the answer is yes.

twixter wrote:
A two-tile bridge over a two-tile river is the standard shape of a 3-D loop.


This is how I was thinking of the 3D loop.
 
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