(Two generic placement protocols)

- The art of being hard
- A minute to learn, a lifetime to master
- Connect & play
- An obviously less than obvious question
- Four fundamental sight lines games
- Are sight line concepts versatile?
- Shooting at territory, you can't miss
- Switching from sight lines to 'knight spots'
- Knightly escapades
The art of being hard
Saying that playing Chess is hard is a platitude, but what do we mean by it? A child may initially find it difficult to learn the way the pieces move, but that is not what makes playing Chess hard. What makes it hard, precisely hard enough actually, is playing against someone of approximately the same strength. Winning against a grandmaster is too difficult for a club player but winning against a player like me would be too easy. For almost all players playing the game will range from 'far too difficult' to 'far too easy', depending on the opponent. The measure of difficulty that players should strive for can be found in a narrow range in between these extremes. Chess is only exciting if you're about equally matched.

As an inventor I don't find Chess difficult. It's design is not overly complicated, except maybe for its rather archaic castling rule. Its history is well documented and its current implementation is arguably the best, although it has been challenged by Bobby Fischer's Chess960.
As a player however, I find it too hard to deeply engage in it. Despite inventing many chess variants, my mind isn't particularly wired for playing them. But generally speaking Chess is not hard to learn and it always effectively displays the right measure of difficulty against roughly equally talented opposition.

A minute to learn, a lifetime to master
Chess takes a lifetime to master, no doubt about it. Artificial Intelligence is so superior nowadays that it is impossible for any human to compete, not even after a lifetime, so there's always room to get better. Since neural networks entered the equation, some ten years ago, that is in principle true for almost all games featured at mindsports.
There are many, many games that would take a lifetime to master, and a sub-set of them takes 'a minute to learn'. The slogan was made famous in the marketing campaign that accompanied the introduction of Othello in the seventies, but the most convincing example is the game of Hex. Hex takes literally a minute to learn and whoever doubts that it takes a lifetime to master is free to put it to the test.

Connect & play
I know, it used to be Plug & Play but why even plug when a tap on a smartphone is enough? Modern times demand that whatever we want should be made as easy and convenient as possible. In that context, 'a minute to learn' is presented as a quality in itself. Take two games that each would take a lifetime to master, then the one that is 'a minute to learn' instead of maybe an hour, must be the better one. That would put Hex over Chess.
Of course there's something wrong with that. Hex is strategically as difficult as it gets and certainly not less difficult than Chess, but it's also a desert, a barren landscape without much variation and quite boring unless you've been grabbed by the ever increasing depths of its uniformity.

An obviously less than obvious question
Given that both games can provide a lifetime of study and improvement, does it matter that one is 'a minute to learn' while the other may take maybe an hour or so? That seems an obvious question to me, with an equally obvious answer. But in a game inventors' pub like the BGG Abstract Games Forum, the question is hardly considered by part of the community because the consensus is that it matters a lot. Its members adhere to the 'simplicity doctrine'. Now why is that?
It's the way the wind has been blowing. 'A minute to learn' sounds good and many people at BGG are sensitive to that, so in terms of inventing it tends to become a goal in itself. This seems a weird strategy if seen in the light of the fact that it will not matter to any dedicated player of any serious game whether his or her chosen game took a minute to learn or a day. But for a potential buyer of a new game it may make a big difference in making a decision whether to buy the game or not. Therefore it is also a big thing for the potential seller, and for the potential manufacturer, and thus eventually for the potential inventor.
Now as it says on our homepage, it's easy to make a small fortune with abstract games, just start with a big one. But the dream somehow persists and it is constantly being fuelled by inventors who actually succeeded in having their games published, or are close to it. There's nothing to be said against that, except that it moves the inventors' goal posts by emphasising the importance of clarity and accessibility. The aim becomes to make a game that takes 'a minute to learn' but nevertheless provides a lifetime of deep strategy and all that preferably in under thirty minutes per game. Some inventors try to modify their games to these ends, which is of course very hard and often leads to 'improvements' that are actually compromises.

Four fundamental sight lines games
Fortunately some games invent themselves and resist modifications that are only meant to please the consumer, and from July 2020 onwards three of them were posted at BGG. The fourth one emerged in July 2021 as a hybrid of Hex and the third one.

The first one was Tumbleweed by Mike Zapawa from Poland. In it single or stacked pieces must be placed 'in sight' of friendly pieces. In doing so a piece receives a height that corresponds with the number of friendly pieces it can see. A player may also use his turn to 'update' a piece of either colour that is already on the board, if the number of friendly pieces it can see is larger than its actual height. If it is an opponent's piece this is called 'capture'.
Characteristically the game becomes territorial because areas surrounded by one player emerge in which no cell has any sight lines to the opponent, making it off limits for the opponent's pieces. The whole game emerges from this 'place or update in sight' concept so it is truly fundamental and also decisive. The only quibble I have with it is the placement of a neutral double in the centre to balance the opening. My inventor's heart tells me that if there is a problem, there should be a solution that is less clearly a 'means to an end'.

Another one was Meridians by Kanare Kato from Japan. It's a 'capture and placement' game in which on a player's turn all opponent's singles or connected groups that have no 'path' are removed, after which a stone is placed. A 'path' is an open sight line between at least one stone each of two different groups, singles counting as a group of one. Groups that have no path are removed from the board. The goal is total annihilation of the opponent. Using sight lines the way liberties are used in Go, you can't get more fundamental than that.

The third one was Stigmergy by Steve Metzger from the USA and Luis Bolaños Mures from Spain. Its concept sprouts from Tumbleweed but it abandons stacks. Instead it introduces the idea of controlling a cell if the number of friendly stones it 'sees' is more than half the number of cells that are adjacent to it. That's at least 4 for a centre cell, at least 3 for an edge cell and at least 2 for a corner. If a player 'controls' a cell then he can on his turn take it, whether or not it is occupied by the opponent. At the same time controlled cells are off limits for the opponent.
Where in Tumbleweed placement is restricted to cells 'seen' by friendly cells, placement in Stigmergy is free except for cells controlled by the opponent. The process and its inherent captures naturally divide the board in black and white regions that are fully controlled by the respective players. The winner is the player with the larger territory, counted as stones and controlled vacant cells. To balance turn order advantage the game appoints a number of komi points to the second player.

One day I thought that Stigmergy's control mechanism constitutes an embedded form of capture that might do well with another goal, and then I saw it fitted Hex and that basically was it. I asked Luis if the thought had occured to him, which it hadn't, and suggested to make it a co-invention which of course included Steve Metzger. Lox may certainly be seen as a fundamental placement and capture game because both Hex and Stigmergy's embedded capture mechanism are pretty fundamental. It is further discussed in the versatility section.

As I write, Tumbleweed is doing well and it eventually got some traction at BGG despite the fact that it does not immediately provide clues to a beginner about how a game might evolve. But it attracted a small following of dedicated promoters that did great work. However, it's descendant Stigmergy is in my view the better game but compared to Tumbleweed it was largely disregarded. Meridians attracted a good bit of attention, especially from inventors, including yours truly. Its 'paths' idea is based on 'sight line liberties' and this presumed connection with Go makes it interesting for inventors as well as players. Lox is as yet largely uncharted but that is likely to change.

Are sight line concepts versatile?
Tumbleweed made sight line concepts a hot issue at BGG. Meridians gave it an additional boost as a game of annihilation but that seems more or less to have exhausted that particular alley of invention. Its capture protocol implies that there's a lot of 'immediacy' in the game and it all works out logically but without much of a handle for changes. The other two are territory based and their core behaviour suggests that more can be build around them to various ends, including new games. That happened and I had a part in it. Three more 'Line of Sight' games that MindSports features are:

Cannons & Bullets was my first take on using sight lines and the new aspect I introduced was the 'double', in C&B's case called the 'bullet'. The general principle is this: when a piece is placed on a cell where it can see at least three friendly pieces, it receives a second piece on top of it that can, on a player's turn, be fired along a straight line and land on a vacant cell or capture the first opponent's piece it encounters by taking its place. There are several variables:

  • The number of friendly pieces a cell will have to see to get a double
  • If moving pieces is possible, whether they also get a double if they land on a cell where they can see three friendly pieces
  • Whether a fired piece may stop on a friendly man, to be reused from there in a later turn
  • Whether it stays a single when it captures or becomes a double if it captures a double
  • Whether it may (also) capture a different way, like 'custodian'

So this is a versatile way to introduce mobility and capture in a placement concept. The game Cannons & Bullets itself is the cradle of the protocol, but it is not the best implementation. That came when I realised that 'territory' might not be the best goal for it.

Loops & Leaps is a game with a looping goal that merges a number of principles of C&B and Stigmergy and throws in custodian capture for good measure. It is an assembled affair build on experience and intuition and as I write it has not been playtested yet. I foresee no problems but I'll probably have ample opportunity to let you know because these newly discovered protocols are bound to render more games by other inventors in the BGG community.

Lox is a Hex variant that is using Stigmergy's 'control' protocol for a connection goal. I happened to look at it and thought "hey, that fits". What I meant is that it could introduce capture in the Hex concept like KnightVision did before, but in a more embedded way where capture is the consequence of the sight lines placement protocol rather than an explicit introduction. Here I have high hopes of a brilliant game indeed. But the initial response by an important inventor to its introduction at BGG is indicative of the way the wind blows. Rather than responding himself, he just posted two reactions of players of the Hex community at Little Golem on the idea of Hex variants. Here is the first one:

"Does it not strike anybody else than me that there are infinitely many potential variants but only one that is the simplest? I see no enrichment in formulating new sets of rules. It would enrich board games if someone found a way to further simplify Hex!"

Simplicity is clearly seen here as the leading principle to design a game. Now as it happens, and the Hex community is well aware of it, the game of Y can be argued to be simpler than Hex. But who cares. Here's the other reaction:

"Each game has a propotion of short term complexity vs long term complexity. Hex is the top 1 game in the world with very little short term complexity and high long term. So any attempt to increase the former is just taking from Hex it’s biggest value."

This is a correct description of Hex: it's all one problem, but it gets deeper and deeper. It's also a devotee's version of what I earler described as:

"Hex is strategically as difficult as it gets and certainly not less difficult than Chess, but it's also a desert, a barren landscape without much variation and quite boring unless you've been grabbed by the ever increasing depths of its uniformity."

Now why did this inventor post these devotee reactions in the first place? The message seems to be to stop inventing connection games altogether because 'you can't improve on Hex'. That seems an odd attitude for an inventor. There's a broad concensus that Go is the top territory game. Should we refrain from making territory games for that reason? There's also this: I did deliberately introduce capture in the concept of Hex when I made KnightVision. Not to improve on Hex, or to take anything away from it, but because I'm a game inventor and I saw that capture could significantly alter strategy and tactics in interesting ways. Interesting in their own right.
Furthermore there's the assumption is that games, and in this case Hex variants, are deliberately made. That was not al all the case with Lox: it was lying there in plain sight for everyone to see. I just was the first one to notice it and put one and one together. Should I have refrained from having it published because Hex is so great? Of course not, but it incited me to refrain from posting at BGG. It's the way the wind is blowing and I hate having to move against the wind.

Shooting at territory, you can't miss
Sight line placement eventually leads to a division in different territories because players cannot place in areas that are densely populated by the opponent. So the games based on it, Tumblweed and C&B in particular, are decided quite early on by that very criterion. In C&B the endgame consists of shooting bullets and filling up territory, but the outcome can usually be seen long before the process is completed and you can't change it by much, if at all. Being able to shoot in all possible directions means that you can almost always find a useful target, and a capture changes the score by two points. That's hardly ever a game decider among beginners, and never a thrilling course of events. That got me thinking of goals where captures might be decisive till deep in the endgame, first and foremost 'connection'. In a connection game a single bullet by any other name, might totally reverse the outcome. So I thought of Hex, being the most fundamental connection game.

Switching from sight lines to 'knight spots'
What happened next marks one of those illogical switches I sometimes experience when thinking about games: I decided that the sight line protocol might not be what I was looking for after all. It's tempting to argue that Lox already had taken that idea to its logical conclusion, as it indeed does, by using Stigmergy's control protocol. But all this happened before I saw the possibility of the Hex/Stigmergy merger that resulted in Lox.
In retrospect, what induced the switch from 'sight lines' to 'knight spots' was a vague vision in which areas got too separated for a connection goal. Nonsense of course because connection on a Hex board will emerge, literally one way or the other. But being irrational never kept me from inventing games, the very reason that I consider many of my inventions as 'accidental'.
Thus I decided to introduce 'knight vision' as a placement condition, that is: a placed piece should be able to 'see' at least one friendly piece at a knight's move distance. As a further analogy with the sight lines in Cannons & Bullets I decided that a piece would get a double, now called an 'axe', if it were placed on a cell that was a knight's move away from at least three friendly cells.

Knightly escapades
On the left you see the hexagonal knight's move, the jump between the acute corners of a 2x3 arrangement of hexagons. Compared to its square counterpart it is a bit longer, which serves its use in the games in which it has been implemented. You can cross an average board in a few jumps. It also allows 'knight tours', visiting every cell of a board once in a series of knight moves, a feature that serves a possible application in games with a unification goal.

There are two immediately identifiable differences between sight line placement and knight spot placement:

  • A sight line can be blocked by placing an opposing piece anywhere along its path while a knight spot can only be blocked by occupying it
  • Areas where one colour dominates are not accessible for the opponent with sight line placement but they can easily be infiltrated with knight spot placements

Here's the 'knight spots circle' of possible placements around the centre. It allows placements over a double row of opponent's pieces and in doing so creates further placement options deeper in the opponent's territory.
If the centre is vacant, then pieces on any three cells of the circle would allow creating a double with a placement in the centre.

The first game based on the protocol is actually called KnightVision and barring a few members who actually played it and got enthusiastic about it, it received a lukewarm reception. An example:

"I find the axe placement spaces hopelessly opaque. I would have to scour the board each turn to find them, especially for my opponent's options toward which I have not been consciously building. I need clarity in my games, and this one doesn't have it, for me."

We see a call here for immediate clarity and immediate accessibility because as I said earlier, it is the way the wind has been blowing at BGG for quite some time. Knight vision placement doesn't meet this requirement and thus it is disregarded. But good games are never non-committal, they may give a lot, but they require a lot too, if one wants to explore their riches. That doesn't meet modern day consumer demand.

I don't work for consumer demand and as an excercise I made two more games on the knight vision protocol, one with a unification goal and the other with a looping goal. Both required a few adaptions in the protocol to serve the games' specific needs.

Unification games are inherently based on movement and having something to unite. The knight vision protocol is based on placement. So you need a placement stage that at some point ends and makes room for movement. Uknight has these features and the rules cannot be said to be non-arbitrary. In such cases shaping them in the game's spirit with simplicity and necessity as leading principles is a good strategy. The game inherently allows cooperative cycles but is otherwise finite and decisive.

KnightShade has a smart way to make sure opposing loops intersect and after playing a game or two it suggested to me that decisiveness will be no problem. But I couldn't be quite sure, so I intoduced a territorial default goal to ensure decisiveness. I also didn't find it particularly hard to make a game with a loop in a player's own colour as its main goal, although the concensus at BGG is that it is very hard.
Neither game is very significant in a larger context of a couple of hundreds of new games of our particular kind that are being published every year. If you find either protocol intruiging, I'd say that KnightVision, Stigmergy and Lox are your best shots.

The interest in sight line and knight spot placement protocols is of a recent date and more games around them may follow, because there are many inventors nowadays. I'm sure I can leave BGG for a few months without being missed. But I'll keep you posted here.

Enschede, the Netherlands,
July 2021,

christian freeling