- 1975
- Is clarity a property of a game?
- Clarity & Depth, how do they relate?
- Can they both be right?
- The problem with new games
- Clarity - state or measure, static or dynamic
- Speciousness, a nice feature but how to get it?
- So what is clarity?
- Mu vs Hex - a comparison between extremes
- Is clarity a function of skill level, or an integral over skill levels?
- History
- Conclusion
I got a foggy notion, do it again
Over by the corner, do it again
I got my calamine lotion, do it again
I got a foggy notion, do it again
(The Velvet Underground - Foggy Notion)

In 1975 Robert Abbott, the inventor of the game Epaminondas, published an article titled "Under the Strategy Tree" in the May issue of the British publication Games & Puzzles (issue No. 36). In it he wanted to explain his concept of clarity as he puts it in the article, and he summarised it like this:

Clarity is essentially the ease with which a player can see what is going on in a game. It is a useful idea for a game inventor to keep in mind during the development of a game, and it is useful in the criticism of games. Most important, it explains what makes a game 'deep'.

That sounds close enough for anyone to whom abstract games of the kind featured at mindsports are at most a side issue in life. Why shouldn't there be clarity and why shouldn't it be related to a game's depth? The only problems are that "the ease with which a player can see what is going on in a game" is too subjective to be be used as a definition and that describing 'depth' of such terms may become elusive in the very attempt to pin it down.

There was no internet in 1975, no place where you could play games with other people all over the world, and there weren't many games of the mindsports type. In the western hemisphere there were traditionals like Chess, International Draughts and Checkers, while hardly anyone had heard of 'eastern' games like Go, Shogi and XiangQi. But in the toy shops one could find Sid Sackson's Focus, Alex Randolph's Twixt and the 19th century game Reversi that had been relaunched as "Othello" in 1971. Gary Gabrel's 5-in-a-row game Pente was on the brink of publication. He had modified the traditional 5-in-a-row idea by adding a modest capture mechanic to it, leading to dramatically altered tactics. Game inventing was in the air!

There was also the game of Hex which was as simple and deep then as it is now, but it lacked a large following. In a way that is also 'as it is now', because although there is a fairly large Hex community at the Little Golem game site, the global spread of Hex still doesn't show anything like the density of Chess or Go. But if we take the number of levels of expertise at which humans are capable of playing a game as a measure of its depth, then there are currently more than enough active players, who are playing at a wide range of levels, to justify calling the game of Hex deep. The problem with this criterion is that it can only be based on large numbers of players who have played many games over a long period of time. It is useless in estimating the depth of a new game.

That's where we were in 1975 and it is nice to see that the newly invented games that were mentioned above are still known and being played in the small circles of lovers of abstract strategy. But nowadays there are many hundreds of other games of our particular kind and there are also AI programs that allow taking them apart in novel ways to learn more about their clarity, depth, decisiveness, balance and possibly even drama. So knowing what we mean by those things would seem appropriate.

Is clarity a property of a game? 
Here is another quote from Robert Abbott's article:

"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".

There's a tautological smell here: the game is deep because it has clarity and the game has clarity because one can see deep into its game tree. It also doesn't explain what travelling down a game tree means, as opposed to looking down a game tree. But apart from that the argument does not take the observer's level of play into account, or it wouldn't say that playing a game will soon reveal its degree of clarity, which obviously addresses new games rather than known ones. This way of suggesting that clarity is a property of a game rather than the result of progressing interaction between a game and a player, may well have contributed to the fact that eventually discussions at BGG about 'clarity' seldom had clarity to spare.

What actually happened, at least in my view, is that Robert fell in love with his own description of the game:

"Epaminondas is clear because the magnitude and direction of the forces are shown by the size and direction of the phalanxes. Thus the patterns that develop during the game graphically display the confrontation of power".

epaminondas position
Like this

Epaminondas had a published predecessor called Crossings, so its evolution had taken a long time and during that time the very idea of 'clarity of a board game' may have emerged in his reflections, becoming ever clearer. So much so that it eventually craved for a general description. Next he totally tailored the description to fit Epaminondas which in consequence emerged as a game of great clarity.

To forego a possible misunderstanding, this is not in any way meant as a criticism of Epaminondas which is an excellent game in its own right. And given its goal, positions look clear enough for that matter. But in terms of their goal, positions look clear enough in many other games that are known to be deep and known to have great clarity to at least some players, like grandmasters. So having Epaminondas serve as a touchstone for the presumed clarity of board games seems like little more than whishful thinking to me.

Clarity & Depth, how do they relate? 
According to Robert Abbott clarity and depth go hand in hand:

"A game can be simple yet lack clarity, and conversely a game can be complicated but still clear. Playing a game soon reveals its degree of clarity. The greater the clarity of a game, the farther you can see into it, and therefore the greater its depth for you".

Then, in July 2000, J. Mark Thompson published a small essay titled "Defining the Abstract", in which he gave his view on clarity:

"Clarity means that an ordinary human being, without devoting his career to it, can form a judgment about what is the best move in a given situation".

That's rather non-committal and it presumes a fairly knowlegeable player but no specific game. He also presents his view on the relation between clarity and depth on the one hand, and decisiveness and drama on the other.

"I list these four qualities because they seem to me to be in tension with one another by pairs: depth vs. clarity, drama vs. decisiveness. For example, if a usable algorithm is known which will always reveal the best move in any situation of a game, then the game's clarity is perfect, but it has lost all its depth".

So games that are too deep will lack clarity and games that are too clear will lack depth. That sounds good, but what about if a game's clarity is less than perfect, for the sake of argument let's say all the way to outright murky, does that mean that it has gained depth? That would make the game Ultima, that Robert Abbott in his article describes as seriously lacking clarity, a very deep game. If the only criterion were the size of its game tree, then this would be true. But as Robert rightly states, it's not the size that matters, but how deep a player might look into it. And Ultima doesn't make that easy, to put it mildly.

Tic-tac-toe on the other hand is one of the few games one can learn and master in the same minute. Everything about it is clear and it has no depth. So when Abbott argues that greater clarity leads to greater depth, then he obviously means something else by either or both, although it's unclear to me what exactly. I tend to be with Thompson, who gives a definition of depth that can hardly be argued against:

"Depth means that human beings are capable of playing at many different levels of expertise".

There are cases where this criterion is clearly met, like Chess, Go, Shogi, XiangQi, Draughts and Checkers for sure, but also modern games like Hex and Othello and variants of which depth is predictable, like Grand Chess. These games have proven to be deep. According to Abbott they therefore should have clarity, while Thompson seems to argue that games lose clarity with increasing depth.

Can they both be right? 
Abbott obviously talks about new games and he's right if he means that some new games are easier to access than others. If someone knows neither Chess nor Hex, then Hex would be easier to understand and thus have the greater clarity. But to a Chess grandmaster who is new to Hex, a Chess position would be much clearer. So what a beginner thinks may be important in terms of accessibility of a game, but it is largely irrelevant as a measure of clarity or depth.

Thompson on the other hand seems to argue that if a game is deep, then a player will find that the farther he looks into a balanced position, the more clarity would wane, and that sounds blatantly obvious because it holds for any non-trivial game, whether it allows 'deep lookahead' or not. Even if a game or a game position seems murky, then whatever clarity it has, still wanes if one tries to look deeper, farther down the tree.

The assumption in all this is that a seasoned player who considers which move to make in a given position, works his way from position to position down the game tree. This may be mostly true, but there may also be considerations and intermediate sub-goals that do not depend on a precise chronology, that yet add to the clarity of a player's vision. The Dutch Chess master and psychologist Adriaan de Groot found, among other interesting things, that strong Chess players were able to perfectly reproduce Chess positions after looking at them for only a few seconds, while it was impossible for them to do the same when presented with a chess board with randomly placed chess pieces. That says a lot about 'clarity'.

The problem with new games 
Regarding the clarity of newly invented games Thompson remarks:

"The difficulty with a newly-invented game, is to discern whether a game is "invincibly opaque", or whether with sufficient experience its rules of strategy would begin to clarify".

Again this sounds very logical, but at the same time it is preceded by this statement:

"Robert Abbott, the inventor of the chess variant Ultima, has lost interest in his creation because he feels it is "opaque". Though Ultima has many defenders, anyone who tries to invent a new and original game will find clarity an important issue."

What's noteworthy is that it introduces the idea of an 'invincibly opaque' game while at the same time acknowledging that the most opaque example that both care to mention still has 'many defenders'. So how opaque is opaque? Why does 'invincibly opaque' become a criterion for a 'difficulty' with new games, if it's so difficult to create it in the first place? Ultima is almost half a century old now and if it is still being played or even mentioned, then there must be something interesting hidden in its opaqueness.

At the same time I recall my first attempt at inventing a game of our kind. It was called Chad, a name I later used for a better game. But the first Chad was an attempt to merge Chess and Go as well as an unintended attempt at 'invincible opaqueness'. I reluctantly trashed it and went on to invent Havannah, which by contrast had a Hex-like clarity.
A game like Hex has very clear rules and a Hex position may look very translucent, but learning to play Hex one inevitably comes across positions that are far from clear. Regardless of the playing level of the observer, at some point things become really, really murky. Given a balanced position, increasing depth of a lookahead does not lead to clarity, even though the reverse may be true.

I also made King's Colour in those early days, which is an intentionally opaque game. In 2021 it entered Abstract Games Magazine's "Unequal Board Spaces Game Design Competition" of rather opaque games. I fully understand if it were labelled a 'low clarity' game because that was the very point. It was made solely for the fun of it. So I'm not saying that games don't have an inherent quality that one might call 'clarity'. What I'm saying is that it is a matter of accessibility rather than of depth.
Some games allow a deeper look ahead than others. In Draughts there are long forced sequences and endgame positions that top players can read out to an amazing depth. Emergo has the same features but in 3-D, and now trying to look deeper becomes far more challenging. But in the class of games that is considered here, both players inherently face the same challenges, so the depth of the look ahead that a game allows is not really relevant for its ability to pit two players against each other.

Clarity - state or measure, static or dynamic 
When consulting assorted dictionaries, the general definition of 'clarity' may be summarised as:

"The quality, state or measure of being clear".

In terms of our games we may assume that a high 'clarity of rules' is a precondition for accessibility. Rules should be 100% clear, that's a invariable state. But there's also 'clarity of vision' and it is not at all invariant. It goes through a number of states if you like, deepening in the process of play and study. And in balanced positions it is never 100%. A designed Chess problem, or a problem in any of the great games, is hardly ever balanced. The only way that comes to mind is a problem that would require you to find an unlikely draw, but usually you're supposed to find a win for one side. That's inherently unbalanced and thus opens up the possibility of 100% clarity by solving the problem. This is the kind of clarity we're talking about here, growing from the interaction of a great game that allows miracles, great players who can perform them and a large audience who can understand them. The latter two are the greatest challenges.

Speciousness, a nice feature but how to get it? 
Nick Bentley is a famous designer of mindsports type games, so far as famous goes in our circles, and we feature his game Catchup. He manages a games website and writes interesting articles about his inventions and about various aspects of the game industry. In that context he decided to challenge Thompson's article of 2000 on one particular point and he published the result as "Redefining the Abstract". The main point of his essay is:

"Clarity should be replaced by Speciousness"

Speciousness may be defined as as: "A seemingly plausible but deceptive appearance of truth", that's to say things that sound good or look good but really aren't.

I always considered Nick Bentley to be a master of speciousness. His views on inventing is that games should comply with his ideas of what players want, and if not, that they should be modified till they do. Central to his thoughts are the players and the games he invents should serve their wishes, as seen by him. He's always interested in everyone's point of view, so that his games may serve them better. It's a form of altruism.

Nick often says things that sound good, like "Ban the Ban" about minimising restrictions in the design of new games. That sounds good because it appeals to our sense of freedom. He illustrates the point by pointing out two restrictions he was able to remove from Catchup, greatly improving the game. So what's wrong with that?
This: it advises you to correct design mistakes you shouldn't make in the first place. If the point of the article is that you should always minimise the number of restrictions, then it says nothing new. A body of rules inherently is made up of options, restrictions and obligations and a good design inherently balances these aspects. 'Ban the ban' states the obvious as if it were special and makes it special by giving an example of replacing a restriction that was questionable to begin with. It sounds great and means nothing new. That's speciousness.

Here's the speciousness that Nick is talking about:

"I think great games are unclear; they make it hard, really hard, to identify good moves, but they do something else to make up for it: they excite in the mind ideas for moves which seem good, but actually aren’t. This has two important effects:

1. It gives players the needed sense of direction and competence even when they’re playing a deep game and in fact have no idea what they’re doing.

2. It sets players up to be surprised when they discover their initial ideas were wrong – in other words it creates Eureka moments, which are among the supreme joys of playing a good abstract game. This is only possible if a game stimulates compelling but ultimately incorrect ideas about how to play well.

I call this quality 'speciousness'"

The first point clearly addresses new players who play new games, because seasoned players do have a sense of competence and a reasonable idea of what they're doing. So it's not a general observation about players and games. The second point is general and would even hold, if only occasionally, for a game's top players. Great games are full of surprises and seemingly good moves that turn out to be contaminated are certainly part of it.
But how would an inventor implement such a feature, other than working out a good idea in the best possible way and hoping? Let's ask the inventor:

"How can a game designer build speciousness into a game?"

Nick: I don’t have a complete answer, but one thing that helps create speciousness is the use of mechanisms that feel familiar to players. Two ways this can happen:

1. Mechanisms can feel familiar because they’re similar to mechanisms in well-known games everyone has played. Example: thanks to games like Connect4 and Tic-Tac-Toe, just about everyone has experience with the n-in-a-row objective. It feels familiar to us, and we therefore have ideas about how to pursue it. If you design a game with an n-in-a-row objective, but whose mechanisms are just different enough to make the strategy conflict with what players already know, you’ll have created speciousness. A great example of this Yavalath, an n-in-a-row game with one little twist that dramatically transforms what players need to do to win. Yavalath’s speciousness is a key reason it delights just about everyone, gamers and non-gamers alike from the get-go."

2. Mechanisms can feel familiar because they embody what I call Intuitive Metaphors. These are mechanisms which demand modes of thought familiar not from games, but from real life. So, for example, the idea of chasing down and capturing something (the goal of Chess) is common not just in games, but in life. So too with surrounding something, as in Go.

Yavalath invites you to make a row of 4 without having it preceded by a losing row of 3. Very clever for a game that was actually designed by a computer program. Nick's is right about the effect of this little twist. Gary Gabrel's game Pente introduced a similar twist by introducing the custodian capture of pairs of stones in the orthodox concept of '5-in-a-row'. Small changes with big consequences.

The second mechanism just states that 'real life goals' do well as goals for abstract games. This is both obvious and usual, or at least far from unusual.

So what does Nick actually say about building speciousness into a game?

1. Build a little alien twist into an existing game.
2. Choose a natural goal.

Fortunately there are many natural goals, chasing a king, killing all troops, grabbing the most, building the biggest, being there first, unifying pieces, connecting things, blocking the opponent. So indeed, make a good game and it will most likely have ample options to make mistakes by means of plausible moves. They come with the territory, there's no need for special requirements and no clue as to what these should be in the first place. It all sounds good but means little. A bit specious, so to say.

So what is clarity? 
At the BGG forum it never became quite clear. The late Richard Moxham whose Morelli is featured at mindsports, posted an attempt to get an answer in Aprll 2018, less than a year before his untimely death. This is the original post:

Clarity (noun): In a pure-skill boardgame, a measure of the ease with which (at levels appropriate to players of all abilities) that game conduces to:

(i) the making of purposeful moves;
(ii) reasonable judgement as to the comparative merit of available options;
(iii) evaluation of overall position.


Richard is no longer among us so we'll have to do with comments he made in the thread, starting with a reply on the first point that I made:

Christian: One of the better definitions I've seen. But discussions about clarity sometimes lack the very subject so I'm inclined to pass on that one.

Richard: A pity, though, because a helpful working definition would be very valuable for future discussion. The point is that the clarity which you refer to as often lacking in such conversations (and naturally I agree about that) isn't the same clarity as the one I'm attempting (or, more exactly, launching an attempt) to define.

[ ..... ]

Anyway, as I say, the word clarity, just like the word depth and many others, is at this point still a tabula rasa. People already use it, of course, and different users mean different things by it, but that's not to say that the issue is 'purely subjective' and therefore fruitless to pursue. What we should be doing is looking for the meaning which most enables us to make progress in the understanding of these games. Or (to stand that on its head) seeking to identify the important quality and then agreeing to use the label to pin it down. For example, there would be nothing incoherent in someone saying that they see clarity as the ease with which a rule-set can be understood and assimilated. Nothing incoherent, but if we were to agree to let clarity be that for future purposes we would be wasting an opportunity, because there are other potential meanings (and I submit that mine, offered above, is at least the basis for one of them) which would better advance the cause.

To sum up, then, you look for the property or properties - consistent with the everyday meaning of clarity, obviously - which contribute most profoundly to the quality of an abstract strategy game, and you attach your word there. It's not an easy task, but it is approachable.

If the search is for a definition of 'clarity' as a property of a board game then it means something else than the clarity with which a grandmaster sees a Chess position as opposed to a beginner.

The fact that Chess masters can quickly evaluate a position they've seen for only seconds, seeing where it will go where beginners merely see where the pieces might go, supports the idea that clarity is linked to experience in a game. Of course the game must be able to provide such clarity, as Chess obviously does. So I wonder if a very seasoned player of Epaminondas could do the same in that game, that is reproducing a position after seeing it for a few seconds and, if appicable, seeing the outcome. I wonder in fact if it might hold for any serious game. In that case clarity equals familiarity and the search for it as the property of a particular game is a wild goose chase.

Mu versus Hex - a comparison between extremes 
I invented Mu in 1980 during a nightly bike ride from the games club Fanaat at Twente University (then still called 'Technische Hogeschool Twente') to my home, a distance of about 7 miles. I was high on pot, as usual then as it is now. On arrival I noticed that it had taken me an hour, which is quite long for 7 miles. I also had no clear recollection of the route I had taken. But with me, Mu had arrived.
Mu is one of the most complex games of our kind that was ever invented, if not indeed the most complex one. A move in the middle game may well consist of up to a hundred separate actions. Hex by contrast is one of the simplest games of our kind that was ever devised. Ed and I first played Mu after he had made an app. But he knew about the game ever since its invention because we both frequented Fanaat in that period.
So I asked Ed if he ever during a game of Mu had felt a sense of loss of direction or lack of strategy. He hadn't. Neither did I for that matter. There are many chain reactions in the game that just need performing, like someone walking up the stairs who clearly sees the purpose and the method, yet has to take every step. Then I asked if he ever had felt a sense of loss of direction or lack of strategy while playing Hex. Turns out we both had felt that particular 'opaqueness' very clearly.
Does that mean that Mu has more 'clarity' than Hex? For both Ed and me that would seem to be the case, and it is based on familiarity and experience. Show me a Mu position between equally skilled players, and I can quickly evaluate the situation. Do the same with a Hex position and if I'm not indeed wholly lost, then I would certainly be unable to evaluate the position quickly. So what does that say about 'clarity as the property of a game'? What are we looking for?

Is clarity a function of skill level, or an integral over skill levels? 
That is a question that came up, and since Richard proposes that it should be a measure of ease in which a game contributes to making itself clear at levels appropriate to players of all abilities, the answer would be the latter. We seek a property, not a result of progressing interaction between a player and the game. The wish for it is stated explicitly in the thread:

Jeromie: The thing I don't like about this definition is that too much hangs on the skill level of the players. Clarity feels like it should be a property of the game itself, not an emergent property of the game/player interaction.

Russ: I'd like that ideal, but to me it seems like in reality 'clarity' (and many similar fuzzy terms, e.g. 'drama' and 'decisiveness') are surely bound to be subjective judgments by individual players. Then any resulting objectivity about them is empirical and demographic, a result of large numbers of players agreeing that "Game X has high clarity" and "Game Y has low clarity, it is very opaque"...

Jeromie: I would describe clarity as a measure of how effectively the game conveys all of the information necessary to make meaningful decisions. Thus, clarity is more about information presentation than the scope of the decision space.

Russ: 'Information presentation' seems to me not at all "a property of the game itself", but a property of the graphic design and other such presentation choices made in a particular physical manifestation of the game.
E.g. in my experience Shogi with kanji characters has significantly less 'clarity' (in the sense of effectively conveying information) for (non-kanji-literate) new players than Shogi with newbie-friendly pieces with little arrow diagrams on them, or with pieces using Hidetchi's Western Chess-inspired graphic design, even though they are all the same game, i.e. Shogi.

Why do we feel that clarity should be a property of a game, rather than a property of the vision of a seasoned player?

Jeromie: Has this term come up in other discussions? I'd love to see the history of how it's been used instead of trying to come up with a definition in a vacuum. I'm describing what the word conveys to me based on my understanding of English, but I also understand that all fields have their jargon that can have non-obvious meanings. Do you see clarity as a desirable, neutral, or negative property of a game? In your proposed definition, how would it relate to calculability?

Russ: AFAIK 'clarity' became jargon-esque in this context thanks to the article "Defining the Abstract" by J. Mark Thompson in 2000.

That of course is not entirely true. So far as I know Robert Abbott was the first to coin the term as 'a property of a game' in his 1975 essay "Under the Strategy Tree". It was in a time when there appeared maybe five new games every year, instead of five every day. A new game could make a big splash and Robert was enchanted by his own words:

"Epaminondas is clear because the magnitude and direction of the forces are shown by the size and direction of the phalanxes. Thus the patterns that develop during the game graphically display the confrontation of power".

And who is to blame him, it sounds perfectly logical. But it isn't. It may be a handle for accessibility but in terms of clarity the game is no different than many other games of a similar kind, in that it doesn't matter. Clarity is not in the game, but in the vision of a player. Clarity of vision is shaped by experience and study.

I'd like to wrap it up in a slogan that is not entirely correct, but it conveys the message in three words:

Clarity is Familiarity

Christian Freeling

Enschede, July 2021


This article has been published before in the Autumn 2021 issue of Abstract Games Magazine (#22)