Electron Dance

Repetitive Strain

This is the eleventh part of The Ouroboros Sequence, a series on puzzle games.

Chromatron 4

Sooooo… I was trying to put together a few words building on some of the Ouroboros comment discussions. It started out as a short thought experiment but I kept expanding on it until I realised this was sort of a deep dive. Welcome to inside baseball, puzzle edition.

Do not think of this as My Magnum Opus Thesis of Puzzle Design but just a guy trying to get a handle on certain concepts. I’m happy to be shot down, have a contradiction identified or be told I’ve forgotten something.

Let's talk about the “laboriousness” of turn-based logic puzzles, because if a puzzle feels like hard work, you’re more likely to throw in the towel rather than complete the thing. The idea of a puzzle as a chore keeps coming up. Compare the "laboriousness" of Sokoban to something like a contemporary laser reflection puzzle.

But what do we mean by laboriousness? What causes it?

Complexity vs Labour

I’ve previously floated the idea of “number of steps to solution” as a measure of complexity but it is pretty crude. It’s like describing Brexit as “just getting out of the EU” and you wouldn’t want to do that.

Let me demonstrate why. Earlier in Ouroboros, I mentioned I had fallen in love with Dissembler, a very distant cousin in the match-3 family tree. The player’s purpose is to “dissemble” the puzzle and every step takes more of the puzzle away; so the number of moves required is always bounded. If a procedurally-generated level of Dissembler requires over ten moves, that’s a sign a veteran Dissembler player will find it challenging. Yet ten moves in a basic Sokoban game is nothing.


Solution step count can only really function as a relative measure, comparing like with like, but still even then may not accurately represent the mental adversity posed by a puzzle.

Now “laboriousness” is obviously related to solution step count. If I have to carry out 50 moves to solve a puzzle, that’s a lot more work than a puzzle that requires 10 moves. Again, we must be cautious because it depends what those steps constitute and how those steps are decomposed into distinct, invigorating tasks. Give me a paragraph to explain.

Although I don’t like to indulge talk of The Room being a puzzle game, because most of the experience is “hunting hotspots”, it is a good example of how doing the exact same thing again and again does not feel like doing the exact same thing again and again. The Room doesn’t feel laborious, it feels glorious. Those clicks and whirrs and mechanical explosions never get old. Puzzle games built on simple templates can test player tenacity because, after a while, the banality of repetition might bleed through into the conscious mind. Raw Sokoban is very dry and moving a little box pushing fella around a maze of boxes can get old fast.

Nonetheless, I think step count is a much better measure of puzzle labour than it is of complexity. And going forward, let’s assume there is a single solution (aside from trivial alternatives) because that will just complicate our discussion for little gain.

It should go without saying that talking about the laboriousness of a score attack puzzler does not make sense because surviving as long as you can is the whole point. However, that doesn't mean the concept is dead. Compare Threes to 2048: Threes is tight whereas the latter is bloated with unnecessary moves.


In Sokoban, the sequence of moves is important; swap around any pair of moves and there’s a good chance the solution no longer functions. We could call this sequence-dependent or step-dependent, but I'll steal a term from mathematics: path-dependent.

Now consider a laser reflection game, where it does not matter in which order you put the pieces down. Provided everything is in the right place, the puzzle is solved. As the sequence of moves is unimportant, we can call this type of puzzle path-independent.

Algorithm games are path-independent. The algorithm can be constructed in any particular order. That includes Cosmic Express, Trainyard, SpaceChem and it is even possible to cast Blek, a puzzle featuring a living scribble, as an algorithm puzzle. We can fight about it in the comments.


(Aside: path-independence sometimes means a solution of the puzzle can be captured in a single screenshot. If I show you where all the mirrors and splitters are placed, that's all you need to know to solve a laser reflection puzzle. In contrast, if I show you the position of the sausages at the end of a Stephen's Sausage Roll level, it might be helpful but it does not tell you how to get there.)

The Known Unknowns

That’s not quite the full picture because sometimes puzzles don't give you the full picture. There’s a curious island between our technical definition of path-independence and the player's experience of it. Welcome to the beautiful holiday island resort known as hidden information.

I can show you the solution of a Minesweeper level and you can conceivably just go through clicking the squares one after another in any order you want. But, come on, let’s not be fooled. It’s grossly artificial; Minesweeper does not give you enough information in the initial state to solve the entire level. The player acquires new information from each correct deduction and advances step by step. From a player perspective, it is entirely path-dependent. We could broaden our definition of “path-dependence” to include this, but I’m going to call it synthetic path-dependence for today, which makes me feel like I’m writing a load of wank.

Hexcells and RYB that I described last week have synthetic path-dependence but not classic Picross. Picross is transparent from the get-go and there is no requirement to fill the shape in the correct order.


I cannot think of a path-independent puzzle where the player is given an avatar or group of avatars to control. It doesn’t need to be there and the player has an omniscient presence.

Path-dependent puzzles, however, often give the player an avatar. Lara Croft GO, Aaron Steed's Ending, every Sokoban game in history. But it’s not a given. The player is omniscient in Dissembler, Tricone Lab and Fold.


My thinking is path-dependent puzzles tend to be more laborious because of two things: avatars and unbounded sequences.

Path-dependent puzzles often assign the player control of avatars and these puzzles almost always require more action from the player; the solution step count is much higher than an “equivalent” omniscient puzzle.

However, the very dependence on sequence can increase labour. Towers of Hanoi is a puzzle in which a boring as shit pile of discs must be relocated but the player can only move one at a time and never place a bigger disc on a smaller one. It is easier for the player to get lost in a sequence, unsure whether they have actually made progress after fifty moves, or whether they are unwittingly dismantling progress. There’s no natural ceiling to the number of moves and I’ve spoken about the type of claustrophobic rut you can find yourself in, repeating the same loop of moves over and over. That feeling of Groundhog Day in path-dependent puzzlers, where you realise you’re actually repeating the same solution attempt as before, is an experience every player knows and abhors.

The holy grail of a non-laborious path-dependent game is represented by Dissembler. Not only is the puzzle omniscient but it is degenerative as pieces disappear with each step which prevents the solution from continuing to the end of time. (I was looking for an equivalent mathematical term like “path-dependence” but I wasn’t really able to find one. I assumed graph theory would have had a term describing the condition of revisiting a vertex/node, but I couldn’t find it.)

Remember, though, path-independent games with hidden information offer synthetic path-dependence. If we view RYB and Hexcells through this lens, notice these games are also degenerative like Dissembler. Further, the limited information available at each step effectively funnels the player to deductive conclusions.

Hexcells Plus

However, the deeper into Hexcells you get the larger the puzzles become and the more obscure the revelations. Hexcells Plus is dominated with vast grids offering numbers that show you the number of lit cells within two hexes. For some, this brainfest is delightful, but I found it rather tedious - like adding grind to pad out an RPG - and it felt like I was being forced to scour increasingly larger areas for an information combo that would allow me to expand my hex empire.

Countering Labour

Puzzle degeneration is the first counter to laboriousness. The Witness’s panel puzzles are path-dependent but degenerative: each move reduces possible paths open to you as the line cannot cross itself. The player must undo actions to try different strategies.

However, adding in degeneration may fundamentally change design and thus be unacceptable. Some games offer a halfway house: an indicative step count, sometimes as a bronze/silver/gold achievement. Quell, a puzzle where you roll a marble (the game calls it a raindrop) around to pick up pearls, always shows the number of moves you've committed versus the perfect count.

For puzzles which cannot be solved computationally, designers may be worried that more efficient solutions exist and be coy about a step target for that reason. I’d also add this is no good if you only tell the player after the level is finished such in Cityglitch (the level on the map glows blue only if you completed it with the "perfect" move count). This is step count as a par value, an attempt to motivate players to replay.


As Hexcells demonstrates, keeping level size down is the best prevention for laboriousness. The downside, as explained in Claustrophobia, is that there are a limited number of distinct challenges that are contained with smaller level designs and once they’ve been mined the designer must either throw in new ideas or...  expand the level size. The latter is always cheaper.

Role of UI

If you want a path-independent game to feel really laborious, code it up with a grid cursor that moves around sloooowly. This is entirely due to the implementation and not the puzzle design. The point is that user interface design offers methods of mitigating laboriousness. After all, labour is expressed through UI: labour is what the player has to do.

That’s why modern Sokobanlikes offer undos and fast restarts. But it’s give and take: every time a designer alleviates the strain, it means the player can tolerate larger, more complex puzzles. Recently I played Fold+ on Android and was incensed to discover it offered just one undo! Having to restart the level each time I made a mistake became frustrating because it felt like unnecessary labour.


Even laboriousness of path-independent puzzles has been improved with GUI design. Going back to the laser reflection article, compare Chromatron which has you drag pieces in from a distant sidebar onto the board with Archaica: The Path of Light which has the pieces already on the arena. Which one is quicker to assemble into a solution?

Imagine having to drag rail pieces from a sidebar in Cosmic Express and Trainyard instead of just drawing them? SpaceChem has the player drag in pieces from a menu at the bottom but it advises you of shortcuts. Dragging is labour.


And let me end on one of my greatest UI puzzle discoveries in recent years. It’s not precisely about labour but about giving players control over their mistakes. One of my most favourite things about Stephen’s Sausage Roll is that you can undo a restart. This is brilliant.

The Twist

In the Electron Dance comments, Aaron Steed alluded to a particular puzzle design that encourages laboriousness, something he termed The Turn 1 Dick Move. It's where the solution of a path-dependent puzzle involves an "unobvious" move at the start, maximising move rewinding - and puts the solution firmly out of reach if the player does not realise the problem is that far back.

The truth is puzzle developers speak to players through their puzzles. Much of the time, they are straight up trolling and plenty of players lap up this sort of abuse. For these players, spotting the Turn 1 Dick Move generates a wry smile and perhaps a muttered "oh fucking hell". It just goes with the territory. Puzzle designer trolls players; film at 11. The art of the perfect troll is in the eye of the beholder. To see these precise clockwork mechanisms come together to troll the shit out of you can be a wonderful thing.

It's similar to how I don't quite click with much of Bennett Foddy's work and I am never playing Getting Over It With Bennett Foddy. Despite this I can admire his work and know there's an audience for it. Some people revel in this.

Friction is essential to challenge. To eliminate "laboriousness" is to eliminate the puzzle and instead you will have a toy that gives of itself willingly.

Appendix: From n To t

The recording puzzles I hated so much do not really exist in the same puzzle dimension as what we’ve been discussing: the realm of the turn-based logic puzzle. We can’t measure “labour” in the same way because instead of a discrete sequence of moves, the game exists within continuous time (or at least the computer’s approximation of it).

Obviously we could frame recording puzzles as path-dependent as what you record impacts future play, and I guess we could generalise labour from number of moves to solution duration... but this does not sit right at all. Puzzle labour doesn’t really work as a concept for dexterity puzzles, such as Tetris or action modes of games like Spelltower and Big Money.

What makes a good dexterity puzzle is a completely different ball game. And note that just because a puzzle is not turn-based it can be turn-like, in the sense that the player is plotting a sequence of operations. (The genius Recursed is turn-like.)

Update 27 Jul 2018: I originally wrote that players needed to complete Quell levels to learn the perfect move score. This was incorrect and this statement has been amended.

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Comments (15) Trackbacks (0)
  1. Not only is the puzzle omniscient but it is degenerative as pieces disappear with each step which prevents the solution from continuing to the end of time. (I was looking for an equivalent mathematical term like “path-dependence” but I wasn’t really able to find one. I assumed graph theory would have had a term describing the condition of revisiting a vertex/node, but I couldn’t find it.)

    Monotonic? Irreflexive?

  2. bloody hell why would you link someone to foddy.net

  3. I can see why you might suggest monotonic, but that doesn’t really imply the sort of “finiteness” that degenerative carries. I don’t know if irreflexive really holds the right meaning? (I had to look it up. I studied reflexive relations but no one used the term irreflexive!)


  4. Quell shows you the minimum move count next to your current count during the game in the header area (this part is cropped out of trailers it seems). It’s possible to beat the minimum in several levels of each of the Quell games, for which you get an achievement.

  5. I’ve actually been playing Quell and noticed just a few minutes before your comment that it does show you! I thought, ahhhhh, Josh is going to beat me up about this.

    I’ll make a slight change to the article tonight after I get home.

  6. I’m just happy you’re playing it :)

  7. I’ve been playing on and off since you cited it. I don’t think it would make it to my personal top ten, but it’s diverting and doesn’t annoy me. (aside from the infuriating perfect move target!).

  8. The graph theory term would be directed graph/directed acyclic graph, no?

  9. Game theory has a notion of iterative dominance. It’s a little different from what you’re describing, but it’s also kind of exactly what you’re describing. If i’m solving for an equilibrium in a big N by N table, I’ll cross out a row or column when I see that that choice is dominated, and now I’m only working with an N by (N-1) table.

    I would consider giving Getting Over It a go sometime. It can be frustrating, but it doesn’t have to be Dragon Ball levels of waaaah aggro i’m soooo maaaadddddddddddd if you’re not 13 and/or trying to make a living on twitch. I think it’s a pretty fun challenge game (I’ll not be beating it anytime soon), but the taunting trailer and mildly condescending tone in game were just extremely effective marketing for helping it blow up. In a lot of ways, I find Getting Over It much more accessible and enjoyable than something like SSR. Maybe that’ll change over time as my non-gaming life gets less about intellectual challenges (defending in August and never gonna be a big researcher) and more about dexterity/endurance challenges (13 months old and getting way too fast).

    I guess BF’s GOI is also interesting from a laboriousness standpoint, because obviously the main frustration comes from losing progress and having to get back up to where you slipped. But of course it eventually gets easier and easier to regain progress as the player gets better. Or at least should if you’re not being too impatient, but I think for a lot of people there’s the higher order polynomial shape where getting “better” means making new mistakes and being slower than your previous flailing speed for a while, until you get enough better to make up for even that. It seems like good puzzle games have those kinds of dead ends that require a certain amount of skill to notice enough to get stuck by them, and then even more skill to avoid/deal with them.

    P.S., did you ever play SPL-T? I think it might be another good candidate for your “non sokoban-derivative puzzles” list.

  10. 1. Graph theory occasionally deals with paths that don’t return to the same vertex with things like “hamiltonian path”, but I don’t know of a term to cover exactly your case.

    2. One of the things I observed in making Chromatron was that it seemed more fun to make a level where there seemed to be an obvious way to solve it that didn’t work, and the actual solution involved a trick, versus just making a level with a non-obvious solution that involved a trick.

    Sometimes this involved making you do a lot of work of a kind that you often don’t have to in path-independent games–moving every single mirror from where you placed them on your first attempt. Chromatron level 10 is an example of this which is exactly the first-turn dick move, despite there being no turns. If you use the 90-degree mirror in the earliest spot along the path, you will be unable to solve the ending. I thought of this more along the lines of Braid’s unopenable-door-that-ruins-your-key as a “making you think” thing rather than as a dick move, but I’ll accept the latter analysis as well.

    3. I made this for National Novel _Generation_ Month in 2014: http://htmlpreview.github.io/?https://github.com/nothings/nanogenmo/blob/master/2014/hannah.html

  11. @Sean RE:Hannah, I wish you wrote an epilogue or something.

  12. Ditto. I felt like things got monumentally exciting in the middle, but sort of tapered off at the end.

  13. I stopped after the first draft of that project because I’d encountered another challenge for that month which was even more up my street, that of making a computer-generated opera. This is a little off-track for this comments section, but since two of you commented, I feel obliged to offer a clear excuse. http://nothings.org/opera/

  14. Alan,

    In fact I was actually attracted to the Hamiltonian Circuit/Cycle nomenclature which Sean brings up but all the graph theory stuff just felt too much of a leap. I worried that there would be confusion between nodes in the game and nodes in the graph which represent game state. I was hoping for something quite straightforward which says “you can’t revisit the same state” but nothing seemed quite right. I think the degenerative term feels more understandable although I’m still not 100% sold on it.

    I did one course on graph theory but it didn’t hold my interest and moved on, so my memories of graph theory were pretty sketchy :)

    I’ll come back to the rest of these comments tomorrow. I am wiped with all this heat and I got to travel to Gregg’s tomorrow for Side by Side season 4…

  15. Dan

    Nice try, but you’re not getting me into Getting Over It. I’ve certainly spent my time in what Doug Wilson would call abusive games (and that’s mean affectionately) but I just don’t have the stomach for it much any more. Starseed Pilgrim went down like that for me at the end, where some of the challenges were just too difficult for me. So I just did it again and again and again until I had enough luck. I wonder if I’d find VVVVVV to my taste these days which I found AWESOME back in 2010…? The problem isn’t the frustration per se, but the time constraints around playing games so if I feel that I’m playing over and over again without noticeable progress, I just feel like I’ve pouring time down the toilet. My dexterity is not what it was.

    I guess your suggestion of iterative dominance makes some sense but I was thinking a lot about factorial functions and probabilities, where each step leads progressively less possibilities. Permutations with no repetition.

    No SPL-T here I’m afraid. I only have Android devices for mobile gaming!


    Yes, as I said to Alan above, I was attracted to the “Hamiltonian cycles” but in the end these concepts just seemed too far away unlike path-dependent which felt right on the bottom.

    2/ See, you get it, you’re my conscience! I was bothered by the fact you CAN get the equivalent of Turn 1 Dick Moves in path-independent games. You put all your pieces where they should be and discover it’s all hopelessly wrong and have to start again as the final piece or two reveals the problem.

    I actually think T1DM are hard to avoid. The revelation there’s a problem with a sequence often comes near the end rather than in the middle – and it’s not a problem if it can be fixed in the last couple of moves. Thereby, by almost definition, a tricky problem can only be solved by going back a significant number of moves, which puts you in T1DM territory. And if the move count is high, you’re gonna seem like a dick. It’s a theory I have.

    But I know what you mean about “obvious” vs “non-obvious” tricks. That’s something I’m going to explore much later in the series.

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