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

The Steam store page for genius puzzle game Recursed (Portponky, 2016) highlights two reviews.

One is my very own, published on Rock Paper Shotgun. I wrote “Recursed’s brilliance is how it spawns complexity from a few simple constraints.”

The other is from the one and only Jonathan Blow who worked on a puzzle game you might have heard about. “I played for a while,” wrote Blow, “but it seemed really slow / simple.”

I’m only going to warn you once. Strap yourselves in.



Imagine you are at school and your teacher, Mrs. Blow, is explaining to the class how to factorise a quadratic expression. Mrs. Blow goes on for, say, fifteen minutes. Then she hands out the practice sheets and you are a little surprised because there is only one question on it. Everybody struggles with the problem because it’s the first factorisation they’ve ever done. Nonetheless, ten minutes later, everyone has it figured out! You are very proud of yourself.

Mrs. Blow congratulates the class. Then she announces that as everyone has cracked factorisation, the class will now apply it to solving quadratic equations.

Breaking news: there is no Mrs. Blow. No teacher would expect everyone in their class to have digested and mastered a new concept with just one example. The kids would struggle with the next few lessons as they hadn't grasped the basics. Under this teaching regime, how many of them would wind up dropping out?

Yet this is the ideal that puzzle designers aspire to. The tightest sequence of challenges which keeps things fresh and allows the player to grow. No two puzzles are structurally the same. “Think you’re smart, eh? Well, take this,” the designer says as they hurl a new curveball at the player.

Now this bit of game design is proper hard. The sequence is like a trail of breadcrumbs which leads players deeper into the forest of challenge. Insights are not so much fed to but bled from the player. Occasionally they are forced to question their assumptions and have a winning “Oh My Christ! I didn’t realise you could do that!” moment which is of course the best videogame moment (hey, have you played The Witness).

Creating this sequence is a hard problem because the developer is the all-knowing god and it is not possible to see with mortal eyes. To test whether the sequence gets it right is laborious. Once a player has been through the game, they too are cursed with knowing, thus not as useful to review a new version of the sequence. To get the best feedback, you need fresh victims, fresh meat for the puzzle grinder.

I am sure you have heard of the “state of flow” that occurs when you are completely absorbed by a task. Mihaly Csikszentmihalyi, who developed the theory of flow, proposed that flow only happens when there’s a perfect match between an individual’s skills and the challenge before them. This zone is known as the flow channel. If skill and challenge are mismatched, players end up either bored or frustrated. Here’s a really simple graph that demonstrates the relationship.

Designers are pursuing the Holy Grail - a game which ushers players down the flow channel. They have full control of the challenge variable - they designed the levels, after all. But designers have tenuous control over skill and here be the problem. Not all players are created equally. Some have played block-pushers for years while others are just losing their puzzle virginity and think a monster pushing snowballs around sounds kinda fun.

All of these people are put through the same sequence, a one-size fits all approach to puzzle education. Some games offer players a choose-your-own-adventure approach instead, such as Cosmic Express (Hazelden & Davis, 2017) and Stephen’s Sausage Roll (Increpare Games, 2016) where players are not forced to tread a linear sequence but instead dine on an exciting buffet of levels. But, in our classroom metaphor, the adventure map is not offering multiple examples of one subject, but multiple subjects: are you going to attempt the question on solving quadratic equations, the one on vector products or try your hand at Lebesgue integration?

I am being unkind. There is often overlap and sometimes follow-up levels are attempting to shine a light on the current limits of a player’s thinking. Designers will always try to work with as many players of varying ability, but inevitability there are limits. Here's Alan Hazelden, designer of Cosmic Express amongst others, interviewed in an Electron Dance essay earlier in the year, The Developers Who Won’t Hold Your Hand:

I remember one playtest where the player took five minutes to realise in level 2 that the train can only carry one passenger at a time. That felt bad, but I think I stuck to my guns and went ‘nope, this is not unfair, you just have to pay attention to what's happening’. Since it happened to one person I'm sure it's happened to others - I just have to hope that if someone stops playing there they probably wouldn't have enjoyed the rest of the game anyway.

I’m not arguing this is bad or evil. It’s not a dereliction of game design duty. It is fact. You cannot design for everyone. However, designers are biased towards pushing players into the frustration space where skill < challenge rather than the boredom space where skill > challenge. This is Blow’s comment on Recursed: aim for the flow channel or higher, not below you doofus. Stephen’s Sausage Roll could be viewed as this methodology taken to the extreme. Each puzzle is unique; there is no repetition and almost certainly no holding of hands. There is no notion of practice with Stephen’s Sausage Roll. Do. There is no try. You sausage. Or die.

This philosophy is so heavily ingrained in contemporary puzzle design that when presented with the alternate view, it is casually accepted as failure. Jonathan Blow’s non-review tweet of Recursed suggests he has interpreted the bias towards the boredom side of the flow channel as a signature of this-one-ain't-really-worth-it.

This dismissal of “slow” progression reminds me strongly of the arguments against making games “easier” and “more accessible”. And Recursed isn’t unique. A lot of fresh talent starts out in the floor of the flow channel, dipping into boredom space. Tricone Lab (Partickhill Games, 2017) is another one where the puzzles are a bloody breeze for seven aeons but it does, eventually, push back against the player. The question is whether all that is necessary. Tricone Lab dazzles you with lots of tiny monochromatic flying bits - would a tighter sequencing lose more players? The grey interface could probably do with an improvement, but the Tricone Lab player doesn’t have much prior experience to rely on. It’s not a block pusher or a Match-3 game.

Let’s take a gander at a 2018 paper titled “Model Matching Theory: A Framework for Examining the Alignment between Game Mechanics and Mental Models” by Rory Gloin, Joe Wasserman and Andy Boyan. The authors propose that learning in games can be better explained through the interactions of a player’s mental models. Players don’t need to be taught about gravity, so they can understand a game in which “stuff falls down”. But experience of how the WASD keys move an avatar around a first-person shooter is specialised knowledge. If there is a high match between existing mental models and a game, the faster a player will pick things up.

There is one paragraph in particular that stood out to me. The authors posit that games are particularly good teachers because of:

Repetition. Repetition presents players with the opportunity to review and revise mental models.

Repetition presents players with the opportunity to review and revise mental models. Progression. Games gradually increase difficulty allowing previous inferences to be retested within new contexts.

Games gradually increase difficulty allowing previous inferences to be retested within new contexts. Spectating. It is possible to learn from the experience of other players.

In the world of puzzle games, designers are focused heavily on the progression aspect. As puzzle games are generally solitary experiences, spectating is not a big feature and, indeed, most puzzle players want to find a solution themselves than copy what Brian Eggbrain did in his Let’s Play. But what of repetition?

You can argue that players continue to “fight” a particular puzzle, repeatedly, until they defeat it. Failure is a learning experience. But remember the key takeaway from The Monte Carlo Player. Sometimes players solve a level and have no idea how. This is the worst-case scenario for a designer, who hopes that none of the levels are vulnerable to brute force solution. Random solution is camouflaged failure.

A game designed around “frustration-bias” is a high momentum approach, pushing players to look forward not back. Puzzle games never ask a player explicitly whether they really understood the puzzle but canny designers may pose a follow-up that tests player understanding. If that understanding isn’t there, the level gates progress and the player, it is hoped, will reflect on what they know. Or, more precisely, what they do not know.

Consider the first puzzle panel track you encounter in The Witness which is there to explain the meaning of the dots on a puzzle. When you see black dots and white dots, you have to draw lines to keep them separate.

The first puzzle practically solves itself - drag right for the win. But there are other possible interpretations of this single puzzle. The next few puzzles are designed to nail it.

Further puzzles explore whether all the dots have to be collected together. However, the puzzles shift focus towards heuristics, such as learning to trace around the edge to avoid partitioning.

And because this tutorial has, in the main, encouraged the player to see the puzzles in terms of white dots, one of them challenges that assumption. It's easier to think of the following panel in terms of black dots.

Great design, but I need to confess something.

The Witness attempts to teach its rudimentary rules like this again and again. And one of them did not work for me: the star puzzles in the treehouse zone. I’m not going to spoil them if you haven’t played before but after breezing through several of the star puzzles using random experimentation, I realised I hadn’t a fucking clue what was going on. After some frustration, I buggered off to another zone to get some respite.

It’s time for the point, reader. Even the most amazing puzzle design will lose somebody. Even people who are really into your design. What saved the star puzzles was being able to move back through the completed puzzles and experiment with them.

And this is why, at the end of The Laboratory of Logic, I said “this will prove to be important later”. As I explained, the UI of many puzzle games are not very good at encouraging you to review past challenges. Something like Cosmic Express is not bad, although it’s difficult to see exactly what puzzles you’ve travelled through. The Witness is brilliant because each puzzle is located somewhere on an island and that lends your puzzle memory some geography.

I’ve pointed out that laser reflection games are, ironically, not very good at reflection as they have a tendency to “solve accidentally” and distract you with WELL DONE, LET’S GO TO THE NEXT LEVEL, PLAYER ONE. And while Sokobanlike Stephen’s Sausage Roll does offer replay, the functionality is buried under sixteen tonnes of UI rock and practically useless.

Machine at the Heart of the World (Evidently Cube, 2018) is a game about decrypting instructions. Each puzzle has a unique solution and you literally have to guess the solutions of the simple puzzles. These correct guesses arm you with knowledge. Only then can you solve the complex puzzles that are largely immune to brute force. Machine is built around experimentation but review is key: tapping the left arrow key will shift you back to previous solved puzzles instantaneously. It becomes a reflex to do this. Tap, tap, tap, observe, think, try again. I don’t know of another puzzle game that acknowledges so explicitly your solution history... but I’m sure a reader does. Answers in the comments, people.

Valve were a pioneer of using clever tricks to lead players into predestined drama that also convinced the player they had agency. One of my favourite tricks is the positioning of a fence to nudge the player into looking directly at the first appearance of a Hunter in Half-Life 2: Episode 2 (Valve, 2007).

This intense stage management is now a hallmark of the AAA FPS. It is also where puzzle design is today. Many logic puzzles aspire to giving players a sense of drama, driving them up the flow channel, feeling like they’ve just stolen victory from the jaws of defeat every single time. Wow, YOU solved it with nothing other than your wits! Yet the designer has been shaping your experience, carefully plotting a linear puzzle sequence that nudges you ever onwards... or presenting an adventure map with judicious gating.

Gating can be done subtly. We've already mentioned levels that require players to break assumptions to pass. We could also deploy noise, using unnecessary puzzle clutter that a player can only solve if they have a clear mental model that allows them to cut through the crap. Such clutter is out of vogue - I am not a fan of obfuscation myself.

These are incredibly sophisticated efforts but they do not always succeed. As an example of where tight design can go awry, I offer touchscreen puzzler Invert (Glitchnap, 2017). Invert is a type of Lights Out puzzle; you want all the tiles to be the same colour, and pressing switches will flip an associated group of tiles. Generally, I find Lights Out puzzles dull - although recent Illiteracy (Lucas Le Slo, 2018) was a pleasant diversion - so a game built around them has to mix things up if it’s going to go the distance. Invert is aware of this danger and, after eight levels, offers an entirely different tile formation with its own nuances.

That’s the whole game. Eight levels per tileset. Now those eight levels are not even eight levels because the first few are inevitably thin tutorials to get you to play with the switches. After those tutorials, I was using trial and error to muddle my way through. It was only after the eight levels I would finally start to become familiar with a tileset but it was at this point Invert said bored now: let’s try something else. I was whisked off to another tileset where I had to start learning all over again. Thus I spent most of my game guessing and was robbed of consolidating what I had learnt at the last minute. Defeat stolen from the jaws of victory.

When the player fails to keep pace with the game, enlightened puzzlers allow players to skip levels or offer hints. But look, once again, to the first-person shooter - where are the “low-difficulty” modes for puzzle games? Imagine inserting more levels for the troubled player to give them a better chance to learn. A recent paper by Chris Martens et al, “Generating Puzzle Progressions to Study Mental Model Matching” attempts to procedurally-generate the sort of progression that contemporary designers aim for - a procgen puzzle engine is a far more promising angle for producing a sequence that adapts to the player’s skill level. What learning curve do you want? And the engine spits out five puzzles where one might have done. Remember, as I explained in the previous Ouroboros essay, I didn’t develop a mental model of Dissembler (Ian MacLarty, 2018) over the course of its handcrafted campaign but through its procedurally-generated content:

I had become an honest-to-God Dissembler expert with a head full of heuristics that I could not express in words. I had a deep understanding of how colours could be migrated across the board and the limits of migration. I was able to conjure alternative strategies when the more obvious ones would fail. Dissembler did not teach this through individual examples but through daily practice.

The alternative to designing for different skill levels is to pull the handbrake and encourage review. The Witness was all over this but its design is somewhat unique. It's time to admit that rather than describing puzzle games as a year in Mrs. Blow’s classroom, a better analogy would be Hazelden University, where you get a couple of lectures a week and it’s totally down to you to transport the knowledge into your head through practice and review. At least at Hazelden Uni, we know what is expected of us. But the average puzzle game shrugs its shoulders as if players should have known all this already. What are you, it snarks, a four-year-old?

Now and then, I catch a glint of arrogance in the puzzle genre. It does not come from the developers whose intentions are entirely honorable. But it is reflected in the surface of their games, with a focus on efficient sequencing and the withdrawal of explicit instructions in favour of a design where the player has to figure out the basics. There’s a whiff of a feedback loop here in which design chases the hardcore, as the first-person shooter did, a snake eating its own tail.

I love efficient design. I love discoverable systems. But are player practices evolving with modern puzzle design... or is design leaving some players behind? I can’t help but wonder how many players abandon puzzles because they have not been catered for.

And I wonder how many of those dropouts feel like it’s their fault.

Next: Understanding puzzles is the greatest feeling in the world