Electron Dance
13Nov/1819

The Monte Carlo Player

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

Monte Carlo simulation is a statistical technique where we let a computer rip through hundreds or thousands of randomized experiments, revealing a rich timescape of alternate futures from which we can make deductions. It’s a way of breaking an impasse of uncertainty in a problem. For example, we can use Monte Carlo methods to determine the fair price for a complex financial option whose payoff depends on the future movements of a stock.

And it struck me, as I was making random stabs at a level in Stephen’s Sausage Roll (Increpare Games, 2016), that puzzle enthusiasts engage in a similar exercise.

Let’s return to Electron Dance favourite Dissembler (Ian MacLarty, 2018), a Match-3 game that operates similarly to Bejewelled (PopCap, 2001) yet sports a number of inventive twists such as the board degenerating with each move.

Initially, I found Dissembler merely diverting as you might have gathered if you watched my February stream. For many of the levels the next move was usually obvious. Whenever I genuinely became stuck, I would try random approaches to see if I could uncover the magic move required for progress. I did not feel like I was solving, but acting as a vessel through which The Lord communicated His Solutions. I didn’t rate Dissembler so much as a puzzle but a brilliant zen experience.

Because of that zen brilliance I rushed straight into the daily challenges after I’d exhausted the hand-crafted puzzles. Each day, Dissembler poses five new procedurally-generated puzzles of increasing difficulty. While the first two or three were inevitably a piece of cake and a cup of tea, the fourth and fifth could be traumatic mindmelters. I would occasionally have a short exchange with AppUnwrapper on Twitter about the ferocity of a particular challenge.

One day, I realised the awful truth. I had became 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. That's why I had to come back in May to stream it again to confess it was now Dissembler ❤ Joel 4eva oxoxox

Puzzle designers fret about presenting the most efficient path of puzzles that coax players through the fundamentals and the occasional trick, yet this design philosophy doesn't address learning via osmosis that only accompanies extended play. An engaged player, working through puzzle after puzzle, is a player committed to “deliberate practice”, a term that launched a billion self-help blogs and books.

The term reflects that an individual needs to be invested for practice to have an impact; you can practice piano for weeks but if tickling the ivories bores you, you won't learn anything. This shit is real, by the way, because I struggle with the homework of two children every goddamn week.

Deliberate practice guides players to heuristics that aid solution. For example, a Sokoban player will quickly learn not to push blocks into a 2x2 square, because this locks them into place.

Designers concoct puzzle tutorials that nudge players towards the low-hanging heuristic fruit and after that puzzles usually require combinations of existing heuristics or even fresh thinking.

I’ve been playing Tametsi (Grip Top Games, 2017), another entry in the Minesweeper/Picross family. After a few levels, players realise a shallow review of the board will not be enough and stepping through the consequences of potential moves is the only way to make progress. When you do this, you’re either looking for a contradiction or cells which bear the same result under all the scenarios. Hexcells Plus (Matthew Brown, 2014) plays out similarly but Tametsi pushes much harder on this, even handing you a pen to scrawl potential answers over the board.

But imagine this insight never comes together. An alternate you that keeps scanning the shallow state of the board and goes no further. There is nowhere obvious to click and, inevitably, you begin to guess. You guess on cells that seem "likely" which then earns you new information enabling progress. Not every guess is correct.

The problem is these guesses are not producing insight. This isn’t solving a puzzle through smarts: you’ve become a Monte Carlo player. You might as well be pulling the handle on a slot machine. Eventually you lose heart and consequently continued play will be even less likely to produce the relevant insights.

Deliberate practice only delivers knowledge if we keep trying new things, keep pushing our boundaries of understanding. When faced with a new challenge, we often need to start out with a guess and work our way through the consequences of that choice. We often need to be a Monte Carlo player to prise out new understanding. How else will we get a foothold on a fresh puzzle, find its sharp corners, its obstructions, the dark places that derail solution attempts? The secret might be quite buried a la Aaron Steed’s “Turn 1 Dick Move” in which an unobvious early move is necessary to unlock the solution.

Take a look at the difficult level Ursa Minor 11 in Cosmic Express (Hazelden & Davis, 2017).

The goal is to build a rail that will get each passenger to their required destination “box” then allow your galactic toy train to exit the level. At first glance, the level appears to be segmented; purple travellers on the left, orange travellers on the right. [Update 19 Nov 2018: Matt W in the comments points out the rest this the paragraph is not true. Technically it is true under a specific, special condition, but not generally. I can't say more than that without minor spoilers. Not sure how I can fix this article without ripping out this example entirely!] The crucial insight is determining there is only way to open the level, to travel straight down, and deviating from this makes solution impossible. Where does this insight come from? Maybe you’re smart enough to see it off the bat. But you might need to experiment many times to get a feel for the level’s texture.

If you advance directly from experiment to solution without experiencing an epiphany, then Monte Carlo has backfired. And once the player has fallen into a long-term pattern of guesswork, those feelings of puzzle claustrophobia are not far behind, particularly as large puzzles are resistant to Monte Carlo. The final level of Cosmic Express, Nova 7, is my classic example of this.

Here is the level Nova 7, a wide open space - overloaded with possibility.

Cosmic Express

Experiments yielded nothing of value. The solution always seemed to fail and I could not see how to subvert any failure into triumph. My purposeful experimentation gave way to complete guesswork, embracing Monte Carlo as my only hope. Hours of attempts, a dearth of progress. Eventually I abandoned Cosmic Express, the game unfinished, for weeks. (We’ll return to Nova 7 in a later Ouroboros post.)

Developers of all stripes are concerned that Monte Carlo play pushes players towards embracing luck instead of skill. Echoplex (Output Games, 2018) is a recording puzzle game in a similar vein to Rose and Time (Sophie Houlden, 2012) where you are chased by your own afterimages; think of the phantom ninja levels from N++ (Metanet Software, 2015) but in 3D. In a video about the “premonition update” the Echoplex developers explain they received feedback that some players were running blindly through levels and often solving them via luck. This is Monte Carlo as a brute force solution and a terrible result for the player.

Here’s one last thought to chew on.

A little Monte Carlo is often required to see the iceberg of complex logic hidden below the serene surface of a puzzle. This sort of architecture, where it is hard to read the puzzle without experimentation, suggests an undo is vital. Undo allows us to rifle through alternate futures rapidly. It is a technology which augments our thinking. But like the smartphone, it may not change us in ways we like. We jump when the smartphone hollars at us Hey BUDDY, someone has responded to you on Twitter! Do we like being wired this way? Always on, always ready to engage? Is the undo as harmless and beneficial as it seems?

Think about how the undo encourages experimentation even when careful analysis would be the better choice. Consider Minesweeper/Picross games where guesswork is anathema, requiring the player to spend their time silently staring at numbers instead of actively clicking out guesswork. And if undo is blocking some players from thinking about a puzzle, then surely undo is an inducement to Monte Carlo solution and the risk of brute force methods. I’ve watched more than a few YouTube videos where solution was achieved through an undo-fuelled Monte Carlo binge. It strikes me as unlikely that any designer would be happy their logic puzzle goodness had collapsed to “keep rolling the dice until the solution appears”.

Those iceberg problems, though, are likely to be the consequences of undo rather than their progenitor. Designers, consciously or unconsciously, are aware that undo makes puzzles that you were once supposed to solve in your head a lot easier. The Echoplex problem was “fixed” by making the game harder: they added a time limit to ensure players had to plan their solution.

Undo is a player weapon which designers had to respond to in a similar way. Undo drove designers to concoct increasingly intransigent puzzles that resist brute force and such puzzles need undo - they would be frustrating as fuck otherwise. The player with an undo is a smarter adversary, thus the designer must rise to the challenge of the augmented player.

The establishment of undo as standard changed how players engaged with puzzles and how they were designed. And that is something you cannot undo.

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Comments (19) Trackbacks (0)
  1. I love “turn 1 dick moves” when they are part of an optimal solution, but not of other possible solutions. To achieve that is very useful in zach-like games where players compete optimizing solutions.

  2. (I know I subverted the definition of the term, but it’s a useful generalization I think)

  3. Well now I feel bad about my corporate finance class and the “check my work” function that students have on their online homework problems. Why do they use check my work to brute force their way through easy problems, fail to learn the patterns, and get stuck on hard problems? Sounds like I need to get Zach Gage to help me design a more engaging course.

    Odd that Monte Carlo is making it harder to value not-so-complex financial instruments in this case.

  4. Hi Marcos, I get what you mean – you’re really talking about puzzles that support multiple solutions, particularly Zachlikes which are very open when it comes to solutions. I don’t know if it’s a dick move any more, though?

    I haven’t had a chance to play your new thing, yet! I’ve shifted my spare time into Electron Dance away from playing games. At some point, I’ll get round to it!

    Dear Dan,

    Thank you for your letter which I read with great interest. I’m glad you’ve seen the error of your ways. Your students are cheating.

    Love
    Joel x

  5. I got some thoughts but I just wanted to say that the thing you said about Ursa Minor 11 is not true and I opened to check my solution and found another one but it didn’t help me with the CENSORED and now I just spent the best part of an hour trying to figure out the CENSORED after I decided I wasn’t going to get any grading done and should go to sleep.

    Anyway I bought Snakebird.

  6. Hello Matt, I was wondering when you’d turn up on the comments in this one expecting you to have capital-T thoughts to share.

    I was all sorts of confused about your Ursa Minor claims, though. Are you saying it isn’t true it you thought it wasn’t true and don’t have the proof? What I do know is that Electron Dance is far too often the cause of tardy grading for your students.

    On Snakebird: Wisely done, Mr. Freeman! I’ll see you up ahead.

    I don’t know why I thought a Half-Life reference was appropriate.

  7. Typos! “it isn’t true *or* you thought it wasn’t true”

  8. I am saying that the thing you are saying is wrong: it is possible to solve Ursa Minor 11 without starting down. Proof: Link

    Also Electron Dance isn’t leading to tardy grading (tardigrading! going to curl up into a little ball and shoot myself into space where I will be able to survive the extreme conditions; let me know when the planet is being more sensible and I’ll return), we have the week off for Thanksgiving here and I was unsuccessfully trying to get a head start, it’s leading to me not getting enough sleep. As usual. Well, what was really leading to it was spending too much time pootling in Snakebird, and then getting my briefcase and before I got the grading out of the briefcase being sat on by the cat which is a rare occasion so I petted him for a while, and then when I had given up and decided to go to bed checking this post and being COMPLETELY UNABLE to keep from saying “I wonder what the solution that’s already stored up in there is, it’ll only take five seconds to check” and “ooh there’s a CENSORED” and “hmm I think I can actually do this that’s not the way Joel is talking about” and “aah! I can but it doesn’t solve the CENSORED” and “fiddle fiddle fiddle” and “gahh!”

    So yeah though the level select in Snakebird is perfectly classic and signposts “Here’s the levels with a star which means fuck you particularly hard” well, I find it a bit unsatisfying. I’d really like something more like Stephen’s Sausage Roll or Cosmic Express where the levels are broken into themed chunks–which I think they are, kind of, but the level select doesn’t make absolutely clear what level will use what thematic element?

    And though it’s probably good that they aren’t doing the SSR thing where you have to clear all of one island before you get to the next, the unlocking is opaque; Cosmic Express refrains from doing that thing but the unlock paths are visible a constellation ahead. (HAVING CHECKED THAT, QUITTING THE APP, THANKYOUVERYMUCH.)

    Also the interaction is a bit clunky. I’d really like “M” for “quit to map” instead of having to hit “escape” and select the menu. Plus since the kind of fatfinger mistake I make often involves moving the wrong bird, I tend to mix up the “switch bird” and “undo” keys.

    What I really want, I think, is names for the levels. Cosmic Express doesn’t have that but every Cosmic Express level isn’t a struggle and an achievement the way they are in Snakebird. It’d feel less bland to say “I finally solved ‘take a short bird off a long gap'” than “I finally solved level 20.” And hmm, at least Cosmic Express and English Country Tune have names for their worlds (though the CE names have flat nothing to do with the puzzle content). Also ECT and Sokobond and SSR and Good Snowman (not CE though) all let you see the shape of the level from the level select screen, which helps give the individual levels a bit more character.

    The level select scheme in SSR is really good to have–it gives you a bit of a respite between the assaults on your brain.

  9. Oi I certainly forgot to close that tag. Or include the text that was supposed to link to the image.

    Anyway that comment was self-parodically on brand for me but I did have those thoughts. I might have them a bit less now that I’ve finally solved level 20.

    Also in case the direction I went in the linked screenshot was the one you meant, here’s one going the other way: actual text to link to this time

  10. Oh GAWD, Matt. It looks like my memories were broken – I actually wrote down at the time “Ursa Minor 11, straight down” but I think I was thinking about the, you know, CENSORED solution. That’s really annoying. It doesn’t break the article but what a shame I’ve misremembered one of the key examples.

    I never want to hear about tardigrades again. I’d managed to expunge Star Trek: Discovery from my mind which took all knowledge of tardigrades with it.

    I’m impressed with your depth of feeling for level selects for puzzle games. Admittedly, I did bake part level selects into an earlier Ouroboros article, too, but I don’t think I can hold a candle to your level select interface critiques. I get what you’re saying about the level select, but I just threw myself into it and did it purely sequential order. I never attempted the star levels until I’d got through the full set of normal levels. And, to be frank, there isn’t much point trying them until you’re done. They’re more of a preview of things to come, a promise that you’re going to be good enough one day to do these.

    I think the Cosmic Express is one of my favourites because it’s easy to navigate and shows all the connections. But I can never remember what the levels are (except for Andromeda 14 and Nov 7). SSR has charm but it has real problems – as we’ve discussed – around repeatability. The Witness is favourite because of its tied to geography and I know where all of the different puzzles are – I still remember – despite having to walk around.

    I played Snakebird on the phone and the interface on that small scale was really annoying. So many times I’d make the wrong snake move – you have to tap the snake first that you want to control. Undo, undo, undo. No undo would have killed the game for me.

  11. See, it’s like I can say “I finally beat Level 23,” which really took a lot of “this isn’t even possible” and a reasonable amount of “I have managed to do this thing that isn’t possible, and it’s absolutely zero help in solving the level,” but you don’t even know what I’m talking about! (It’s the one with the eleven-square blue bird, and there’s a SPOILER and a SPOILER on the upper island, and then there’s a central one-square gap and the portal is at the end of a long maze of spikes.) But every SSR-head knows what it means when someone says “Twisty Farm deserves to be in a museum,” and curls up in a ball at the words “Cold Frustration.” (I know you said you’re stuck on all the Cold levels, but one of them is worse than the others.)

    About the main post–you’ll pry my Undo from my cold dead hands. Another bit of ish I have with the Snakebird interface is that the undo isn’t smooth like in SSR & related games–you can’t hold to rewind, you have to keep hitting backspace and hearing the cute Snakebird undo noise. This, the no-name levels, and the simplified select screen that doesn’t show the connections all seem like part of the presentation as a cute mobile game–which is fine, except since it really is a brutally difficult puzzler the UI ought to accommodate that, I think. (BTW sequential order wasn’t an option for me, because I did the demo first which has a discontinuous set of levels, so when I bought the full version I got some nonsequential unlocks. Not that I would’ve gone sequentially anyway.)

    OK, really back on the topic. Here and in some other games there are times when I’ve klutzed my way through a level and not felt bad about it. My snakebird just happens to get itself in the right shape and that’s OK. It feels better when you know what you need to accomplish at the macro level and it’s the micro fiddling that gets accomplished by button-mashing. One thing that games do to prevent this is teach you a technique that has to be accomplished several times to complete a puzzle–there’s one level where turning around a snakebird at the edge of the level is nontrivial, and it needs to cross the level several times. You can mash through it once but to finish the level you’ll need to figure out how to do it.

    The flip side of this is the level that’s set up so everything falls into place just so. Sometimes there’s only a few state changes you can make to get you out of the seemingly impossible equilibrium, or only a few things you can do whose effects aren’t obvious. And you need to try them till you see what works. e.g. the end of Snakebird 23, where having done one of those things it turns out that your snakebird is just long enough to finish the level without getting destroyed. Which is something I didn’t measure out before trying my solution–but it made sense when it happened, and if it hadn’t fallen out just right it would’ve been perfectly flummoxing. Or I’d have had to go back to the drawing board.

    What I’m really thinking of, I guess, are some moments in English Country Tune where you try something and a whole bunch of things fall into place like a row of dominoes. Which is possible because the gravity mechanics in ECT can be opaque, so I can’t always say “I’ll do this and then everything will fall this way.” Which reminds me, I have this theory that your issue with Snakebird is partly with puzzlers that involve gravity, because when a puzzler involves gravity the effect can be far away from the action and that makes it harder to plan ahead without doing the equivalent of blindfold chess…. wait I already said that in relation to Jelly no Puzzle.

  12. Okay, so, if you’re going to bring this up NOW Matt, then I have to tell you. Level 23 sounds like it was on big deal over here. I’ve got notes for each freaking level based on my playthrough during the summer. Explicitly for the last part of Ouroboros. Here I say (and I’m just giving you the raw notes here):

    I remember this [from when I first played] but not the solution. There’s a gate to get through. At first I thought I had to lift it and sneak through. No, you have to raise it completely and crawl underneath. There’s some getting used to pushing the bar without blocking and I had to loop some twice. I spotted early that without the bar coming back down I can’t reach the other side at the bottom, over spikes. That was no problem. Did not get stuck.

    Oh I completely think we’re in a post-undo age and certainly who wants to go back to solving puzzles without an undo? I just think it’s an important observation that undo made puzzles harder (and I ahve a similar view on micro-checkpointing/instant restart in games like VVVVVV, N++). I think the “undo” came first, leading us into harder puzzle territory rather than the other way around; can you imagine doing something like SSR without an undo? THAT’S RIDICULOUS.

    My original Snakebird experience is quite, quite different to what you’re describing in your comment :) I didn’t have a clue what I was doing, fiddled around, went aha-ok-that works then moved on. None the wiser about what I’d actually done. My point being is that without that element of deliberate practice, it is still possible to feel quite lost and not learning anything.

    I don’t think gravity is the problem for reasons I’ll get into later. But the straightforward counterexample is Full Bore, which has gravity running all the way through it.

  13. That’s… NO big deal over here. *ahem*

  14. Fine then. (Also even spoilers ahoy.) For me level 23 was more Monte Carloesque in some ways… at perhaps a higher scale. What I mean is that I was unable to envision the end state that would allow me to succeed in the bottom row. So I went through some extreme convolutions to do some nonobvious things that I couldn’t possibly see how they would help–like lifting the gate to the top of the hill on the right–and of course they didn’t help. Also spent some time thinking about how to do something actually impossible (hooking the gate under the sliding block on the right) that also wouldn’t have helped if I could have done it.

    Even the real solution required an experiment, because there’s a mechanic that can’t be worked out from first principles–you can’t move the head into the square the tail would be vacating, that’s been clear since about level 2, but you can push something into the square the tail is about to vacate. That more or less has to be stumbled across–you think “I need to move the gate above the gap while supporting it from below,” and that’s the only way it could possibly be done when you try it, so you try it.

    Then I just had a level where I saw the wacky thing that just might work almost instantly and solved it in about a minute (unlike 23, it didn’t require intricate maneuvers to set up)–level 37, where (spoilers) the snakebird has to fall into the portal. That’s something where if you think “that can’t possibly work” you might get stuck because you won’t try it.

    To tell the truth from the beginning of this series I figured you’d tried a few levels of Snakebird and decided it wasn’t for you rather than hatesolving your way through the whole thing.

    About microcheckpoints–the game I can think of that avoids this is Bit.Trip Runner, where a mistake puts you to the beginning of the (about minute-long) stage, which means you practice the early parts of the stage till they get instinctive. And it’s a rhythm game so it’s like internalizing a piece of music. I wall-of-texted Shaun about this a ways back. The puzzle game analogy I can think of is something like that level where you have to turn the bird around multiple times (it’s level 17) so you need to master it. In fact you have to do that once to finish level 2, I Monte Carloed my way through it, and then in level 17 I had to stop and figure out what I was doing.

  15. Jehoshaphat Christ, level 37. I think I know exxxxactly which one you mean. I don’t want to get too deep into my second Snakebird experience as I want to leave that for the end of the series. How much of it was hatesolving vs intelligent contemplation is something I want to get into at that point. This convo is getting too close to me revealing my cards early in the game :)

    Sorry for late response, I have been completely down in the bunker working on A Field of Flowers.

  16. Congrats on finishing A Field of Flowers!

    Yeah so Level 37 was not a problem for me at all, was the thing. I fiddled with it for a few seconds, thought “I bet you can probably do this,” did this, done. But it’s the sort of thing where if you don’t see you might be able to do this, you can spend hours on it, I bet.

    Anyhow gaming time has been spent on an Exciting Secret Project but I took a little time and managed to solve the last non-starred level of Snakebird. So now I have the starred levels left. Yay…?

  17. Thanks Matt!

    Good luck with the star levels. Some of them are hard, if I remember rightly. That one with the three snakes and frames and void to cross. Ha, ha, good times.

    Now, whenever you say “Exciting Secret Project” I assume it’s a new Matt W text adventure.

  18. You are correct! Well, approximately one-eightieth correct.

  19. Exciting Secret Project is released into the wild!


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