And now for something a little different. This Feature’s going to be odd. Fortunately, it’ll be short. Unfortunately, it’ll be dense. Though it’ll probably make the assholes who complain I never back up my claims with sources happy.

It’s also going to be the start of a casual, three-part argument about the nature of tabletop roleplaying game adventure and challenge design. It’ll bring together a lot of things I’ve mentioned in passing. We’re going to talk about creative problem solving, dice-rolling as gameplay, and ultimately, how to properly lock a door in a dungeon.

I ain’t going to explain the actual argument, though, or how this all got started. Not until the last part. Instead, I want to talk about open-ended, creative problem solving.

Riddle Me This…

Here’s a candle. Here’s a box of tacks. Attach the candle to the wall so wax can’t drip on my nice carpet. If you succeed, I’ll give you the Orb of Macguffin that you need to win the adventure. If you can’t solve it in time, though, my pet sphinx will eat you.

This Is Your Brain on Functional Fixedness

Did you solve the problem? I don’t actually care. That isn’t even my puzzle. It was actually presented by psychologist Karl Duncker in his 1945 book, On Problem Solving. Others have written about it since then, including Malcolm Gladwell, and a lot has been made about how few people can find a solution to the problem, but Duncker’s point wasn’t about the low success rate, and neither is mine.

His point was that presentation is everything. Kind of.

First, let me give you the most common and commonly accepted correct solution: pour the tacks out of the box, tack the box to the wall like a tray, then set the candle in it. Easy peasy.

Except it’s not easy. Some have found success rates as low as 5%, though it’s probably closer to 20%, and the way I presented it made it particularly difficult. I think. I haven’t run the numbers.

Let me explain…

When Duncker presented his version of The Candle Problem, he used visual aids. He gave participants pictures of the available accouterment with which to solve the scenario. Duncker discovered that one change to the visual aids hugely affected the success rate. If he showed people a picture of a box full of tacks, most people couldn’t solve it. If he showed people a picture with the tacks on the table next to the box, suddenly lots more people could solve it.

Like this…

Now, Duncker wasn’t great about publishing his actual stats, but lots of people have done the experiment and similar experiments since then, and the results have been consistent with Duncker’s findings even if actual success rates are a little tough to pin down.

The most interesting version, to me, as a Game Master, because this does have to do with Game Mastering, I swear, is the one conducted at Stanford in 2003 by cognitive scientists Michael C. Frank and Michael Ramscar. They did it without visual aids. They did it narratively. They did it how I did it above. They found that only around 20% of people can solve it with normal, natural wording, but with slight tweaks to the wording, they could more than double the success rate. The difference between saying “a box of tacks” and “a small box filled with tacks” was dramatic.

Now Duncker and others were trying to demonstrate something called functional fixedness. It’s this prewired tendency in the human brain to see things in terms of their function or use to such a degree that you can’t see them as anything else. In The Candle Problem, to most people, the box is just a superfluous container. It holds the tacks. It’s not even part of the puzzle, really. If you separate the tacks from the box for people, suddenly, they can see the box as more than just a container.

Now, I find this shit cool. As a Game Master who wants to give every player the best narrative and gameplay experiences possible, I find everything to do with cognitive science fascinating, and especially anything about problem solving, decision making, and group behavior. I want to know how human brains work because I make games for human brains and because I don’t just want to make naked, screaming assertions based on anecdotal experiences.

Yeah, I know, I’m weird like that.

Anyway…

Functional fixedness is an interesting thing to know about, but there’s more to the story, because The Candle Problem is part of a broader class of open-ended problems in cognitive science.

The Problem Of Insight

Duncker’s candle thing is an example of what are called insight problems. They’re open-ended problems that can’t be solved with normal, step-by-step reasoning or problem-solving skills. Instead, finding a solution requires a sudden reframing of the situation in the solver’s head.

I’ve mentioned The Nine Dots Problem before. It’s another example of an insight problem. Take three rows of three equally spaced dots and try to connect them by drawing just four straight lines. The most common solution requires you to draw outside the dots.

Here…

Most people struggle to solve the problem because their brains get stuck following an unstated rule that the lines can’t go outside the bounds established by the dots. Such problems are thus called constraint-relaxation problems. The solution requires you to recognize that you’re following a constraint that doesn’t exist.

There are all sorts of insight problems. In addition to functional-fixedness problems and constraint-relaxation problems, there’s representational change problems, lateral thinking problems, and lots of others. I ain’t going to do a whole survey. It’s a subject you can have all sorts of fun researching for yourself.

The important point is that, as Game Masters, most of what we think of as open-ended or creative or outside the box type problems are actually insight problems. For example, if the players recognize they can use a display pedestal as a battering ram to break down a door, they’ve just solved an functional-fixedness type of insight problem.

The other important point is that insight problems aren’t about information gathering, intelligence, reasoning, or creativity. They’re really just about getting lucky enough to break your own brain.

I shit you not.

Your Brain Is Always Overclocked

Let’s talk about someone else way smarter than me. Let’s talk about Daniel Kahneman, who basically invented the entire field of modern decision-making and problem-solving psychology. Kind of. I’m being hyperbolic, but the dude was a genius. He wrote a lot of very dense books about how brains solve problems and make decisions. Want some good, dense, summer reading? Check out Thinking Fast and Slow.

The big takeaway from Kahneman for today’s purposes is that your brain just really can’t handle anything you ask it to. It’s got too much sensory information coming in, too many concepts and associations stored inside of it, and a body that is way too complicated to actually operate. So it’s constantly looking for ways to limit the data it has to work with.

The reason most people struggle with The Nine Dots Problem is that the human brain imposes constraints just to limit the number of possibilities it has to consider down to a manageable number. The Candle Problem is hard because your brain simplifies things by boiling them down to function and utility whenever possible, or else it’ll just overheat from data processing.

In cognitive science, these necessary limitations are called heuristics and biases. They’re shortcuts and assumptions and constraints and limitations your brain imposes so that you can actually solve problems in anything approaching a reasonable time frame. What we call outside the box thinking is just your brain cutting through a mental shortcut. That’s why insight problems are usually very easy to solve once you overcome one particular cognitive hurdle.

But that also makes them kind of unfair tests of anything.

This Ain’t an IQ Test

Insight problems aren’t actually solved through reason, creativity, experiment, or effort. They’re not solved by anything we normally associate with intellectual problem-solving. Instead, everything is down to the solver’s initial understanding of the problem or a sudden, insightful shift in that understanding. Thus, people either solve them instantly or else sit there completely blocked until suddenly, they have a solution. It’s the mental equivalent of one of those 3D Magic Eye pictures snapping into clarity.

Insight problems aren’t good tests of intelligence, reason, or creativity. They actually measure how strongly a particular mental heuristic or bias is wired into the solver’s brain and how often they’ve broken it in the past. Personal experience is actually a key component.

But Duncker, the two Michaels, and many others demonstrated another vital component.

Presentation.

Narrative Problems are Problematic

Duncker demonstrated that you can hugely, drastically change The Candle Problem’s solve rate just by taking the tacks out of the box. Mike Frank and Mike Ramscar showed that tiny differences in word choice can double the success rate from one-in-five to even odds. As a Game Master, that shit actually bothers me a lot. It should bother you too.

See, as a Game Master, most of what I do is narration. Sure, I’ll draw an occasional diagram or present a visual aid for clarity, but my games are mostly just talky-talky. That’s how tabletop roleplaying games be. So it’s kind of a big deal that some problems become a lot harder to solve in talky-talky form. But it’s even worse when a tiny change in wording can take a problem from easily solvable to impossible.

That’s notwithstanding the fact that insight problems seem to have very low general success rates even when they’re presented perfectly with wording that befits a cognitive behavioral lab. If I’m looking at coin-toss level odds of any given player finding any solution to an entire class of open-ended problems instead of sitting there blocked, that ain’t great. Especially given that these things aren’t actually testing reasoning, creativity, experimentation, or effort but rather just lucky flashes of brain-breakage.

Scientifically, I’m not sure I can call “maybe the players will think to use a statue as a battering ram,” a fair problem-solving, gameplay challenge anymore.

Of course, if the probability that any given player will find a solution to an insight problem is 50%, then a group of four or five such players has a 90% chance of coming up with something. Even if the odds of one player finding any solution are 20%, that means a party has over a 60% chance of coming up with something. That’s just basic math, right?

Here’s the problem with that argument. The two problems. First, we’re really talking about coin tosses here. Psychologically, insight problems really are a toss of the die. They’re not skill-based or intelligence-based. They’re not testing what Game Masters think they’re testing.

But second, teams can make insight problems harder.

Teamwork Don’t Make This Dream Work

By their very nature, insight problems don’t make great group problem-solving activities. They’re not in the same class as things like mysteries that hang on deductive, inductive, or abductive reasoning. When you’re doing inferential reasoning, you can make incremental progress by reasoning. Organizing facts, identifying relationships, brainstorming explanations, looking for contradictions, and testing hypotheses all advance you to a successful solution. So, they’re things groups can effectively talk through. But insight problems aren’t advanced by reason. The only thing groups can do is say, “We could try this,” and, “That won’t work” over and over. Without the useful, creative eureka that makes the solution trivial, there’s nowhere to go but blocked.

Now, even if that’s true, which it is, because I only say true things, more people pulling their mental slot machine levers over and over hoping for a jackpot does increase the odds of success. But that’s only if the group doesn’t talk.

What keeps people from easily solving open-ended, insight problems, though, is that they’re basically mental traps. They’re problems because our brains are trapped by their own wiring, and the solution arises if you get lucky enough for your brain to rip itself free. But mental traps are easily reinforced. Your brain likes being trapped. It needs to be trapped to function. All it takes is one dumbass saying the wrong thing to reinforce everyone’s mental biases, and then no one’s breaking free.

It’s like this…

If the group starts talking through The Candle Problem and everyone keeps talking about just the tacks and the candle and no one says, “box of tacks,” gradually the box gets forgotten completely. It gets edited out of everyone’s memory. Worse yet, if some dumbass says aloud, “All we’ve got is tacks and a candle; how are we supposed to work with that?” then everyone gets kicked away from that vital eureka moment.

A group trying to solve an insight problem is equally likely to dig all its brains deeper into whatever mental trap it’s in as to help each other escape based purely on careless talk.

Which is the real problem…

Insight Problems Aren’t Hard; They’re Brittle

I hope it’s totally obvious at this point that I’m not just talking about solving The Candle Problem or talking just about overcoming mental constraints. I’m talking about an entire class of open-ended, creative problem-solving challenges that Game Masters love to throw at their players. In the past, I’ve called them open-ended creativity challenges. That’s what happens when the Game Master throws an obstacle in front of the players and trusts the players’ abilities to creative their way around them using whatever they have in their packs or repurposing whatever random stuff is scattered about the environment. Washed-out bridges over rivers, blocked doors with no lock or key, spike-filled pits dividing the room, shit like that.

Almost every “I don’t design puzzles; I don’t design games; I design situations,” ends up at an insight problem, but without the careful design of a cognitive behavioral experiment. They’re a hallmark of “old school” play, especially, and often touted as “emphasizing player skill over what’s on the character sheet,” but scientifically speaking, that’s a load of crap.

I have nothing against letting players creative their way around anything. I would never stop my players from building a raft out of fallen trees. I wouldn’t stop them from crossing a pit with some rope, a ladder, and some pitons. If my players use a statue as a battering ram, that’s awesome. This crap is what makes tabletop roleplaying games so great. It’s also why you can’t have a real tabletop roleplaying game without a real, human brain running the show. The Game Master’s job is to adjudicate the players’ every creative action. Decide whether their plans can succeed, whether they can fail, and find a way to determine the outcome.

But knowing what I do about game design, cognitive science, and the psychology of problem solving, I also can’t call an insight problem a fair gameplay challenge. Not because they’re too hard, not because of the odds, but because they’re not really fair and reliable tests of the players’ mental skills.

It ain’t that it’s hard to come up with an outside-the-box solution to The Washed-Out Bridge Problem, but, rather, first, that it’s not really a group-oriented reasoning challenge, and, second, that it’s extremely brittle.

What do I mean by brittle? I mean the challenge is easily wrecked by things outside mine and my players’ control. If I say the wrong word when I present the problem, I can cut the players’ odds of finding a solution in half. That ain’t a fair test of my players’ mental skills. If my word choice or hasty diagram glosses over an important affordance, I can make the problem completely impossible for normal human brains to solve. That’s a huge problem if I don’t even know what affordances are and how I can accidentally gloss over them. If one dumbass player unwittingly makes the wrong comment while talking out the problem, they might make the game unwinnable.

Imagine there’s a board game that has a very finicky setup, and if one piece is set up even the tiniest bit out of place, the red player can never win, and that’s not even mentioned in the rule book. Is that a fair game? No. You can get a fair game out of it, but the tiniest mistake makes it unfair and unplayable.

That’s brittle.

Insight problems are brittle. They’re too sensitive to build your core gameplay around. They belong in the game. Or, rather, insight solutions belong in the game and the mere presence of the Game Master makes them possible, but if you want to design actual, good, fun, fair gameplay challenges — if you, like me, believe anyone sitting at the table deserves the best narrative and gameplay experience you can deliver — insight challenges can’t be all you do. They can’t even be most of what you do.

And now that I’ve proven my point scientifically and shown my work, I’m sure I’ll be rolling in apologies by the time I get back from my trip, and no one will ever fight with me again about this.

But how can you incorporate open-ended creative insight-based gameplay in a tabletop roleplaying game? Because that really is good stuff; it’s just not load-bearing gameplay. Well, I’ll tell you. Eventually. But first, we have to talk about the other gameplay extreme, which, ironically, turns out to be the same thing and, ironically, can be solved exactly the same way.

So, stay tuned…