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Designing The Solution Space
by David Rosen on 08/31/09 03:33:00 pm   Expert Blogs   Featured Blogs

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

In the machine learning community, problems are often described by the topography of their solution space (the set of all possible solutions and their corresponding success). For example, if the problem is to determine the correct motor output to make a camera look towards a light, the solution space might look like this:
solution space 1
When the camera can't see the light then the error is 100%, but as it rotates to center on the light, the error starts to drop down to nothing. A common technique to solve these problems is local optimization: start with your best guess, and then keep refining it until the error is as low as possible. On the solution space, you can picture this as a stream of water flowing down the slope.
solution space 2
My intuition is that players approach puzzles in games in much the same way. They start with their best guess, and then observe the game's response, and if there is a clear path to follow, then they meet with success. If there isn't, they try again with their next best guess. One of our key jobs as game designers is to make sure that this solution space is curved towards the 'correct' solution, and not flat, or curved the wrong way. For example, let's look at the solution space for an old-school adventure game that gives no useful feedback for wrong answers:
solution space 3
Here the player has tried eight different solutions, and none of them worked or provided useful feedback on how to proceed. In this case, the player has run out of ideas, and is now stuck. If this is a casual player, he will likely just stop playing. If it is a more hardcore player, he is familiar with sites like Gamefaqs and will use a walkthrough for the rest of the game. Either way, the player will be unable to experience the rest of the game as intended.

The most successful adventure games succeeded largely because they figured out ways to ease the pain of failure, motivating the player to retry many more times than otherwise. For example, in the Monkey Island games, Guybrush Threepwood had witty replies for anything you could try, even if it made no sense. It's important to remember that the player's path will inevitably end in failure a couple times, and you have to think of that as part of the game experience. If player's have fun failing in your game, then you're doing something right!

Most modern games have a much more complex solution space than an old-school adventure game, something more like this:
solution space 4
This demonstrates a second way to get stuck: locally optimal points. These are paths that seem promising, but really lead nowhere. For example, an interesting building you can enter that has nothing in it, or a puzzle that your character is not yet equipped to solve. Giving positive feedback for the wrong path is even worse than giving no feedback at all, because the player is going to be much more hesitant to try again. The only way to find these flat areas and locally optimal points is through play-testing. Odds are that you will find that players are confused by things that you couldn't possibly have anticipated, and you have to tweak them to smooth out the solution space. This way, everyone will be able to find the solution eventually, no matter what idea they start with or how fast they go.
solution space 5
This is different from holding the player's hand, or telling her what to do, because we are still letting her start wherever she wants. We are also not just making the game easy: problems can still be very complicated and difficult; we are just making sure the players can usually find their way through them.

One of the best recent examples of crafting the solution space is Portal. The puzzles quickly get very complicated, but through extensive play-testing the developers found effective ways to guide the player's attention towards the most important things by making them more interesting, and away from irrelevant things by making them less interesting. For example, in one level there is a box which is very important to solving the puzzles, and they found that players kept ignoring it, because it seems tedious to carry a giant box around with you. To solve that, they decided to paint a heart on it and have the AI voiceover talk about it constantly, calling a weighted companion cube. Suddenly, all of the players were happy to carry it around with them, and it become a viral internet phenomenon. Similarly, a lot of the levels started out with introduced too many elements at the same time, causing a really lumpy solution space, so they added small intermediate levels to introduce each element one at a time, each with a much smoother solution space.

I am a visual thinker, so it is helpful for me to visualize game design in this way. I hope it is helpful for you as well! Please let me know  in the comments if you can think of anything that could help expand this metaphor, or counter-examples to show that it's inaccurate.

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Tyler Glaiel
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that's an interesting way of thinking about it

Luis Guimaraes
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It's not impressive the Portal's box exemple. Today's games has so much "nothing" that players can easily guess "they put a box here just to show i can carry boxes, but with no use at all". Interaction with no use at all for the sand-box trend. When everything the player tries just works, and not only every good idea, but every idea, then comes out the optimal solution (I somehow enjoyed Far Cry 2 until I found a sniper rifle).

Kevin Reese
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This article was fascinating! Great work.

I suppose it just the differences in how brains work, from folks to folks -- but personally I would have never conceived of plotting this subject in the way you have, with your visual 'solution space' approach. It certainly is an interesting perspective on the data involved.

About half-way through your article I began to get worried that you were focused, as your primary goal, with making the solution to a game problem as plain-forward, apparent, and logical as possible. But you addressed this completely (and most perhaps most succinctly with the line "If player's have fun failing in your game, then you're doing something right!)

It is funny to imagine: it would no doubt completely boggle a contemporary 12 year old gamer's mind (beyond belief!) to try out any of the earlier Sierra games, and seeing that - ack! -- they actually had to type out commands in pidgin English sentences to accomplish things; and some of the tougher challenges were very far from obvious; and on top of that there were game-ending pitfalls without warning (say you missed picking up a key item from earlier on, for example.)

And I'm not even going to mention a game like Zork. Honestly I can't even fathom that there was more than 5 people that finished that game without any assistance.

Certainly this is fascinating stuff. I want to mull this over, and come back with more comments when I can think up something interesting to say.

One thing that just strikes me right now though: I can see how a solution space can be well applied to static problem, such as rote machine learning. But when applied, as you have, to gaming -- isn't there a much larger variance, from person to person, on how each person would approach each problem? Could the variance (theoretically) be incorporated into the solution space? Or even randomization for that matter.

And I'm also curious -- you explain how the solution space idea can be used to refine and improve existing qualities of your game. Did you also consider that perhaps you could you also sort of, uhm, utilize the solution space idea in a reverse manner, so to speak, for the invention of puzzles (instead of the refinement of pre-existing puzzles.) Said another way: do you think you could conceivably set out to find a sort of 'optimum template' of a solution space before creating a game's puzzles, and then once you found that optimum template, use it as a guide in creating new puzzles?

Luis Guimaraes
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@ Kevin

Maybe it wasn't what you were talking about, but came a nice idea from that: the exact inverse of David's machine (one more use for this), I'll use a simple "physical" puzzle to keep things easier to explain:

Such as: you have two corridors to follow, one have a door, and the other has the key of that door. As a game/level designer you want to make good re-use of your level, and also get the player to overwalk throug it to make a feeling of the known-safe place, or in other words, home-zone, so you can surprise the player with something unexpected or just, give the next place a real feeling of new-unexplored area, since the last area is overwalked by the player.

So you script your level flow this way: The first corridor choice of the player will be the corridor of the locked door, no matter which side he chooses to go first, and the other will be the place where the key is found. So the player's path will be:

Locked door → Key → Exit

No matter the first choice.

Nathan Mates
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Interesting premise, and one that I'd generally agree with. How do you think this applies to RTSs, where in most of them, there's "OneTrueBuildOrder(tm)" for the first ~5 minutes of gameplay. If you deviate from this, you're behind the optimal economy, and likely to fail against any player (or AI) that's following the build order better than you are. The results of your decisions aren't apparent until 10-30 minutes later, which is quite opaque. How do you make that friendly to people?

Luis Guimaraes
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@ Nathan

Good point, I forget that, the "OneTrueBuildOrder(tm)" is the reason why I don't play RTS games. I's guess you're right, the analisis on this article is a potential creative solution for that, since in theory it's is a solution for robot-memorized strategies in other genres such as the key puzzle I said, the player may have already played, but won't ever find a shortcut.

For the helping-side of this analisis, which is the core of this article, some help on what to build would just make no difference since the quick-click would become the strategy and, after the first-5-minutes strategy helped by the system, would be a following-5-minutes players optimal strategy. What RTS games need is a bit more of tatics in its core gameplay. I personally like the AoE3 cards system, since every map changes a lot the strategies, but at the end there will be an optimal strategy for each map and each card deck.

Luis Guimaraes
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@ David

It brought something else on touch: adaptative difficult. It's easier to make it for combat and enemies, but what you study here comes to show some ideas of how to make adaptative difficult on progress puzzles. I thought about making the solution space wider after every player mistake, and it came also with some points for combat/enemies adaptative dificult improvement.

For exemple, Instead of just lowering A.I. or damage or health of enemies, it could be a choice making the solution space wider, by simply adding weak points that they didn't had before, to help the player with an way around straight damage or such.

JB Vorderkunz
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@Kevin - I remember playing KQ4, getting all the way to the final area, and NOT HAVING THE DAMN KEY! I quit in disgust and never went back. Which brings me to...

@David - THREE CHEERS FOR THE SECRET OF MONKEY ISLAND! I've got my ticket, how about y'all? Interesting article. I'd really like to see an actual game sequence illustrated using this method - how do you map the possible choices onto a grid (i.e. what are the axes)? What is the relation between, um, field distortion/depth(?), and the [trivial or non-trival] consequences of a given choice? How do you link series of choices? (stacking maps?) moar pleez =)

Anthony Brice
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"For example, an interesting building you can enter that has nothing in it"

But...but...that was my favorite thing about Stalker. :(

It made the environment feel more real, as if everything wasn't explicitly crafted for my maximum enjoyment.

Caulder Bradford
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"For example, an interesting building you can enter that has nothing in it"

That was also one of the hallmarks of Shadow Of The Collossus' design. A huge, beautiful, interesting world, but very little of it actually had vital importance to the game, as the primary focus was locating and killing the Collossi. I think this raises an interesting point about also creating an "atmosphere" in which the player is presented with these challenges and problems. All the empty ruins, desolate plains, and scenery without a deeper purpose, was actually used to focus the player narrowly on the Collossi. If the game had just been a serious of linear, square rooms each with a Collossi boss fight, the whole experience would have been drastically (and tragically) different.