Fantastic Frontiers: Cry Havoc, And Let Slip The Quantum Ogres!

A while ago, I read this interesting piece on the nature of freedom and player agency in a role-playing game. The basic question is whether it's reasonable to create a game that bends multiple choices to the same outcome, despite promoting the illusion that an alternate decision would have avoided that outcome. In this case, the outcome is a fight with an ogre, where the ogre just magically teleports to whetever location the players decide to go next. It prompted a number of helpful exchanges:

• Here's a proposal to solve the perceived problem from Courtney Cambell ("C") which emphasizes the role of information in making choices substantive. It's not wrong to have a quantum ogre as the outcome of a meaningless decision. But once players obtain information that should make that decision meaningful (which a good game should always offer!), then we have problem if the information isn't actionable.
• Here's some pushback, with a good set of comments by Courtney and Justin Alexander following it.
• And here's a nice overview from Alexander Macris of some fundamental questions related to maximizing player agency, and making a game feel (and actually be!) "fair".

All of these pieces are well worth reading, although the immediate problem being addressed is one that arises in rather different forms in other types of games. For an RPG, the problem is that the GM is engaging in a sort of trickery that confuses the players and might violate an implicit social contract to be a "fair judge" in the adjudication of choices. But for a computer game, the problem is often that the mechanics of the game are hidden behind an opaque GUI that needs to be probed by trial and error, and might be too complicated or feedback-deficient to ever allow for pattern recognition.

In a board game, there's no risk of deception or obfuscation. Everyone knows the rules, and has access to identical information. Instead, the problem is hiding enough of the information to make the choice feel unpredictable at all, without becoming totally random.

To make this more concrete, consider the following advice from a friendly wizard:

There is [a way around Mirkwood], if you care to go two hundred miles or so out of your way north, and twice that south. But you wouldn't get a safe path even then. There are no safe paths in this part of the world. Remember you are over the Edge of the Wild now, and in for all sorts of fun wherever you go. Before you could get round Mirkwood in the North you would be right among the slopes of the Grey Mountains, and they are simply stiff with goblins, hobgoblins, and orcs of the worst description. Before you could get round it in the South, you would get into the land of the Necromancer, and even you, Bilbo, won't need me to tell you tales of that black sorcerer. I don't advise you to go anywhere near the places overlooked by his dark tower! Stick to the forest-track, keep your spirits up, hope for the best, and with a tremendous slice of luck you may come out one day and see the Long Marshes lying below you and beyond them, high in the East, the Lonely Mountain where dear old Smaug lives, though I hope he is not expecting you. (The Hobbit, 7.145)

A perfect wall of impassible mountains. How convenient!

Here we have three choices: goblin-infested mountains, Necromancer-infested shadowlands, and You-Know-What-infested Mirkwood. Gandalf is presenting this as a sort of Hobson's choice - "do as I say or die" - but presumably he doesn't have the actual ability to compel the dwarves to do anything. He's just giving information that makes the best decision blindingly obvious. Thorin and company are apparently getting railroaded by world-design into some spider- and elf-related encounters! At times, one starts to suspect that the suspiciously long chains of encircling mountains and forests in Middle Earth that turn Erebor and Mordor into fortresses with a single door are Tolkien's way of keeping his hobbits from wandering off to escape his carefully-prepped arachnid miniboss events.

This is a real choice, though, if a bit artificially discrete. Discrete choices often run into the problem of making the answer too obvious, which feels like a loss of player agency. In a novel, this might be a good way to comment on the nature of fate, but in a game, it takes an interesting decision and makes it boring.

So I've decided to take the whole "quantum ogre" idea and make it as literal as possible! A quantum wavefunction is typically distributed in a neat Gaussian distribution, rather than occupying a single point like a classical photon, or being spread out uniformly in space like a traveling-wave field. This is reminiscent of the three distinct encounter types in RPG-style games: random, pre-existing, and roaming.

In a game like last night's Runebound, we have pre-existing encounters printed out on little cards. They're essentially discrete quantum ogres, in the sense that no matter where you go, you'll get "the next green encounter on the stack". This creates a zero-information Hobson's choice: take the next encounter, or don't. There's no way to scope out each of two possible encounters with scouts, or ask around at a local tavern, or anything like that. This is the sort of encounter model in an MMO, too, where you walk into a dungeon and it's full of fierce enemies standing stock-still -- in neat little battle-sized clumps, waiting for you to defeat them one by one, as their buddies just down the hall politely wait their turns indifferent to the nearby tumult. This creates a world that feels static and not very dangerous. Lots of strategic planning, but poor verisimilitude.

Swoosh! Outta nowhere!

At the other extreme, we have the Final Fantasy overland map. You wander around for a while, and suddenly there's a pixelated screen wipe and you're facing some Cactuars that weren't there a second ago. You can escape, maybe, but there was never any other choice at all. The world is a threatening, terrible place, and you're playing strategic defense 95% of the time. The random number generator is playing the fiddle, and you need to dance to it. This supports the theme of hostile wilderness, but gives you no strategic choices, not even illusory ones.

Probability Ogre distribution function.

A real quantum ogre needs to be the third kind of encounter, fuzzy around the edges, but with a discernible peak in the center. You can roughly spot the zone where the ogre might be, but you can only weigh some relative probabilities. The one certain fact is that the closer you get to his lair, the more likely you'll bump into him as he takes his daily constitutional (this one, or that one). Of course, you could just go around him, but maybe there's a quantum dragon over there, and the ogre is the lesser of evils. And here we have some interesting continuous decision-matrix material: Do we walk midway between them, to minimize the chance of any encounter at all, or do we walk closer to the ogre to avoid the dragon, at the cost of higher ogre-risk. And is it worth walking through the Dismal Swamp to avoid both? Now we have the same interesting narrative pressure that Gandalf gave Thorin, but with a range of possible player decisions to optimize that go beyond "stick to the path".

Mathematically, the information we have about each encounter should be equivalent to the width and height of the Gaussian distribution. We need to use narratively-meaningful encounter attributes to generate these values. (Well, technically, using discrete dice will give a binomial distribution, but we know they're equal in large-N asymptotic limit!)

In the Fantastic Frontiers rules, the logical variable to use for the distribution width is the encounter's movement speed, and the logical variable for the distribution height is the population size. Since the area rises quadratically on a 2D map, it makes sense to use linear-quad scaling (one of my favorite design elements!), and let the height rise as the square root of the population. Here's an example.

A previously-spotted encampment of 12 ogres has movement speed 4. The square root of 12 is 3.46, so let's round that off to 4, and call that the base probability for entering the ogres' territory. (The wings of the bell curve will be chopped off, for simplicity.) Every step closer to the last location where the ogres were seen is a step deeper into a hex-ring of radius 4, and boosts the target chance by +1. To implement this as a bell curve, roll a couple of d20 against this target. (Just one die would give a linear distribution, not a bell curve.) If both results are at/under the target (for a roll-low check), then the ogres are encountered!

This makes the world feel a little more dynamic. The ogres are wandering around, instead of just waiting for us to come back and clobber them. But we still have the basic mechanic of being able to strategically plan for ogres, using our hard-won ogre-related information. It's the best of both worlds.