Game Design Sketchbook: Testing the Limits of Single-Player

[Jason Rohrer]

Game Design Sketchbook: Testing the Limits of Single-Player

With i45hg, Jason Rohrer examines the difficulty of creating a single-player videogame with the depth and replayability of the classic board game Go.

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[fepayton]

Quote 1:
Can you make an AI-free, randomness-free, physical-challenge-free, single-player game with gameplay depth akin to that of Go?

Quote 2:
Go is often cited as a touchstone for profoundly deep gameplay that emerges from a shockingly simple set of basic game mechanics. You can learn the rules in less than a minute, but you can spend the rest of your life plumbing the depths of this game. Go is a game that you can return to over and over. It will always have something new to show you. It will never grow old.

Given the above I have two thoughts:
First: I can see the argument that no single player game could match an opponent based game,
Second: The exact "depth" of Go is not explicitly understood and possibly not describable.

While I can see the argument, I cannot agree with it.

In the article there was the idea that once an optimal path was found in a fixed puzzle or game, then the depth of the experience would end. This in turn necessitated some additional mechanic (like randomness or AI) to substantiate the experience. I feel this assumption is a fundamental flaw.

Consider Checkers. People have spent ages playing, practicing and bettering themselves at it. We teach it to our children and we can (and some have) purchased volumes of strategy. Not exactly Go, but a game that could fit as one with considerable depth. In July of last year, Checkers was solved. Does it diminish its depth?

Consider Go on a small board (e.g 5x5 or 9x9). These are relatively well understood and off much less depth than the full game on a 13x13 board. An exceptionally small board 3x3 is not much more difficult than tick tack toe and the absurd board 1x1 is deterministic.

If the small Go boards are so easy, is it possible that the difficulty of Go is an illusion and that it will be one day solved, like Checkers? Is Checkers solvable only because it is on a sufficiently small scale and that a 40x40 Checkers board would open up hidden complexity?

I think our answer is found in one's high-school English literature class. Our protagonist is beset my a number of categorized opponents:
man vs man: The classic opponent or AI model
man vs nature: Fighting time or physics
man vs the supernatural: An uncontrollable force such as randomness
man vs himself: A challenge of our own ability and limitation (and the win!)

Person vs itself is an unending challenge. It is also a challenge that is set at our level and provides us with endless contemplation.

What I don't know is what keeps me playing.
When I play Go against grand champions, they crush my boggled mind with a small library of elementary tactics and well studied attacks and counters. I'm confused, their bored and no-one wishes to profoundly converse over the debacle. It is only when we meet players akin to ourselves, that depth ensues.


Facing the limitations of ourselves is what I will argue creates the depth. The other half of this equation is that you want a simple game. The simple rules of Go are nothing to the complex patterns that emerge.

Emergent behavior is difficult to create. This is by definition, as it emerges without design. From this I offer two possibilities:
1) You have asked for the impossible.
-or-
2) Unexplainable genius will create your game, but you will have to be patient.


Do I think that there could be a game, for a single player, playable only on a computer that could capture the hearts and minds of millions and befuddle scholars for centuries?
Short answer: Yes.
Long answer: I believe sir that you have described the golden idle that every single game designer dreams of, that every gamer hopes for, and every responsible accountant and investor rejects as an absurd risk.

 

[ycc]

Adding to fepayton, I think that another flaw in your argument is that single player games are not deep because of 'cheap' gimmick like randomness, while multiplayer games are not. Following that logic, if you play against an opponent and won, does that mean you will win every time? The answer is probably no, because
1) The opponent is not going to pull the same moves every time,
2) You won't remember the whole sequence of moves.

So basically, multiplayer games like Chess or Go are only interesting because you won't know what your opponents will do each time even though you have played them before. This is just a much more sophisticated level of randomness, but fundamentally, both single player and multiplayer games rely of providing a different challenge each time to be interesting.

 

[GregN]

Jason,

I think this article is important. dissecting the elements of videogame mechanics and trying to define some of them is a daunting task that no one ever even attempts to do (except devs behind closed doors). I have only seen this sort of deconstruction one time before which was Will Wright's SXSW keynote. (Well, and Raph Koster, but he's an MMO guy, and I never really got into those)

But that's like 3 people! in a sea of reviews, forums and discussion rarely does anyone ever talk about the basic elements that make-up a game.

One of the tell-tale traits of the indie community seems to be it's desire to discover a few more game mechanics, or at least be freed from the constraints that say you must make a game within such-and-such set of restrictions.

I've tried to do similar things: I made a pacman that shot projectiles; I made a tetris that uses 43 different shapes instead of 6 -- just to see what works.

Of course the task you chose for yourself -- to construct a game that doesn't utilize an element of randomness, and is single player -- is just about impossible. Randomness is almost always necessary. Solitaire wouldn't work without it, nor minesweeper. When you first muss up a rubick's cube, that's random. The shape queue in Tetris is random. That basically leaves the Go & Reversi strain of games, and they are 2 player. If a game is multi-player that's where the element of uncertainty is introduced, otherwise, there really must be randomness of some sort. The randomness does seem to be responsible for a majority of the replayability. You mix up the pieces and then you play, getting a new challenge each time.

 

[GwionBach]

Jason, that's an excellent article, and once of the best justifications I've heard so far for the advancement of game AI.

I've been doing AI in the game industry for 14 years, and it's progressed tremendously in that time. In particular, the use of planning systems has opened up a lot of doors for improvements in AI behaviors (in particular, Jeff Orkin's planner for F.E.A.R., described at http://web.media.mit.edu/~jorkin/, is generally recognized as one of the best game AI systems ever seen in a videogame).

We're now at a point where we can really start to do amazing stuff with game AI -- the industry knowledge is there, the computational power is there, and the market is big enough to justify the investment. All we need is for the industry to start taking it seriously.

 

[Purum]

would you say that the depth of solitaire is discoverable within the specific rule set of (for example) solitaire "freecell"? or would you accept that solitaire is a game with many types of "layouts" that broaden it's "depth"?
If the latter, then i would argue that Solitaire is deeper than suggested. It may be obvious to you, but I dont know if you generate the possibility space of that game by instances -subsets of rules (freecell being completelly different than spider solitaire) -, or if you group them and then say that its closest relative is "spit" or other card games.

 

[Dom Camus]

I don't accept the claim that Chess and Go are "good" games.

Certainly they have earned their special place in the history of games, but I consider both (and particularly Go) to be overall quite weak designs. Their good features are numerous - they have deep strategy, they reward both experience and invention, they are highly replayable and they have simple rulesets (particularly in the case of Go). However, their weaknesses are significant. First and foremost, for a great many players they are simply not as much fun as less famous alternatives.

Both games exhibit a thoroughly unforgiving form of tempo which stifles scope for interesting play. In a two hour game of chess a player might make only one or two interesting moves, most of the time being forced to choose between a set of relatively uninteresting positional plays or countermoves to the opponent's predictable offensives.

Both games are also very unforgiving of errors. By this I mean not that an error confers a disadvantage - which can (and arguably should) happen in almost any game. The problem is that an error will usually be game-losing without any opportunity for a subsequent superior play to recover the lost ground. This is bad for gameplay, leading to an atmosphere of paranoid caution and a preference for dull plays if one is seriously trying to win.

Finally, it's worth observing that in a sense chess does have random elements. With every move the players explore some subtree of the game space the properties of which are not fully known. From the perspective of the players these properties are pseudorandom, or at least they might as well be. Chess is at its least random when both players know a great deal about the region of the game space they are exploring. And yet these are often the least interesting games. I think that correlates quite well with your thoughts on single player games.

 

[shMerker]

Chris Crawford approached this when he attempted to taxonomize games, entertainment, and art in The Art Of Computer Game Design. He put forward the idea that what makes games interesting is the appearance of interactivity. An AI is ultimately another set of rules to be mastered. It's the inability to fully understand those rules that creates the challenge. Human beings can be the same way. The main difference between a human and an AI is that a human will change and grow. But as long as you don't understand an AI (or any set of rules) it can maintain the appearance of interactivity.

Don Camus, I'm curious how your argument doesn't extend to virtually all multiplayer games. The scenarios you describe seem to apply to very skilled players, But I'm trying to imagine a game where players of that caliber would not have the same situation. If two players are playing perfectly at, say, a timed game of pong, and one of them makes a mistake, he now has a disadvantage of 1 point. If from that point both players play perfectly he will lose by that one point. "opportunities for skillful play" did not arise, not because of the game's design, but because the other player simply didn't allow it. The opportunity could be imposed in some way by the game's mechanics, but doesn't that also negate the importance of the earlier error?

fepayton: I believe go is more often played on a 19 by 19 board. When I was shopping for a set last year I never even saw a 13 by 13 board.

 

[fepayton]

skMerker quote:

"fepayton: I believe go is more often played on a 19 by 19 board. When I was shopping for a set last year I never even saw a 13 by 13 board."

Good call, it is usually 19 x 19. Oddly enough, a quick Wikipedia search revealed that the original was 17x17. Being an exceptional novice, with the patience of a cat I usually play on a 9x9 with friends. It is apparently large enough for some of the more complex patterns to form, while being much faster than a full game (to which I must confess that I have never played).


More on topic;
The "appearance" of interactivity was mentioned. I think this is a point that deserves additional consideration. Appearance (as opposed to factual existence) is a core part of games. Often I see designers refer to the illusion of choice, or the semblance of intelligence (as example from an AI). Whilst I managed to mix up the numbers, I argue that Go may actually possess only the appearance of complexity, possible due to the large board size.


Dom Camus mentioned the Unforgiving nature of errors. I think he has a point. I remember years ago playing Quake with bots. The bots were exceptionally simple AIs: they were able to navigate the terrain collecting health, and they had perfect aim. The only thing that made them semi-enjoyable opponents, was their persistence on using the shotgun and ONLY the shotgun. They were hard to fight. At close range they were lethal, and even at long range they were punishing. By an "intelligent" standard they were far from perfect players, but that is what made them "enjoyable". Their imperfect understanding of the mechanics allowed for a win condition.

Jason (in his article) argued that for a game to be fulfilling it could not stand only on mechanics, but would require an additional factor (such as chance or an opponent).

I don't think that this "3rd party" is a necessity but I will concede that AI and chance are easy compared with finding a mechanic to create "emergent depth".

I think "appearance" is such a good word because it implies that we don't know something about that is going on. I think it important to present this as a separation between skilled players and perfect play. Skilled players can be beaten. Perfect play cannot. Be it opponent or AI, mechanic needs to facilitate a "possible" win condition.

When we fully understand the mechanics as they are applied to the games world or scope, the opportunity for perfect play exists. By retaining the mechanics and gradually enlarging the scope I think we might be able to obfuscate the "perfect solution" or even a simple heuristic solution.

I would argue that Randomness, AI and Opponents sufficiently hide perfect play from us but I think (though this is just my gut speaking) that there are other innate mechanics that could also accomplish this.

Thoughts?

 

[slyder35]

Anyone remotely interested in this thread and who enjoys physics-based puzzles - try this site:

http://fantasticcontraption.com/

 

[Dom Camus]

I'm curious how your argument doesn't extend to virtually all multiplayer games.

Your Pong example will do nicely to illustrate the difference. In Pong, if I lose the first point this has no impact on my capacity (or lack thereof) to win the second and subsequent points. In Chess, if I lose a pawn this has (all other things being equal) a substantial impact on my capacity to do well in subsequent exchanges.

 

[shMerker]

Except that now you're on the branch of the tree that requires you to score two more points than your oppponent instead of one in order to win. The ratio of your win conditions to possible outcomes has still been similarly reduced.

 

[gooneybird71]

The obvious reason is that digital games are designed solely as modern entertainment to generate profit, games like go or chess are extensions of understanding and a chance to put reason, logic, and planning into practical action. They are timeless in a sense due primarily to the technological media upon which they are based and the simple rule set.

Modern computer games much like the rest of modern popular media are completely tied to not only the physical media they are made on but limited in their cultural relevance to whatever theme is currently popular. COD4 for example will presumably not be very interesting to a teen 50 years from now, chances are good that no one will even have a system that can run it, and the cultural significance of the theme will likely be viewed through very different eyes than it is today. Another example is, the proliferation of WW2 games of recent years, any guesses why they all just happened to come at approximately the same time?

Cultural relevance, 50 year anniversary of Normandy, Pearl Harbor, coupled with the major film releases by Spielberg, carrying right on through and culminating with the documentary series "The War". These are cultural memories which are leaving our societies as that generation passes on, most of the kids of my generation grew up with a grandparent who was a veteran of the conflict and everyone has heard stories of the hardships and unity that the conflict inspired.

Not only that but the technology base of WW2 was very "human", no lasers, no fly by wire, no supersonic, no satellites, no GPS, just boots and treads on the ground and props in the air and eyeballs on the line. Mostly this time is romanticized by the children of the children of the participants because it was a time of action and decision, irregardless of the fact that it was in all actuality a lot like it is today. People after all haven't changed, only the technology and economics has changed.

So, computer games by their very nature prevent themselves from attaining the same level of endurance of Go or Chess, its simply not possible in the same way that TV shows lose their relevance. Popular culture is just that popular, for a time at least until something else comes along, games based on popular culture are forever doomed to that same inevitable irrelevance in history.

-Gooney

 

[Vortigar]

Gooney:
I beg to differ, Tetris, Pacman, Missile Command and Space Invaders are, like Solitaire, Patience and Rubik's Cube, exceedingly simple designs that could be replayed into virtual eternity.

The multiplayer aspect of Chess and Go makes all the difference in this one I'd say. Some iconic multiplayer games of this time are Starcraft, Super Street Fighter 2 Turbo and Unreal Tournament (99). These three are still played competetively until this very day, players not getting bored with their mechanics.

Another factor that weighs heavily in this kind of discussion is whether a game is mature. Go and Chess have had their depths plumbed for centuries. This is the reason I brought up the three above. All of them have (almost) ten years of digging under their belt allowing players to know the possibilities of these games in depth. Like Chess and Go, most of the competition within the games above is a dreary repetition of the same couple of tactics over and over. It is only through mistakes and oversights or weird gambits that situations mix up and a winner can really arise. This is only possible because of the deep understanding that has been built up about these games over the years.

You could make a mistake in Chess, but if your opponent doesn't know how to capitalize on it to its fullest extent this is no problem. Same goes for Street Fighter. Make a mistake against a noob and you lose a bit of healthbar yet are otherwise fine. Make a mistake against a good player and you'll lose half your lifebar and get cornerlocked, all but guaranteeing you'll lose the round (as a mistake in chess would also all but guarantee your loss).

Jason:
To answer your question of creating a single player game with the depth of Go. No, you can't create one. And none exists (on board or digital). The second player is required to create systems of simple rules that don't get exhausted after a while. You can however create computerized equivalents of Solitaire, Patience or Rubik's and they already exist in the guise of minesweeper, Missile Command and Tetris.

aside:
Of these SSF2T (or ST) is the only one that can truly be compared as, like Go and Chess it is a game of complete information (ie. you don't know what your opponent is doing off screen in Unreal).

aside 2:
WW2 has never stopped being relevant. It has a huge impact on everything we do. WW2 games are not an 'of late' phenomenon. Since Wolfenstein they never stopped coming out in one form or other. WW2 movies, though more popular sometimes, also continue to be made and it will be some time before that flood ends.

 

[gooneybird71]

Gooney:
I beg to differ, Tetris, Pacman, Missile Command and Space Invaders are, like Solitaire, Patience and Rubik's Cube, exceedingly simple designs that could be replayed into virtual eternity.

I still think thats too short of a perspective. The digital games are nothing like what they are being compared to (the analog meatwear games like Rubics Cube) , Space Invaders?!?! Have you tried playing that lately? PacMan?

I've got two kids, they are about the same age now that I was when Space Invaders came out, so last christmas I bought one of those little controllers that had 5 classic arcade games in it, just hook it up to the TV and its exactly the same thing that the original Arcade game was. The kids played it for a couple minutes then quickly turned it off to play Lego Star Wars on the PS2. Those old arcade games are only relevant to those of us who grew up with them, no one else is remotely interested in them, especially when given the choice of the modern culturally relevant games readily available today.

Just because a game is played for 10 or 20 years doesn't make it an enduring game. Chess and Go are enduring games the former on the order of thousands of years old and the later 500 years or so, these are games which have crossed cultural, national, and economic, and most importantly temporal boundaries. One could have conceivably played a game of Chess with Jeremy Bentham, or Abraham Lincoln.

No computer game ever made will endure in that way because of the technology required to play them.

Computer games are made as disposable entertainment, just like paper magazines, pulp fiction, tv series, and radio, indeed I believe film falls into this group too, time will tell (difference between technical innovation and temporal endurance).

Quit frankly I do not believe a computer game can achieve the enduring status that a game like Go or Chess has.

As for cultural relevance do not confuse cultural relevance with historical relevance, WW2 is very rapidly loosing its cultural relevance simply because the number of people who actually lived through it is shrinking drastically. In 10-20 years it will have the same cultural relevance as WW1 or The American Civil war does now. WW2 represents culturally a time of black and white views and good versus evil motivations, a time when the righteous was easy to see and the damnable obvious. Now I know that literally that is not true, it stands none the less in popular culture.

The WW2 era is rapidly becoming romanticized at least when compared to the relative complexity of the rapidly evolving global culture that we live in now.

-Gooney

 

[Vortigar]

Once again you're comparing Go and Chess to single player video games, something I highly disagree with. Those games have survived for so long because (or partly because) of the element of competition, which is why I mentioned UT, SF and SC. If you want to compare Tetris to something, you'll have to compare it to Solitaire or the like.

As for any computer game standing the test of time: Tetris has lasted so far. I admit the others I've mentioned haven't aged nearly as well, perhaps Missile Command.

Calling out on enduring games is a bit of a cheap shot won't you say? Can you imagine being able to talk to the guy who invented chess? Those are the days we are living in with video games, history is being created right here and now, what they remember of it in a century is not so easily discerned out of hand. I wonder how they viewed chess 500 yrs ago. It took almost 400 yrs for chess to become a competitive sport. Video games will be remembered, no doubt. But which ones will be remembered specifically?

Can you assure me now that in 300 years video games will not have crossed cultural, national and economic borders? I hate to be blunt. But they already have. Of course no president or something has played video game yet, but we're talking an industry that's only 30 yrs old. The previous minister of finance of Holland had a few pinball machines in his office btw (bit of a tangent, but games will get there is what I'm trying to say here).

I have faith in Tetris to last. A competitive 'standard' game has yet to be found though, most nowadays require too much specific knowledge to even play at a basic level. I say a video game will come along that will stake a claim among Chess and Go as a brain teasing challenge for the ages. You'll agree with me that it doesn't exist yet though I wager.

WW2 side thingy:
Yeah, historical relevance, not cultural. The second world war still reverberates a bit though. Here in Holland you will sometimes find young people calling Germans Nazi's, there's some primal hatred still felt here. It's definately getting less and less though. Attendance at the May 5th ceremonies (liberation day here) keep on dwindling over the years. We still invite the Canadians and Polish that liberated our little piece of Holland over though (their number is becoming less and less as well of course).

We're actually busy de-romanticizing the war over here, the realization that most of us quietly went along with the Germans is slowly creeping in. The Dutch resistance was a notably small group you see. Most films these days highlight this in some way or form (Zwartboek for instance). On another note, we have some pretty active neo-nazi's in the country as well.

ps.
Heh, normally I'm the nay-sayer in discussions like this

 

[shMerker]

To answer your question of creating a single player game with the depth of Go. No, you can't create one.

I think that depends on your definition of single player. If you take a strategy game and give the player an AI to play against all you're really doing is overlaying another set of rules over the game concerning how it will react to what the player does. If this AI is complex enough it could even generate the depth normally reserved for a human player on the other side of the board, but it would still be essentially the same as before, a new set of rules added on top of the game. If you were to define a computer capable of passing Turing's test (in the context of go that is) as a player then your assertion would be correct by definition. Any game as complex as playing go with a live opponent is automatically a multiplayer game.

 

[fepayton]

gooneybird71 quote:

No computer game ever made will endure in that way because of the technology required to play them.


Computer games require allot. They need rare earths, raw materials, a system of power and to be shielded from conductive materials and water. They are not as simple or robust as a chess set or a deck or cards. In this I see your point.

I have to disagree that an advanced technology will eventually fail to endure. I have two reasons for this:

First)
A computer is fast, not complex. Sure we can draw mind numbing 3D with blistering 6.1 surround at 72 fps, but these are not inherent to depth. In the same way CounterStrike resembles paint-ball, computers spend their energy of accessories to a game, whose rules are relatively simple. Gapping away from simple rules (a particularly bad and complex "gun game mod") does not encourage depth. The simple mechanic of run-shoot-get-flag, made for a good game, regardless of medium.

Second)
Technology provides the ability for expression. There are "timeless" movies. Movie technology is older and more rooted, but movies still require a great deal beyond the simple.

I think that your points about cultural reliance are good and a desirable trait in a timeless game. That said however, I think technologically bound mediums do not hamper rule sets and stories in their quest to become timeless cultural monoliths.


I don't mean to labor this point, but Jason's original article conjectured about what was possible and what could be done.

I see allot of people looking back on what has been done and what has been created. Go is well over 4000 years old. I'm sure it went through a few "patches" before it became what we think of as Go today. I'm almost certain that technology (mainly the ability to disseminate the printed word) has advanced the depth of Go and the fulfillment of play.

Long rant cut sort:
Just because it hasn't been done doesn't mean it CAN'T be done.

Examples include: the airplane, the round world, and going to the moon.

I sit firmly in the position that culturally significant computer games CAN exist.
My reservation is (from looking at the examples above) that the games that does it will be a leap forward for humankind.

 

[Veylon]

Let me thrown RPGs onto the fire here as profoundly non interactive games. Generally speaking, your only options are to either: 1) Win and go on with the plot OR 2) Die. Oh, there are sidequests, but they tend to be more like fiddling with your pen during a game of minesweeper than something that has to do with the game itself.

I guess what I'm looking for is a game that has the following:
1) Multiple choices/options/missions for the player.
2) NPCs with AI
3) Environments that change over time, depending on the heroes choices.
and, crucially
4) A Time factor

Imagine that you are asked to rid the country of a terrible dragon that goes on rampages. To kill it, you need some special sword. But, instead of doing something, you go on various missions like rescuing pets from the bottom of coal mines. Now, logically, various villages are going to get ravaged by the dragon, the countryside would be going up smoke, refugees everywhere, etc. But, if you concentrate on dealing with the dragon, those poor pets in the mines won't last forever either. On the other hand, maybe the dragon can be bargained with, delaying the rampage either temporarily or permanently. But if you save the country by bargaining, you won't be the Dragonslaying sort of hero that could lead the country, say against the Evil Empire. You might have to bargain with them, too.

My point is that the players choices should have consequence and cost. The plot should logically follow from what the player chooses to do. Also, the plot should follow from what the player doesn't choose to do. And no one can do everything. Leveling up should have a cost in terms of what isn't done. If you put off saving the princess from the Dragon to go grind, she might not be around later.

Of course, this kind of game doesn't lend itself to completion, in either a positive or negative sense. Maybe you can just spend the entire game leveling up and watch everything go to hell without you. Or maybe you are such an awesome player that you can go after the Evil Overlord right off the bat and kill him in the first hour. But does that really solve all the world's problems? Probably not.

 

[teknoarcanist]

As far as modern programming has been able to discern, there is no such thing as a 'true' random-value-generator. Every single one depends upon either an input by a user, a secret process, or both.
Let's imagine, for purposes of metaphor, that you're a programmer, and you've created a chess-playing AI.
Now when other people play against your AI, they treat it like another player: they move, it appears to respond intelligently, and if they're like me, it invariably beats them every time.
However when you, the programmer, sit down to play against your AI, an interesting thing occurs. You, in all your master-brain-glory, understand fully how your program functions. Where its moves appear seemingly random to others, to you they are perfectly predictable--as you understand the processes behind generating them. You know, with 100% certainty, that your program will respond with Y output, given X stimulus.
Because of this, you are not playing a multiplayer game so much as a complex single-player simulation.

Therefore we can conclude that randomness--or seeming randomness--is contingent upon the user's ignorance of its workings.

Given this, it seems entirely possible to design a game framework based on the following logic:
A) "Player" has pre-existing knowledge of "The Process"--how the "System" he is playing within will respond to his moves, given its laws.
B) The game begins. "Player" provides input.
C) The "System" interprets the "Player"'s input.
D) The "System" uses the "Player"'s input to generate a response, based on the manipulation of the given input's values by the rules of "The Process"
E) The "System" offers its response an output.
F) The "Player" responds--providing additional input. Return to B) and repeat.

Let's offer a comparison.

A) I sit Mr. Jones down. "Mr. Jones," I say, "every number you give will be added to the previous value and squared."
B) Mr. Jones says "Six."
C) I take Mr. Jones's Six and determine its relation to the prior value (in this case, 0).
D) I enact the process of adding and squaring; the pre-existing [0] plus Mr. Jones's [6], squared, results with [36].
E) I tell him as much.
F) Mr. Jones says "Four."
C) I take Mr. Jones's Four and add it to the existing 36.
D) I square the resulting [40] to get [1600]
etc etc

In this case, Mr. Jones has acted as a seed, providing input to a system which then uses it to generate values. Because he understands this, it is not random. If he didn't know the process before hand, it would appear random.

But here's the pivotal point: if he understood the process, but did not possess the faculties to anticipate it beyond a certain point, quasi-randomness is achieved.

Say "The Process" is to take the input, divide it in half, add it to the prior value, triple the result, and multiply that by ninety-three. Mr. Jones might puzzle out the result given a minute to think, but it's not something he could carry very far, or through very many iterations. He is only human.

Back to chess, we see a similar example. You may be able to guess at your opponent's next move, and even to think two or three moves into the future. But you do not possess the computational faculties to carry it, say, twenty moves ahead, as a chess-playing algorithm with a sufficient processor does.

In this way, it would be possible to generate a game system which relies upon input from the player, fed through a pre-determined and publicly-known process to create a result. The fact that the process is known allows it to be predicted by a strategic mind. However, the process's complexity precludes any human from doing this very far.

The only foreseeable problem is that this still leaves us with the Peg Solitaire dilemma--once you've beaten it, all you have to do is retrace your steps. Given that, some initial SOMETHING is needed to differentiate each game. The closest I can come to a real answer would be to procedurally generate the environment of a game--say, the shape of the Go board--based on its layout at the end of the last game. This is sort of a half-assed cop-out to the actual technical challenge you presented, but I think it could be conceded for practical purposes.

All in all though, this is one of the more interesting articles I've ever read on game-design theory, let alone on The Escapist. Finding the right way to respond (and then express that response in a way that makes sense) had been itching in the back of my mind for the past couple days now