Learning to Cheat Without Breaking the Rules, Part 2: Frameworks for Cheating

Posted on December 24, 2011 by metatim

For the same reason as in Part 1, these posts are illustrated using the Hand of Fate: Comic Strip Playing Cards by Karen Rubins.

In the first part I explained how a sequence of games taught me to become comfortable with bluffing and even lying outright, from a position of not being able to do either. That’s simple. The harder question is this: what kind of games can teach you to bend or break rules?

To tackle that, we should probably step back and ask how games teach us anything. And to tackle that, we should probably make sure we have a working definition for a game.

Here’s one provided by Greg Costikyan (emphasis added):

A game is a form of art in which participants, termed players, make decisions in order to manage resources through game tokens in the pursuit of a goal.

Yes, something like that. From there it seems clear that playing with decisions in a game is how we learn. So the question becomes instead: what kind of game could let us play with the decision of whether or not to break rules?

Form or Content?

I don’t know of one, but I imagine you could make a game about cheating (in the rule-breaking sense, not just bluffing or lying). Perhaps players take the role of political factions within a Kafkaesque bureaucracy, with in-game costs and benefits for following or breaking in-game rules. Or it’s Moon colonists with competing sets of societal rules, struggling for domination while following or breaking the rule sets of the competing factions. Or, I wonder, do football simulations these days give you the option of going for a risky tackle, knowing that you risk a red card if it goes badly? I don’t know, but they certainly could.

But in the process of abstracting away the costs and benefits of cheating, it feels as if something gets lost. Just as making decisions in poker has a very different feel when real money is on the table, a game with a cheating theme seems far removed from the potential power of a game that is about cheating the very rules of the game itself.

So we want a game whose rules somehow give players interesting decisions to make regarding whether or not to follow those rules, which sounds like an almost Gödelian paradox. So let’s take a step to one side and look at exactly what it is that drives whether or not rules are followed in a game.

Game frameworks for cheating

There are two key dimensions to consider here, I think:

1) Do people play the game to win, or do they play it for fun? Perhaps more accurately, does the pleasure come from winning – or striving to do so – or just from taking part? There’s a spectrum here, of course, and players of the same game could be at different points along it. For the sake of simplicity we’ll assume it’s binary.

2) How are the rules enforced in the game?

  • By design. In video games this is simple: the game should only let you do what you are allowed to do. Other kinds of games can also facilitate enforcement by their design – for example, playing a piece in Connect 4 makes a distinctive noise, so it’s hard to secretly take an extra turn if your opponent is briefly distracted.
  • By the other players. In most well-defined tabletop or party games, it’s understood that the players are watching each other to ensure they all play by the rules.
  • By a moderator. Generally speaking, if a game can’t work with either of the above approaches, it resorts to some kind of moderator who enforces the rules.

Let’s take a look at how cheating works across the 6 kinds of game this framework implies, and in particular whether choosing to bend or break rules is an interesting* choice for the players to make.

I should probably define ‘interesting’ here. Let’s say that an interesting choice is somewhat balanced (one choice is not obviously better than another), not damaging to longer-term goals, and is fun. And then let’s not try to define ‘fun’ or we’ll be here all day.


Games Played to Win

Play to Win, Design enforced (e.g. PvP video games)
The rules are enforced by the design of the game. As a corollary, anything you can do ought to be allowed, since cheating is theoretically impossible. In reality, it’s not that simple.

A reasonably notorious example is ‘snaking’ in Mario Kart DS. By performing a particular manoeuvre when cornering you get a speed boost. For certain karts, you could perform this manoeuvre almost continuously, alternating left and right – ‘snaking’ – and you could gain more from those speed boosts than you lost by taking a wiggling route. This takes some skill and practice, which makes the benefit seem fair. And since it’s possible in the game, it should be permissible, even if it’s not clear it was the designers’ original intent.

In practice, however, snaking gives such a big advantage that a player that does it will almost always beat a player that doesn’t, no matter how skilled. People are playing to win – that’s what usually makes a race fun – but if even one player is snaking, anyone that can’t snake can’t win, and so, implicitly, can’t have fun. For that reason, the London DS meetup group I played with had a no-snaking rule, and I see on the internet that other groups did as well. Snaking was considered a kind of cheating, and nobody would want to play with you. So no-snaking becomes an informal rule, and this becomes effectively the same as Player Enforced Play to Win.

(You can dive much further into this topic with Sirlin’s “Playing to win” archives)

Play to Win, Player enforced (e.g. Chess or Go)
As noted by Kirk Battle in this Kill Screen article, players can apply a certain level of flexibility to how rules are enforced in a game like Magic: The Gathering, and get a better game as a result. But this is not a situation in which such ‘cheating’ represents an interesting choice.

In it’s more blatant form, cheating in these games will always be considered bad form, and if discovered can have bad social and future gaming consequences. Chess or Go (when played without an audience) fall into this category. A player would only choose to cheat if they thought the short-term advantage would outweigh the risk of long-term negative consequences if they were found out. That’s not a very interesting choice either, according to the criteria above.

Play to Win, Moderator enforced (e.g. Football, Tennis)
Cheating outside of the moderator’s sight gives an advantage, and can’t be stopped in this system. You’re playing to win, and if you don’t exploit this fact, maybe the other guys will.

We see this in competitive sports like football or tennis, and it seems to be (I say this as an outsider) a key part of the entertainment: arguing about whether something counts as a foul, which side of the line the ball bounced on, and in general whether or not the moderator’s decisions are accurate.

Does this mean there’s some scope here for a game that could teach us about cheating? It seems close, but if people are playing to win, it gets dangerous – some degree of violence attempted outside of the moderator’s views seems likely, so I’m going to disqualify this on the grounds of encouraging non-fun behaviour.

Games Played for Fun

Play for Fun, Design enforced (e.g. Endless MMOs)
If you (and everyone else) is playing for fun, things change. If something is possible, and makes for more fun, few can blame you. If you were (somehow) playing Mario Kart just for fun, and through a streak of bad luck found yourself in dead last by some margin, perhaps it would be okay to snake your way to 7th place – that would be more fun for all concerned.

In Kingdom of Loathing, a kind-of MMO in which fun is primarily derived from exploration, an ‘exploit’ was discovered to generate more meat (the game’s currency). Who could resist such an exploit? Why resist it? Could you really begrudge those that used it?

In the case of online games like this, the rules are enforced by design, but there’s also some moderation in the form of game updates and code changes in response to things like this. In this particular case, the exploit effectively crashed the game’s economy, which impacts everyone’s ability to have fun. (Brilliantly, this was fixed with the addition of some entertaining currency sinks, rather than some kind of hard rollback).

So cheating is kind of interesting here, but again becomes more about player- and moderator-enforcement, so strictly speaking this category is ruled out.

Play for Fun, Player enforced (e.g. Mornington Crescent, DDR)
At this point, what constitutes ‘cheating’ is massively dependent on the players: having fun is more important than the rules. We’re right on the edge of what constitutes a game here and it’s an area I think most adults struggle to give themselves permission to enter. The most well-known example I can think of in this category is Mornington Crescent.

Less directly, this arises in Dance Dance Revolution (aka Dancing Stage), in which (for the benefit of the one person reading this that doesn’t know) players must step on specific directional arrows in time to the music. On the arcade machines, a raised bar is supplied behind the player, ostensibly to prevent anyone from falling off the dancing platform backwards. At a high level of gameplay, working out how to shift your bodyweight between feet while meeting a high-speed series of instructions is part of the challenge. However, some players realised they could lean their weight back on the bar and tap away with their feet without worrying about this issue; this also uses less energy. Is this cheating? As could be expected, that depends on who is playing.

In both of these cases, the decision of whether or not to cheat tends to have very little riding on it, so is unlikely to be interesting.

Play for Fun, Moderator enforced (e.g. Schooner or Later)
The Moderator’s role is to ensure people have fun, arguably as a higher priority than ensuring that people follow the rules. In this context, you might ‘cheat’ but do so with the moderator’s implicit or explicit blessing; or you might try to cheat by hiding your action from or misleading the moderator, and since people are only playing for fun this shouldn’t lead to anything particularly harmful. With the right set of incentives and approach by the moderator(s), this could well provide a framework in which a decision to cheat is actually interesting.

In conclusion, returning to our grid of possible games, here’s what the options for learning to cheat look like in each:

This final category is where The Haberdashery’s Schooner or Later comes in, the game that led me to cheat in a manner that could only be described as brazen, and shocked me into this whole line of thinking. I’ll describe how exactly that came about in the third and final part of this series.

Tim Mannveille tweets as @metatim, and has previously not cheated in order to earn stickers he made up at the Edinburgh International Film Festival.

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Learning to Cheat Without Breaking the Rules, Part 1: Games about Lying

Posted on November 3, 2011 by metatim

For no particular reason, these posts are illustrated using the Hand of Fate: Comic Strip Playing Cards by Karen Rubins.

At the recent Sandpit event at the National Maritime Museum, I played a game called Schooner or Later by The Haberdashery. A good game begets stories. This one begat many. In my case, it led me to an act of betrayal I didn’t even realise I was capable of. But to understand that, you need some back story.

As a child growing up in the late 80′s / early 90′s, TV shows like ‘Allo ‘Allo, Dad’s Army, and Frasier taught me that you should never lie, because if you do, you will be forced to lie about the lie in ever larger ways, people start opening doors at unexpected times and asking you ever more difficult questions, and, inevitably, hilarity ensues at your own expense, and then you have to admit that you forgot their birthday / ruined the dinner / taught the parrot to swear.

In some part due to these chilling fables, I grew up determined to always tell the truth and to be totally trustworthy. But that turns out to be impossible. So this is the story of how games taught me to get comfortable with that.

Cheat
In the card game Cheat, players take it in turns to lay groups of cards from their hand face down while declaring what those cards are. The following player can instead choose to call ‘cheat’ on the previous player, in which case the cards are checked, and the loser picks up the cards played so far. There is a restriction: you can only lay down cards (or claim to do so) that are adjacent to the most recent set played, so 2′s or 4′s can be played on 3′s, and so on.

While I understood what the game was about, I literally could not bring myself to ‘cheat’, even though it was part of the rules. If I ever found myself in a situation in which I had no valid cards to play, I would always choose to call ‘cheat’ on the most recent player rather than bluff myself. After all, if I started lying, people might start bursting out of doors and asking how the dinner was going, or something. Needless to say, I didn’t tend to do very well. But I felt as if I was playing honourably, and hilarity would certainly never ensue at my expense.

Extreme Cheat
On a sixth form school trip, we played a variant: instead of being restricted to cards adjacent to those most recently played, players could only ever play (or claim to play) 2′s. We played with two decks, and jokers were wild, so there were twelve 2′s in play, but nonetheless it was abundantly clear that players would have to cheat most of the time just to get anywhere. My never-cheat strategy was clearly going to backfire very badly here.

But something very interesting happened. One player, let’s call him Zippy, put down eight cards and said “Four 2′s”. The next player, who I’ll call George, called ‘cheat’, and turned over the top four cards, which turned out to be 2′s. George accepted his fate and picked up the whole pile.

I looked around at the other players – about eight of us. Almost everyone else seemed to know what Zippy had got away with, and nobody said anything about it. The game was called ‘Cheat’, after all, and apparently that meant that actual cheating was fine. With the bar raised in this way, I no longer had a problem claiming to play 2′s every time – but I never “really” cheated like Zippy did (or like others did later, by hiding some of their cards when no one was looking). Still, I had crossed an important threshold.

Poker (Texas Hold ‘em)
On that same sixth-form trip I played my first game of Texas Hold ‘Em, betting with monopoly money. I had a good feel for the probabilities, and with a little luck actually made it all the way to the showdown – me and one other guy, a guy who knew how to play poker properly. Whenever I had good cards he somehow knew it and folded. Whenever we were both in the pot he would win. I rapidly lost my remaining stake. I was playing half the game he was.

A few years passed and I next played Texas Hold ‘em at university for £1 stakes. The lesson had sunk in. I understood that everyone else playing understood that what you bid was only partially related to what you had; it also related to the impression you wanted to create about your hand, and even yourself as a player – perhaps you were trying to build a reputation as a certain kind of player that would influence your success much later in the game, or even a later game with the same players.

But here was the crucial part – you can always fold. I could ‘play’ with bluffing as much as I liked, but if it ever looked like I was going to be found out I could fold and no one would know I had ‘lied’ about my hand. Again, I didn’t do that well, but I got comfortable with the idea of bluffing – especially on those rare occasions when everyone folded and I took the pot with a losing hand, and somehow people failed to start appearing out of doors asking those difficult questions. It turns out that real life is not a sitcom.

The Turn
Around this time, I had an epiphany. I wanted to be 100% honest and 100% trustworthy. Then I realised that this was impossible. To be trustworthy, you have to be able to lie. If one person trusts you to keep something secret (“Don’t tell him we were talking about his surprise party”), and another person asks direct questions about it (“What were you guys talking about?”), at some point you will have to either lie or betray that trust.

Really, my sitcom training should have taught me this. ‘Allo ‘Allo has just about the most obvious example you could think of where lying is justified: resisting Nazi occupation! And if it’s legitimate there, then maybe it could also be the right thing to do in less extreme situations.

After some consideration I decided to go with being trustworthy, which meant I had better learn to get comfortable with lying.

Werewolf
In Werewolf (and its variants), players are secretly either villagers or werewolves. In the night phase werewolves secretly choose a villager to “kill” – to take out of the game. In the day phase, everyone argues about who they think is a werewolf, and they choose someone to lynch (take out of the game) on that basis. The phases and player killings continue until only villagers or werewolves remain.

Arguably even more so than Cheat, this is a game which depends on lying. The werewolves must claim to be villagers during the day phase to avoid being lynched, otherwise the game falls apart. It’s also a step up from poker when it comes to being perceived as a liar: instead of hiding behind folded cards, at the end of the game all will be revealed. Hilarity may well ensue.

In this context, with my training in Cheat and Poker, and thanks to my earlier epiphany, I finally realised I was willing and able to lie when necessary, and even got moderately capable at it.

I learned I needed to lie, and games gave me the opportunity to learn how.

But by a similar token, I could understand that sometimes in life you might have to break “the rules”. Clearly games can be designed around the idea of lying. What kind of game can actually teach you to cheat, or at least encourage you to bend the rules?

That’s what I’ll take a look at in the next post.

Tim Mannveille tweets as @metatim, and has previously written about Sandpit game experiences and a game based on cheese sandwiches.

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A Game Based on Cheese Sandwiches

Posted on August 8, 2011 by metatim

After being blown away by a Sandpit event in 2009, getting very competitive at Time*Trails at the 2010 Hide&Seek Weekender as team Fruitbat, and having all sorts of weird and wonderful experiences at other Hide&Seek events, it was time to give something back.

That something was Competitive Sandwich Making, at the Seaside-themed Sandpit on August 4th 2011:

With a table layout like that, it’s pretty clear what the game is about: tessellation. Before the games had officially started, a group of players liked what they saw, and we figured we might as well kick things off a little early (you can see the queue to register in the background):

The Rules in brief:
Every 15 seconds, all 4 players simultaneously choose a cheese piece, and add it to either of their bread slices. The winner is the player that manages to tessellate the most cheese on their slices, with no overlap or overhang. (For the purposes of scoring, the pieces have their area written on the reverse side, hence the calculators).

Over the previous couple of weeks we’d had some excellent feedback from play-testers, and had resisted the many temptations to make the game more complicated, so on the night it all ran very smoothly (although you apparently can’t emphasise enough that pieces can be turned over).

It became obvious very early on that people who liked the game, really liked it. We had learned from our earlier Time*Trails experience that people like ‘achievement’ stickers (us included), so we created two types:

The winner of any 4-player round got to be a Big Cheese, and we let them know that if they won a game against 3 other Big Cheeses, they would earn the title Earl of Sandwich.

We considered setting a time towards the end of the evening for the Big Cheeses to reconvene for such a match, but this didn’t seem in the spirit of a drop-in game, and would clash with the final scheduled games in any case, so instead we just hoped that it would happen organically. Brilliantly, it did: just before 10pm, four Big Cheeses came back to play, and we had our first Earl of Sandwich:

The 1st Earl of Sandwich (second from right), and other Big Cheeses

As the other games came to an end, and after the excitement of the Big Cheese face-off, we started to gather a crowd. We figured we could quickly run a couple more qualifiers…

… then have one final Cheese off, to crown the 2nd Earl of Sandwich (who also achieved the highest in-competition score of 95):

The 2nd Earl of Sandwich and current high score holder (second from left), and other Big Cheeses

In Conclusion
People that liked tessellating seemed to really enjoy the game, playing it repeatedly and coming back for more later. People that didn’t like tessellating could see what the game was about from afar, and avoided it accordingly (we saw them!).

There is an important caveat to this, however. The tessellation challenge was designed to be approximate: sharp-edged cheese on rounded bread slices, not to mention that half the pieces were based on squares and half on rectangles, leading to slightly incompatible angles. While this seemed to encourage an addictive attitude of “I could do better if I had one more try” at the Sandpit, when I later tried the game out with some post-grad mathematicians, there was noticeably less appetitie for imperfection.

So to extrapolate and exaggerate:

If you like tessellation, you’ll love this game. If you love tessellation, you won’t.

If We Did It Again, We Would…
1) Bring a better camera (these were taken with a mobile and had some Photoshop work to fix them up)
2) Take notes!
3) Improve the ratio of instruction time to playing time, which ended up being 50:50 as the game is quite short; perhaps by covering a few basics and then explaining the rest as the first game played out, as there’s quite a lot of quiet time during the first few rounds.

- Tim Mannveille & Clare Huxley

Epilogue
One of us (Tim) got to play Ordnungswissenschaft, compellingly categorised as involving:

Movement, strategy, timing, Brechtian despair

When I later tried to look up quite what ‘Brechtian despair’ might be, I found it in the same paragraph as a reference to cheese sandwiches. Clearly, this means something.

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Inception Diagram and Explanation (spoilers, obviously)

Posted on December 13, 2010 by metatim

If you’ve somehow found yourself looking at this page but actually want to avoid Spoilers for Inception, you should leave now.

Right.

People are posting Inception Theories all over the internet, but even the ones that agree with me aren’t explaining it properly. So naturally I’m here to try to put that right.

Of the major categories of theories out there, my preferred interpretation of the film is this: Mal Was Right. More specifically, at Mal’s external direction, Saito incepts Cobb to believe he must wake up, and Ariadne purges him of his demons. Here’s a diagram that shows what I think the underlying setup actually is (click for full size):

I’ll first explain what’s happening in that diagram, and then explain as briefly as possible why I think that’s the case, closely referencing lines in the film at each point.

The Diagram

Prior to the moment shown here, the flashbacks seen in the film took place. Mal (Marion Cotillard) and Cobb (Leonardo DiCaprio) went into limbo, Cobb incepted Mal so she would want to wake up, which she did first by joining Cobb on the train tracks in limbo and then by jumping from the building after failing to convince Cobb they were still dreaming. She thus reaches the top level of the diagram.

Cobb remains in a nested dream. In that level, he believes Mal is dead, blames himself, and although he wants to get back to his kids he’s punishing himself for what happened. At the same time, he is haunted by his subconscious projection of the pre-incepted Mal, who just wants him to hang out with her in limbo forever.

At the top level, Mal realises that Cobb is effectively in danger, as he could potentially be drawn back into limbo and lose his mind. She calls Miles (Michael Caine) for help; Miles brings Saito (Ken Watanabe) and also realises the character we know as Ariadne (Ellen Page) might be able to help. They formulate a plan to incept Cobb so that he will wake up.

The Reasoning

When interpreting a film like Inception, a good guideline is to try to take as much of the film as possible at face value. The more of it it you treat as being a misrepresentation, the more interpretations become possible, and things quickly get out of hand.

The following is based on notes I took while watching the film for a second time, so while the dialogue may not be word-perfect the sequence of events and key lines are accurate.

The Setup

The first scene to note is in the helicopter, when Saito requests that Cobb perform an inception. Cobb asks for a guarantee, but Saito has no way to prove he can and will arrange for Cobb to go home. His final plea to Cobb is interesting:

Saito: Do you want to take a leap of faith, or become an old man, filled with regret, waiting to die alone?

Cobb seems to be moved by this, and ultimately agrees.

The next scene to note is when Cobb visits Miles, where the following exchange takes place:

Miles: Come back to reality Cobb… please.
Cobb: This last job, that’s how I get there.

That’s top-level Miles, creating the subconsious idea that after this job, Cobb can come back to ‘reality’.

Miles then arranges for Ariadne to join the team. As they begin to train her, Ariadne investigates Cobb. At one point he is connected to the dream machine alone and she joins him, to discover that he is attempting to lock away the projection of Mal, but evidently can’t resist going back to her. She presses upon him the idea that this won’t be enough:

Ariadne: You’re trying to keep her alive, aren’t you? You can’t just create a prison of memories to hold her in. Do you really think that could contain her?

Once the inception begins, Saito is shot, and it is explained that under their heavy sedation death will put you into limbo, where time passes much faster and you can effectively lose your mind. At this point there is a reprise of the earlier dialogue as Cobb expresses concern that Saito will fall into limbo and forget their arrangement, but Saito reassures him:

Saito: I will still honour our arrangement
Cobb: No, you will be an old man
Saito: Filled with regret…
Cobb (seemingly unsure of why he is saying this): … waiting to die alone.
Saito: No, I will come back, and we will be young men again.

The Missing Scene

Later, Ariadne pushes Cobb for more detail on what happened in the past, and we are given a more detailed flashback. He explains how he planted the idea that they were not awake, and this idea remained with her even after they both escaped limbo by lying on the train tracks.

Mal is seen at a chopping board, toying idly with the spinning top in her left hand. At this point, one particular scene is conspicuous by its absence. We know Mal uses the top to determine if she is still in a dream. The natural thing to do would be to spin the top, but we are not shown this happening.

We can infer what must have happened. If the top had kept spinning, Cobb would have been forced to admit she was right; therefore, it must have stopped. Why was this not enough to convince her? The clue is in this piece of dialogue:

Cobb: If this is a dream, why can’t I change anything?
Mal: Because you don’t know you’re dreaming.

Mal’s hypothesis would appear to be that as the dreamer, Cobb shapes the world to his own assumptions – he doesn’t think he can change anything, so nothing changes; he doesn’t believe they’re dreaming, so the top falls. (This idea is also endorsed by Saito’s line from near the beginning: “In my dream we play by my rules.”)

While this might seem a bit of a reach, we can also infer that the use of totems, invented by Mal, changed after this point. It instead became about the heft of the object, and rules about others touching the object were introduced. Cobb learned from the mistake of using the top.

(We might also ask why such a scene wasn’t shown. My guess is that showing Mal make this argument in any more detail would lend too much weight to the “It’s a dream” interpretation at the end; it would also risk alienating the audience seeing it for the first time, for whom the top is a key navigational aid).

The Final Setup

Finally in the flashback we see Mal’s apparent suicide, where she asks Cobb to make a leap of faith. Now we understand something strange is happening – Saito echoed this line in the helicopter, then associated with it the risk of becoming an old man, filled with regret, waiting to die alone.

If Mal was right, and her suicide woke her up, then the situation depicted in the diagram arises. The best way for her to get Cobb to wake up is to incept him, just as he did to her. But this would be difficult, because he knows how it is done. We’re also told the mark for an inception must believe they came up with the idea themself. As we’ll see, this is exactly what happens.

At the close of this interlude, Ariadne lays out exactly what Cobb has to do in order to move on:

Ariadne: Your guilt is what powers her. If we are to succeed you have to forgive yourself, and confront her

After the apparent failure at the snow fortress, it’s Ariadne who proposes they enter limbo to bring back Fischer. There they confront Cobb’s projection of Mal. Guided by what Ariadne has said earlier, and helped by Ariadne in the moment, Cobb finally rejects her:

Mal: We can still be together… right here.
Ariadne: You can’t stay here to be with her!
Cobb: I’m not. [...] I can’t stay with her any more because she doesn’t exist.

The Inception

Ariadne and Fischer kick out of limbo, leaving Cobb to bring back Saito in a climactic scene given special emphasis by being introduced at the very start of the movie. Here, the inception takes place: Cobb echoes the lines he has been primed with, convinced that it is his own idea that he and Saito are not really awake, while actually delivering exactly the message the real Mal wants him to receive (full dialogue taken from IMDb):

Saito: So have you come to kill me? I’ve been waiting for someone to come for me…
Cobb: Someone from a half remembered dream…
Saito: Cobb? Impossible – He and I were young men together, now I’m an old man.
Cobb: Filled with regret…
Saito: Waiting to die alone…
Cobb: I’ve come back to remind you of something… something you once knew…
[the camera dwells on the still spinning top]
Cobb: that this world isn’t real…
Saito: To convince me to honor the arrangement.
Cobb: To take a leap of faith, yes. Come back, and we’ll be young men together again. Come back to me…
[Saito reaches for the gun]
Cobb: Come back…

As Cobb delivers these lines, he looks confused, as if he’s not sure where they are coming from. He has been incepted.

The plan as originally stated seems to be complete, and Cobb returns to his kids. He spins the top, but does not wait to see what happens to it. It’s apparent that at least the first result of his experience is that he is no longer concerned with which world he is in; having forgiven himself and let go of his regrets, he allows himself this moment of happiness.

If the inception worked, it’s possible over time he will come to believe that Mal was right after all, ultimately committing suicide. On the other hand, thanks to Ariadne guiding him to reject the temptation of his projection of Mal, he’s no longer in danger of falling prey to limbo. As such, even if the inception doesn’t work, eventually enough time may pass that he will simply wake up when the dream comes to an end naturally.

Bonus Points

The idea built up in Cobb’s mind is that if he does not escape the dream, he will become an old man filled with regret. It’s interesting that the song chosen to signal the end of a dream is “Je ne regrette rien” / “I regret nothing”, associating waking up with having no regrets.

Even under a more straightforward interpretation of the film, Ariadne is very mysterious. Aside from having an obviously fitting name for someone that will lead Cobb out of the labyrinth, Cobb observes that he has “Never seen anyone pick [dream architecture] up so quickly”; she’s also aware of the plan while in the dream, despite the fact that Cobb later says to Fischer (possibly as misdirection) that to do so takes “years of training”. Her active part in investigating and then purging Cobb’s hangups is also particularly obvious on a second viewing.

Finally, a nice line which is by no means definitive, but still gives you pause if you’re thinking along these lines at the time you hear it:

Cobb (on the phone to his kids): Mommy’s not here any more.
Child: Where?

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