Saturday, October 17, 2009

Movies: I want to play a game, Part 2 – Hate the game, not the player.

To boil down everything we discussed in the previous post to its most essential point: If you were a victim in a Saw movie, the only salient survival factor that could be known, and therefore acted on, would be the number of players in your particular game. There are at least two other potential factors that could determine whether you survive or not, but they are unknowable prior to your death or escape and there's crap-all you can do about them. You're better off assuming that they aren't in play.

Once we've established the focus of our thought experiment on the number of players, we can divide the traps into two groups: 1) single- and two-player games and 2) games with three or more players.

At this point, the skeptical reader might well ask, "CRwM, why arbitrarily divide them into these two groups?"

Fair question. The reason I divided them into these two groups is that, after working through all this, I found that single- and two-player games essentially have the same strategy. Once you go above two players, though, there's a host of new issues that you have to take into account. However, because we haven't walked through the thought experiment together, that what I think is a natural division looks arbitrary from this point in the journey. Which is to say, lighten up Francis.

On to the survival strategy for single- and two-player games.

Let's get single player games out of the way because they're the simplest and least interesting.

A truly single player game is one in which only a sole person in the trap can affect the outcome of the game with their choices. The player could be the only person in the trap - examples of this include the web of razor wire web and the flammable slime traps from the first film and the fly-trap death mask from the second film – or they could be the sole decider in a trap that involves others – examples: Amanda's test, Jeff's various trials in Saw III, the hair-puller from Saw IV.

The strategy for a single player game is simple. Always play. You don't, you die. Arguably, there are reasons that somebody might choose to die. Many of the traps are disfiguring or involve profound psychological trauma. Though it never really happens in the flick, it isn't hard to imagine a game player deciding that the cost of escaping just isn't worth it. But, for the sake of this thought experiment, we decided to assume that every player wants live regardless of the costs.

So, if you're in a one-player Saw trap, assume it is well built, assume it is a valid game, choose to play along, and you will have done everything you could to live.

Told you it was simple.

Two-player games are a little more interesting. First, they rarely happen in Saw. There's only been two of them. Second, each of the games was a unique game type that demanded different strategies. Third, the characters in the first two-player game failed because they understood the form of the game they were playing but couldn't bring themselves to play, but the characters in the second game misunderstood the game and one of them still survived.

In the jargon, Jigsaw's two player games are either zero sum games or deadlock games. Because the term deadlock game is somewhat obscure and the term zero sum game has a common usage that doesn't fully jibe with the meaning of the term in game theory, we'll get some quick definitions out of the way.

In a zero sum game, the sum of wins (+1) and losses (-1) always come out to zero. If somebody wins, somebody else lost. In Sawian terms, it means that there are two players in a trap and only one of them can get out alive.

Jigsaw doesn't make many traps that are zero sum games. For all the bizarre radical individualism in his personal religion, Jigsaw's big on teaching lessons about interdependence and teamwork. However, he does occasionally build a zero sum game trap. Most notably, the bathroom trap that anchors the entire first film is a zero sum game. Dr. Lawrence and Adam get locked in the world's filthiest bathroom. The good doctor can only get out if he kills Adam. Failure to kill Adam means not only will he be screwed, but his family gets it as well. Adam is expected to saw his own foot off and escape, leaving the doc and his family high and dry. Basically, only one of them can win. It's built into the game.

In the film, both Adam and the doc bite it. They fully get that they are playing a zero sum game and are ultimately unable to play on those terms. The opt not to play – instead they try to work their way out of their predicament – and both end up dying.

Sadly, the only way to survive a zero sum game is to play before you get played. If, as we agreed to assume for this discussion, survival is your ultimate goal, then no matter what the other player chooses, you must choose to play.

The other type of two-player trap is the deadlock game. To explain a deadlock game we need to touch on dominant and dominated strategies. In simplest terms, a dominant strategy benefits you no matter what the other player chooses to do and a dominated strategy screws you no matter what the other player chooses to do. Not every game includes dominant and dominated strategies; but when they do, always play the dominant strategy and never play the dominated strategy. In a deadlock game, the dominant strategy also leads to the most mutually beneficial outcome. It's one of those happy cases where everybody following rational self-interest actually leads to the best result.

The best example of a deadlock game in the Saw franchise is the mausoleum trap at the beginning of Saw IV. This over elaborate trap works thusly: Player 1 and Player 2 a both connected by a neck shackle to chains that lead to an automated winding drum in the middle of the floor. The game begins when one of the players's movements trigger the winding action. The winding action pulls the two men closer together. Eventually, it will strangle them both. The key to player 2's neck shackle is connected to the back of player 1's collar. Once player 2 is free, he can get retrieve a key for player 1's collar. Player 1 has his eyes sewn shut and cannot see. Player 2 has his mouth sewn shut and cannot effectively communicate with player 1. Various stabby and slicey weapons are shattered about. This is a deadlock game. Both players can win if they both play the game correctly. There's no need for either one to die. In fact, doing the rationally self-interested thing means they both escape.

But we don't always do the rational and self-interested thing. In this case, the problem is that one of the players literally cannot see what the rationally self-interested action would be. Unable to communicate, player 2 can't explain to the blind player 1 what is going on. Assuming he is under attack by the trap maker, player 1 starts lashing out with stabby things left about the field o' play. Player 2 is eventually forced to fight and kill player 1. He frees himself and escapes.

There are two neat survival tip hidden in that mess. To really be a player in a game, you need to be able to make a genuine choice to play or not play. If, for some reason, you can't understand what it means to opt in or out, then you aren't really choosing to do either and you don't fit our definition of a player. That sounds bad, but it doesn't need to be. Think in terms of the mausoleum trap. If player 1 had simply not acted in any way, player 2 could have easily freed them both. What's the take home: Don't act like a player if you're not a player.

One of the most interesting things about the mausoleum trap is that it's a deadlock game that, if one of the players does not choose the dominant strategy, becomes a zero sum game. This curious shift in the mausoleum game is important; it provides us with the key (fittingly enough) to surviving games with three or more players. But, that's for the next entry. Let's recap.

ANTSS READER! You've just found yourself in a Jigsaw trap with one other person! What do you do!?!?!

First, determine the number of players in the game. You may need to decide that, for some reason or another, you are not actually a player in the game, but just another trapped person. That's cool, but act like what you are or you'll fuck everybody up.

Second, the players need to determine the actual rules of the game. If you can't complete this step, go back to step 1: Somebody thinks they're a player, but they aren't.

Third, no matter what your partner chooses, always, always, always choose to play.


Pauline said...

Arrgh! Now you've got me thinking. So, its research night aboard ship. SyFy (not Sci Fi or Skiffy) has "Saw" movies playing this evening. A pizza, a bottle of wine and Big Toe's thought process applied. We'll see.

CRwM said...

Pyrate Queen,

If you haven't read "The Invisible Hook" yet, it applies market theory and some of these concepts to pirates in the golden age of piracy. Good times. I recommend it.

Pauline said...

It is on my Yule list. No kidding!

Vardulon said...

Is the Zero Sum equation in Saw changed at all by the presence of Adam's key in the film's opening seconds? While that key would have opened just his own lock, couldn't the game have been survivable for both?

Although the key was unbelievable dumb, so maybe it just needs to be discounted.

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