Ex Situ Redux: Study Shows The Princess is in Another Castle 7/8ths of the Time

[Editor’s Note: This is a republish of an old Ex Situ which was part of a set, but I thought with my addendum that it deserved its own article.]

Yonder at The Minus World, there was a cleverly-conceived, confusingly both underwritten and overwritten, and woefully trying-too-hard-to-be-funny report about the frequency of Princess actualization. The original link seems to be dead, but here is a reprint:

New Haven, Connecticut – Profoundly sidetracked Yale scholars have been working feverishly to determe the statistical accuracy of finding the hypothetically kidnapped Mushroom Kingdom Princess in a castle. It has been agreed that 87.5% of the time, prospective rescuers will not happen upon the Princess and will instead hold a brief conversation with a fungus man who will inform them vaguely that her whereabouts are elsewhere. While probability and numerical accuracy have been officially cemented, researchers remain consistently baffled as to why she keeps getting yanked to begin with, or if the bitch is even worth it at this point.

Addendum: The calculation to find the Princess Probability isn’t even accurate. Taking into account the Warp Zones, there are  many different paths Mario might take during the course of the game, each with a different total probability of the Princess being in a castle, hereafter referred to as .

In World 1-2, there is a Warp Zone to Worlds 2-1, 3-1, and 4-1. In World 4-2, there are two Warp Zones, to 5-1, 6-1, 7-1, and 8-1 in toto. So let’s break the Mushroom Kingdom into two sets: A and B, where each possible path to get to World 4-2 is in A and each possible path to get from World 4-2 to the end of the game is in B.

Here is a chart enumerating each path in A, where an “X” indicates a completed castle, is the total number of completed castles for that path, and is the total number of Princesses being in a castle for that path:

Path	World 1	World 2	World 3	NC	NP	Notes
	X	X	X	3	0
		X	X	2	0	Warp from 1-2 to 2-1
			X	1	0	Warp from 1-2 to 3-1
				0	0	Warp from 1-2 to 4-1

And a similar chart for set B:

Path	World 4	World 5	World 6	World 7	World 8	NC	NP	Notes
	X	X	X	X	X	5	1
		X	X	X	X	4	1	Warp from 4-2 to 5-1
			X	X	X	3	1	Warp from 4-2 to 6-1
				X	X	2	1	Warp from 4-2 to 7-1
					X	1	1	Warp from 4-2 to 8-1

So the total number of paths possible is:

(which really is just )

To calculate the probability of The Princess being in another castle, , we can calculate and subtract it from 1 to give us:

is equal to the number of Princesses being in a castle in all possible paths, divided by the number of castles in all possible paths:

(Note that , since each possible total path results in 1 Princess being in a castle.)

So instead of  , the correct calculation is:

Furthermore, since each path has a probability of being taken and the total number of instances of a Princess being in another castle summed over all paths is , we can calculate the expected values for the number of times the Princess is in another castle and the number of Princesses being in a castle:

To summarize: on an average full game of Super Mario Bros., one should expect:

• The Princess to be in another castle about 78% of the time
• The Princess to be in another castle 3.5 times
• The Princess to be in a castle 1 time

We here at J. Cart. Overanal. feel this probabilistic description is far superior, assuming we didn’t screw up the math. Comments or complaints about wonky symbol useage are welcome below.

Darkwing Duck: Champion of the Free Market?

Contributed by J. W.

In Darkwing Duck Season 1, Episode 7 (“Dirty Money”) Darkwing is hired by a banker named J. Gander Hooter to find out who’s been removing the ink from the nation’s printed money. Showing Darkwing a stack of unprinted bills, Hooter presents an observation that subtly explains the core philosophy and flaw of the central banking system (i.e. the Federal Reserve): “This paper was once worth $10,000,” he says. “Now, without the ink, it’s worthless. Without printed money, the economy will self-destruct.” The episode never really returns to this point – in fact, the entire question of the missing ink goes largely ignored – but the fact that a children’s cartoon would even mention the economy’s self-destruction and the fact that printed money is essentially worthless paper makes it hard to believe that there’s not a greater metaphor at work in this episode.

Prior to hiring Darkwing Duck, J. Gander Hooter had hired an investigative firm called SHUSH, which is represented by a character named Agent Grizzlikof. Appropriately, Agent Grizzlikof is a bear with a Russian accent (a double layer of meaning, given that the Bear is the symbol of Russia). Throughout the episode, Grizzlikof demonstrates a Soviet’s penchant for excessive bureaucracy and an insistence that everything be done “by the book.” Before allowing Darkwing to take part in the investigation, for example, he demands that Darkwing become a member of SHUSH. This involves a lengthy application process that includes a physical obstacle course (Darkwing is literally made to jump through hoops) and a mountain of paperwork. Seeing the huge stack of papers before him (the D-11 Stroke 6 Destination Disclosure Form), Darkwing remarks that “This is worse than the obstacle course.” On cue, he is informed that “Those are just the forms for permission to fill out these forms,” at which point 7 or 8 new, even taller stacks of papers are brought to him on a forklift.

According to J. Gander Hooter, however, Grizzlikof’s methods of over-regulation have failed (a jab at the failure of Communism, perhaps?), which is why he’s hired Darkwing Duck to take over. In contrast to Grizzlikof (whom Darkwing describes as a “predictable paper-pusher”), Darkwing is praised for his “unpredictable methods,” as well as his “unique brand of logic and deduction.” It is perhaps no coincidence that “unpredictable” and “logic” are both buzzwords frequently used to describe the unregulated capitalist system idealized in libertarian/free market circles. As Dr. Robert Murphy writes in his Politically Incorrect Guide to Capitalism, “Aside from the ‘fact’ that it hurts the poor, the other major objection to capitalism is that it is allegedly chaotic [unpredictable]. After all, in a market economy no one is ‘in charge’ of car production, and it’s nobody’s job to make sure that enough newborn-sized diapers get made.”

The actual villain of the episode is a cleaning lady named Ammonia Pine (interesting that the villain is a worker, the central mythical figure of Marxist philosophy), who secretly works for the shadowy syndicate known as F.O.W.L. Her goal, unlike most cartoon villains, is not to steal a large sum of money, but to wage economic warfare. “With SHUSH off my tail and all the money scrubbed,” she cackles, “the banks will go down the drain like scum in a bathtub.” This dastardly scheme is championed by the High Command at F.O.W.L., with whom Ammonia Pine communicates via a small telecommunication device. Once the banks fail, they say, “Our economic experts will move in to mop up.” Towards the end of the episode, High Command reiterates this point, describing the manner in which they can “begin taking control of the banks and financial institutions.”

Thus, in a single cartoon we have a Russian bear whose mountains of regulation prove ineffective (Darkwing is only saved from Ammonia Pine’s giant vacuum cleaner when he tears Grizzlikof’s SHUSH manual into pieces and uses its pages to block the vacuum’s vent system); a villain who realizes that power comes from destroying (and then controlling) banks and financial institutions with the help of “economic experts”; and a hero whose greatest virtues are his lack of rules (i.e. he is unregulated) and his unpredictability. Sounds to me like two critiques of Communism (its bureaucracies and its thirst for economic control and power) and a wink at free-market capitalism. This is perhaps no surprise, given that Darkwing Duck first aired in 1991 when the Soviet Union was well on its way to collapse.