Monty Hall Problem Revisited

After attempting to answer someone's supposed counterargument in the comments section to my earlier post, I realized that there's a better explanation of the Monty Hall Problem that will hopefully satisfy/silence the doubters. First, I'll restate the problem:

Monty Hall Problem

Of three doors, one is good. First, you select a door. Second, Monty Hall eliminates one of the doors for you - the door he eliminates is not the door you selected, and not the good door. Third, you have the option of keeping your original door, or changing to the only remaining door. What should you do?

SOLUTION

For the sake of this explanation, imagine that you play the game many times, and you always pick Door A, which means Monty will always have to eliminate either Door B or Door C. Every other aspect of the game is still fair and random, meaning that at the beginning of each game, Door A, Door B and Door C have an equal probability of being good.
Now let's consider the moment after you've selected Door A (because you always select Door A in this example) and Monty must eliminate Door B or Door C for you.

1. If Door B is good, he will eliminate Door C (1/3 of all occurences)
2. If Door C is good, he will eliminate Door B (1/3 of all occurences)
3. If Door A is good, Monty must choose whether to eliminate Door B or Door C. He does so with equal probability, so:

• If Door A is good, sometimes Monty eliminates Door C (1/6 of all occurences)
• If Door A is good, sometimes Monty eliminates Door B (1/6 of all occurences)

In 1/2 of all the games you play, Monty eliminates Door C (1/2 = 1/3 + 1/6) and you must then choose between Door A and Door B:
That means that for every 6 times you play the game, you'll have to choose between Door A and Door B 3 times. Of those 3 times, 2 of them will occur because Door B was the good door, and 1 of them will occur because Door A was the good door and Monty randomly eliminated Door C.

And the other 1/2 of the time (3 of every 6 games) you find yourself left with a choice between Door A and Door C, and it's twice as likely that Door C is the good door:
In either event, your chances are better if you change your original selection.

Superman Depantsed

My favorite free video podcast on iTunes is the Vintage ToonCast, which features an assortment of excellent old cartoons. Among them are 13 of the 17 original Superman cartoons made by Fleischer studios (Popeye, Betty Boop) in the early 1940s. Some stray thoughts/observations/reasons why you should watch them:

• The narrative is as reliably formulaic as later Scooby Doo cartoons, if not exactly as fill-in-the-blank simple: The villains announce/begin their dastardly activities, Clark and Lois investigate, Lois manages to get into harm's way (often as she edges out Clark for access to the story), Clark sneaks away and Superman appears, he struggles briefly but ultimately defeats the villains with ease, Lois and Clark share brief dialogue that demonstrates Lois is still unaware of Clark's other identity.
• This is all punctuated by the oft-repeated theme music, which has the effect of emphasizing how quickly everything gets resolved in the 8-minute episodes, reassuring you that everything is very alright, or will be alright again very soon. It plays over the opening credits, again 30 seconds later when Superman's character is introduced at the end of the prologue, again around the 5 minute mark when Superman first appears, occasionally repeats as he strikes successful blows against the villains, again as he finally defeats the villains, and continues through the epilogue to the end of the episode.
• Dialogue takes a back seat to the very impressive artwork in these shorts. After the expository first act, the rest of the story is told almost entirely in pictures, and all human movements are animated realistically and without exaggeration, (using Fleischer's technique of rotoscoping). My favorite example of this is when we see Superman's shadow or silhuette removing his Clark clothes, as shown in the screen capture above, and often bending over and raising his knees as he takes off his pants. Here are six more such screen captures:

• What little dialogue there is is also unexaggerated. I love the Clark actor's flat reading of the line "This is/looks like a job for Superman". At least once he adds a slight hint of emphasis to the word "is".
• I'm no comic book expert, and I don't know in which of the many Superman incarnations they first suggested any romantic tension between Lois and Clark, but the only tension here is professional, as Lois selfishlessly works to gain sole access to each story, shutting out Clark in the process.
• One of the themes among the cartoons available on this podcast is the surprisingly insensitive/offensive racial caricatures that were common in eras past, responsible for most if not all of the episodes' "EXPLICIT" tags. Several of the Superman cartoons pit our hero against WWII enemies (and one African tribal cult under Nazi control), but the artwork, voices and plotlines are extremely tame and respectful when compared to some of the cartoons featuring Bugs Bunny and others.

I also highly recommend several of the other cartoons on the Vintage ToonCast. I haven't watched all of them yet, but for now I'll suggest these:

• All of the Betty Boop cartoons (#5-10, some unnumbered). I'd never seen one before and was pleasantly surprised, especially by some of the trippy graphics in Snow White (#6) and Minnie the Moocher (#10). Watch them for the Cab Calloway music alone.
  
• The famed "Duck and Cover" video (#36).
• Any or all of the "Private SNAFU" cartoons (#26-28, some unnumbered), depicting a foolhardy soldier, voiced by Mel Blanc (Bugs Bunny), who demonstrates how not to serve your country.
• "Mr. Finley's Feelings" (#54). Cartoon about a person with rage issues done in an interesting tone. Note the use of 1st person perspective, and see if you can spot at least one curious moment (not the flashback) where they violate it.
• "The Trip" (#51). Happy bicentennial America! Let's celebrate with eye candy for the drug enthusiast!
• "Going Places" (#57). Explaining and championing the profit motive (lest you find yourself tempted by communism).
• "The Early Worm Gets the Bird" (#16). Not necessarily the most offensive of the episodes featured on this podcast, but definitely the most thorough exploration of a racial caricature.
• "Fresh Hare" (#1). A surprising and absolutely unnecessary ending to a Bugs Bunny toon.