## Wrap Your Brain Around Monty Hall

Monty Hall

I have always been amused and intrigued by responses to “The Monty Hall Problem”, especially when I talk about it to audiences with a high concentration of engineers and mathematicians. If you are familiar with it, but you’ve always struggled with an unsettled feeling of “this can’t be right”, read further and let me know if my explanation of the solution helps to alleviate the discomfort. If you are not familiar, I guarantee you will give your brain a workout by reading on.

First posed to statisticians in 1975, “The Monty Hall Problem” is well-known among academics because it still sparks debate. Many seem to think that disagreements about its solution stem from issues in the clarity of the problem, but I contend that it really stems from human flaws in the way that we process information.

I often discuss this problem in statistics and cognitive psychology courses for several reasons. It is a great exercise in probability calculation and it can be used to teach basic mathematical modeling (and its purpose). An added benefit, since almost all of my students were psychology majors, is that it also illustrates a flaw in human cognition as well as a pattern of problem solving.  Even a knowledgeable statistician feels the need to run simulations to see the solution in action. Even then, fully grasping the mechanisms behind the answer often requires brute force cognition.

In general, human beings have a very difficult time wrapping their brains around concepts of probability. It is much like a visual illusion; we know that the lines are parallel/the circles are the same size/there is no motion, but we can’t make our brains process it in a way that represents that reality. It’s just not how our visual system works. I hypothesize that one of the reasons that probability is such a difficult field for most people is that it involves theory and models, which are distinct from observations and we must represent them differently in our minds to properly deal with them. Applications of probability often involve switching gears from the realm of models to data or vice versa and this is where I think most mathematicians get side-swiped in The Monty Hall Problem.

### The Poser

In essence, here’s the problem:

## Well, Slap Me with a Squirrel!

(Submitted by reader J. D. Mack)

Sometime back in the 1990s I was riding my bike through a residential neighborhood in Bethesda, Maryland.  Suddenly, I felt something like a giant hand slapping the top of my head.  This was followed by the sight of a squirrel running away from my vicinity.

What had happened was a squirrel had fallen from a tree and landed on my head.  Now think about this.  We’ve all seen squirrels leap from tree to tree, but have you ever seen a squirrel miss and plummet to the ground?  I haven’t, so I would count that alone as being a fairly rare event.

But what are the odds that one of these rare falling squirrels would land squarely on the head of a moving cyclist?  I don’t know the exact odds, but I suspect that one would have a better chance of winning the lottery with a single ticket than having that happen to them.

[EDITOR: Now think about THIS: How embarrassed was that squirrel? Probably not as embarrassed as this one was to see itself on YouTube after this bender…]

## Bunk or Buncombe?

(Submitted by friend of the blog, Brian Hart)

I was visiting Atlanta to do a panel discussion on education vs. debunking.  Prior to the panel, I started thinking about the word bunk and debunk and decided to find their original meanings.  A few minutes of Internet research told me that the word was derived from a region in North Carolina called Buncombe County.  A representative from that county in the 1820s named Felix Walker was known to ramble on with long and wearisome speeches for Buncombe.  In Washington, D.C.  the term, “you are full of Buncombe” became a common phrase.  Over the years the spelling changed to bunkum and the meaning morphed into “any kind of nonsense.”  I was able to bring this origin and meaning into the panel discussion that day.

Two days later, my wife and I drove to see her cousins in Asheville, North Carolina.  We arrived in the evening, and when I was talking about my panel and recounting the origin of Bunkum to the cousins, they all laughed and said, “Asheville is the seat of Buncombe County!”  The next day we walked over and took pictures of the courthouse, where the words  “Buncombe County Court House” are written in stone.

Brian Hart in front of the Bumcombe County Courthouse

## On The Luck Of The Irish And Taking Probability Personally

Millions of people around the world celebrate the 17th March in a variety of ways – from marching in a parade down Armagh Street in Dublin; dying the Chicago River green; partying in a number of pubs in downtown Reconquista, Argentina – or falling in front of my slow-moving car in central Perth, while wearing a green “St Patrick’s Drinking Club” shirt, Dr Seuss-style emerald hat and drunkenly texting on a phone.

Kylie Sturgess - Credit to Viva Life Photography

Despite the heart-stopping experience of checking on the well-being of craic-chasing pedestrians (who assure me that they’ve got the luck of the leprechauns as they laugh off tomorrow’s bumper-shaped bruises and hangover) – the day is usually a cheering one, filled with goodwill and Guinness Beer. Around 34 million people in the USA lay claim to Irish ancestry; even President Obama boasts of Irish cousins that he’s visited in the past. Cereal hiding lucky charms, the handing out of shamrocks, potential pots of gold at the end of rainbows – no matter where we are in the world, people are generally familiar with the claim that there must be something to the “luck of the Irish”… and I’m not just saying that because I graduated from a university that features a leprechaun as their football mascot.

The study of luck and how it is viewed is a familiar one to students of psychology and an important aspect of studying superstitions. Many of us may be familiar with the phrase “Luck is probability taken personally”, which I’ve read as being attributed to Chip Denman, manager of the Statistics Laboratory at the University of Maryland. So, how personally is luck taken and must it mean that it’s akin to any other “four letter word”? Can you really up the ante when it comes to being a lucky person and improve the statistical likelihood of having the “Luck of the Irish” (so to speak)?

## It’s a small town; you’d never have heard of it…

(Special submission by friend of the blog, Barry Karr, Director of the Committee for Skeptical Inquiry)

When I was 13, my parents packed up the whole family into a RV and took us on a several week cross-country trek across the United States. We started in Western New York, traveled across the northern section of the US, down into California, and heading back across through the southern states.  (On a historical note, we were there at San Clemente, Calif., the day Nixon flew there after resigning the presidency.)

Anyway, one day, while we were doing the sights in San Francisco, we went into a little pizza restaurant near Fisherman’s Wharf to get lunch.  There were seven of us, my parents and five kids.  While behaving like kids,  and eating pizza as fast and furious as kids are famous for, a husband and wife sitting at the table next to ours got up to leave (I am not sure if they were leaving because of us).  They asked my parents if we’d like the half pizza or so that they had not touched.  I don’t recall if my parents (at that point) accepted or not, but they did engage the couple in a bit of a conversation.  The usual things came up like what were we doing, what we were visiting, where were we from etc.  Then the conversation went something like this:

My Father:  “we’re from New York State”

Woman:  “That’s interesting, so are we, but we moved away some years ago.”

Father:   “Really, what part of New York?”

Woman:  “The western part of the state.”

Father:  “So are we, what town?”

Woman:  “Well, it was such a small town, if I said it you’d never have heard of it. We were from a town called Arkport.”

Father:  “That’s where we’re from!”

Much more conversation and catching up on family and mutual friends followed. And, without doubt,  we took the pizza.

[EDITOR: There’s a definite theme with people with precisely common roots running into one another in far-off locations. I particularly like the common assumption that “it’s too small for you to have heard of.” It further increases the oddity of the run-in simply because the number of people who could have any connection to the town in question is severely reduced. And yet we see it a lot. Is there any meaning behind it? Did they learn anything from this endeavor, or make a connection that was of particular value? It doesn’t sound like it. There’s no lesson to be learned. But it just shows us that unlikely events like this clearly happen for no reason all the time. Which means occasionally they’ll happen even when there does appear to be some hidden message. But that’s only to be expected.]

Related:
Stranger from the Same Land

## Occupy Art

(Submitted by friend of the blog, Brian Hart)

I went to an art opening being held in Santa Monica, California’s Bergamot Station.  One of the many galleries there had an exhibit called Just Occupy, which featured 3 artists’ representation of last year’s Occupy Los Angeles movement.  One of the artists was Ted Soqui, who had photographed a lot of the participants.

One picture in the exhibit that particularly struck me as amusing, was that of a man in a Guy Fawkes mask, relaxing on the sidewalk.  Since my friend, Paula, had attended Occupy Los Angeles, I thought about her, took a picture with my phone, and then e-mailed it immediately to her.

Image seen in gallery. Photo by Ted Soqui

When I checked my mail several hours later, I heard back from Paula.  She told me that not only was she there that night, but she had seen the photographer take that very picture with his high-end camera and had photographed the subject herself, seconds later!

Image from demonstration. Photo by Paula Lauterbach

Occupy this, OddsMakers!

[EDITOR: In this day and age of copyright infringement concerns, can Paula be sued for taking virtually the same photo within moments of original? I’ve seen crazier lawsuits lately…]

## Punk Through Time and Space

Years and years ago, I think while I was still in high-school, the punk show on my favorite radio station in Seattle played a set exclusively of early 1970s Australian punk.

Now that’s a pretty arcane sub-genre for you; but I really liked the sound of some of what I heard, so I dug around online and downloaded a bunch of music from a variety of the artists played. One group in particular caught my ear:  The Scientists.

The Scientists are actually pretty well known (as far as ’70s Australian punk acts go), but still, what are the odds I would ever see them live?

Five years later I’m living in Perth in Western Australia and my girlfriend’s father, who was a band manager back in the day, asks if we want to go to a show some old friends had put together. It was a sort of reunion party for the Perth music scene of the ’70s, all these old promoters and managers watching bands that hadn’t played together in decades. And who gets up on stage but The Scientists!

I was flabbergasted. The chain of events that was necessary to take me from hearing those songs on the radio to attending that show is so convoluted and improbable it would strain credibility in a piece of fiction.

[EDITOR: I like stories like this because they reveal the thought process we ALL go through in moments like this. We count every single twist and turn along the road that had to be just right to lead to a specific end result and see it as next to impossible. And indeed, when you start WITH the end result and look at all the details, the odds are, well… crazy. It’s the same argument you often hear against evolution, with comments about the odds of random mutations and natural selection leading to US as just too improbable. Had you planned for that end result from day one and it actually occurred, it would be mind-blowing.

But there’s a subtle flaw in the process that we usually miss: you can’t start from the precise end result because you’re biased by your perspective. You have to start from the beginning knowing nothing. An example starting from the end: What are the odds of YOU winning the lottery? Well, pretty darn slim. Starting from the beginning without a bias on the results: What are the odds of SOMEONE winning the lottery? Nearly guaranteed in most cases.

Applied to this story, if we started from the beginning, ignorant of the results, and we add in a tolerance of years to the equation, and said, “what are the odds of this person seeing a band he loves perform live in the town in which he now lives via invitation” the odds are suddenly a lot less spectacular, even if there’s a few factors that bump them up a notch. Take it a step further and make it “what are the odds of ANYBODY seeing a band they love…” and you’re in that range of a guaranteed event.

And yet when it happens to you, and you feel that sense of awe of everything coming together, not to mention combining it with the amazing power of music, the statistics and figures and likelihoods and other options and open-ended criteria fade away, and you’re instead left with a simple reaction: rock on! And I don’t know about you, but I really like that.]

## Stranger from the Same Land

About 10 years ago I was visiting New York City overnight with a friend. As we were walking down the street in Brooklyn a car pulled over and the driver asked for directions to such-and-such.

We said we didn’t know, we were just visiting from North Carolina. The driver said they were visiting from Cary, NC (a suburb outside Raleigh). I laughed and said that I lived in Cary, and he said he lived in the Preston subdivision. I told him that I lived in Preston’s “rival” subdivision at the time (suburbs are so weird like that haha).

I hope he found the place he was looking for…

[EDITOR: This is the sort of story you tend to hear a lot of, or variations of it. Certainly you get people who grew up together running into each other, but you also get stories of people from the same neighborhood, school, street, etc. who never met (sometimes separated by time, sometimes by pure chance) finding each other somewhere else. This one seems ripe for statistical analysis, as it’s clearly common enough, and when you consider populations, tourist destinations, transplant rates, etc., it’s definitely guaranteed to happen pretty darn regularly, which is exactly what we see here. But it’s still pretty jarring when you see it.

Years back I filmed a movie in Salt Lake City with Nick Cassavetes before he had stepped into (and nicely filled) his father’s directing shoes and was still acting. We spent a lot of time off-set together and when hometowns were discussed it turned out he had lived in mine when he was younger. We narrowed down the exact building in which he lived, which was directly next to the DMV. It was particularly infamous to me because during one of my lengthy visits to that lovely bastion of hope and cheeriness a crowd had formed by the window to watch as a man stood nude in his full-height living room window, displaying himself gleefully to everyone there. Thankfully Nick confirmed this was NOT when he lived there and he was definitely not the man in the window. But it’s a perfect example of those funny little hometown connections in a very unexpected place that lead to a great story.]

## Battlestar Portlandia

(Submitted by friend of the site, Brian Hart)

At a restaurant in Los Angeles one recent Monday, I spotted Battlestar Galactica’s executive producer and writer, Ronald D. Moore, at a nearby table.

It should be noted that the highly acclaimed, re-imagined series went off the air back in 2009, and I saw Moore there in January 2012.

On Friday of the same week, I was watching the show Portlandia on the IFC channel, and one of the comedy pieces revolved around Battlestar Galactica.  Fair enough.

However, the main joke became that the couple watching the show became obsessed with it, and demanded that Ronald D. Moore write new episodes specifically for them.  Several original BSG members appeared on the show, doing a table read, along with Ronald D. Moore himself, playing a local Portland actor, “Kim Reynolds”.

Spin up the FTL drives, and make a Jump into coincidence, these odds are crazy!

So say we all!

[EDITOR: Brian seems to have a penchant for running into celebrities right around the time they’re mentioned in podcasts or featured out of place on television. Maybe it’s less coincidence and more that Brian relentlessly stalks them until they happen to line up to make a good story…?]

## Kindergarten Koincidence

When I was in kindergarten some 20 years ago, I became close to one of the ladies working there and she was my favorite teacher of them all.

When I was in the 8th grade (about 9 years later) my favorite teacher showed up in my dream for the first and only time since I went to kindergarten. Later that very same day when I was riding my bike home from school, who do you think I run into on the sidewalk, if not, my old kindergarten teacher.

To this day, I’ve carried this story with me as a perfect example of a “one in a million event”. Although I am a statistician by education, and can point to several high-probability factors in this story to increase the odds a bit, I still think it’s a really cool story.

[EDITOR: I’ll refrain from speculation as to what happened in the dream.]