The Devil’s Footprints

(Submitted by Skepticality listener Jim Fitzsimons)

Ok, here’s an excellent coincidence! This past Monday (Feb. 9) while at my day job, an old book of (mostly) urban legends came to my mind. The book was called ‘Strangely Enough’. I had blogged about it five years ago. I looked up the blog and reread it and in it I mentioned a favorite story in the book about the Devil’s Footprints which appeared overnight in England in 1855. It was claimed that the prints went in an unwaveringly straight line across several miles, over houses and haystacks, across rivers and lakes; all in one night.

Later that same Monday (Feb. 9), while at my night job, I was listening to the February 3rd episode of Skepticality. During the contributors’ segment at the beginning of the show, Tim Farley talked about those same Devil’s Footprints as part of his Skepticism, Past and Future.

Cool, no? Well, it gets even more coincidental!

Tim mentioned the date of the event. People woke up and discovered the uncanny prints in 1855 on the morning of February 9th.

That means I had thought of the book, looked up my blog piece on it, read about the Devil’s Footprints, and then, later, heard Tim talk about them all on the 160th anniversary of the event!

How crazy are those odds?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 262.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

I can actually do a little bit of calculation with this.

At first glance it might seem that some of the odds in this case can be calculated. After all, we know how many days of the year there are. If the likelihood of the events occurring on a given day was the same as the likelihood that it would occur on any other day, then the odds of thinking about the Devil’s Footprints on its anniversary are approximately 1 in 365, or .0027. And the odds of hearing about it on that same day (given it’s the same year) are .0027 x .0027, or .000007.

However, there is a lot here that is nonrandom. For example, Tim Farley talked about the Devil’s Footprints as part of his Skeptical History segment precisely because the anniversary was that week. The probability that any given person would listen to the episode on February 9th is quite high–not easily calculated, but definitely much higher than 1 in 365. Furthermore, the probability that the Devil’s Footprints would come to mind is not the same for all days. Memories are activated by cues and cues come in all manner of form. Integral to the story of the Devil’s Footprints is snow and even if it is not snowing, cold weather may easily trigger a thought or two about the incident, especially to someone who has studied it. The date itself may have triggered the memory without the author’s awareness.

For these reasons, what appears to be a crazy coincidence probably isn’t all that crazy.

London Encounter

(Submitted by Skepticality listener Peg Gantz)

In 1996, my son and I flew from Glens Falls, N.Y., (via Albany, N.Y., and Newark, N.J.) to visit my daughter, a college student doing a semester abroad in Bath, England. We flew in to Heathrow and took a train to Bath. At the end of our visit, we spent a couple of nights in London.

The day before our visit there had been an IRA bombing on a London bus, so security was very tight. Because of a suspicious package, and announcement was made that the tube would not stop at our intended station of Covent Garden, so we got off at the stop before and started walking in what I hoped was the correct direction to Covent Garden.

As we stopped on a traffic island in the middle of a street, I asked a man who also was on the island if he could direct me to Covent Garden. “Sorry,” he drawled, “but I’m from Texas, and I’m lost, too.” We went our separate ways.

Two days later my son and I were in line at Gatwick airport. (Yes, we flew IN to Heathrow and OUT from Gatwick; no idea why, but the tickets were a gift from my brother, who’d used his frequent flyer miles, so I was not about to question it.) A man stood in line behind us, and it was the Texan we’d encountered on a traffic island somewhere near Covent Garden in London! We exchanged greetings, made note of the unusual coincidence, and again went our separate ways. (And in case you’re wondering, I never saw him again.)

I’ve often wondered what were the odds of lost U.S. citizens from different parts of the country meeting for the first time on a London traffic island, then encountering one another again in line at the airport.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 261.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

Unfortunately, I have no answers for this one except to say that low-odds events must happen occasionally. This story actually reminds me of one of my own.

We (my husband, our two boys, and my parents) were flying from our home in Los Angeles to Vancouver the day before our ship sailed to Alaska. Our boys were (and still are) both constantly drawing and one of them was doing so while the plane was boarding. A man noticed, complimented our son’s work, and offered to draw something for him. In a few minutes my son had a personalized cartoon of Homer and Bart Simpson, drawn by a man who had worked as an artist and director for the show for many years.

The next day we saw the man and his family as we were boarding our cruise. He and his wife had two boys of their own, a bit younger than ours, and were booked on the same cruise and post-cruise activities. As you can imagine, we were able to spend some time together and became friends.

The odds are good that at least one family on a flight from LA to Vancouver is scheduled to board a cruise ship the next day, but the odds that two families who don’t know each other are scheduled to board the same ship AND interact are likely pretty small, although not nearly as small as running into someone in an airport that you saw on a traffic island days before in a highly populated city.

The Case of the Big Mall Coincidence

(Submitted by Skepticality listener Andrea Monticue)

Last Sunday, I was driving and listening to the audiobook by Mira Grant, “Parasite.” The story takes place in the near future, and the characters live in the Bay Area of California. In the book, the main character and her sister decide to go shopping at “the big mall in San Bruno.”

Guess which parking lot I was pulling into when I heard that phrase? Yes, the “big mall in San Bruno,” California, otherwise known as Tanforan.

I go to that mall about once every couple of months. I’m not a fan of big malls, but there’s a Barnes & Noble there.

The only reason I’m listening to “Parasite” is because I enjoyed Grant’s zombie trilogy.

Below are the extended notes provided by statistician and podcaster Kyle Polich for use in Skepticality Episode 260.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

(Kyle studied computer science followed by artificial intelligence in grad school with a focus in probabilistic reasoning and planning. His general interests range from obvious areas like statistics, machine learning, data viz, and optimization to data provenance, data governance, econometrics, and metrology. He enjoys exploring the intersection of statistics and skepticism and sharing related insights with others including through his podcast Data Skeptic. Visit Kyle’s blog Data Skeptic, and give the podcast a listen.)

I suppose the question here is: “What are the odds of arriving at a specific location just as a character from an audio book is arriving at the fictional version of the same location?” but actually, that might be the wrong question to ask.

This seems like a case of postdiction, also known as the hindsight bias, or put more simply, a case of remembering the hits and forgetting the misses.  Most people have had the experience of thinking of someone and then immediately getting a phone call or text message from them. I have to confess, that always does feel a little spooky, even to me. But in reality, if every time I thought of a friend, acquaintance, of loved one, they ended up calling me right away, I’d be endlessly annoyed with how many impromptu calls I’d have to take. Yet, the goose bumps that sometimes accompany these infrequent coincidences make them memorable.

There must be dozens, maybe hundreds of other malls in the bay area that the author could have chosen.  As of the time of recording, the Wikipedia page for San Bruno, CA lists five specific locations that are not parks or schools, one of them being – you guessed it – the Tanforan Mall. For me, this is enough to say that it’s not surprising that a story taking place in San Bruno might feature a scene at this location.

If you studiously compiled a list of actions taken by characters in Parasite, I suspect you’d be surprised to find how long this list is with only one memorable overlap to your own actions. So while precise likelihood is hard to establish here, I think this tale is a great reminder that experiencing a few seemingly odd coincidences every so often is really the norm, not the exception. Google Littlewood’s Law for further reading if you’re interested. And just to prove the point, I want to say congratulations to a certain listener who has recently taken a new job. I won’t say who, but if you’ve had a career change in the last 3 months, my congratulations go out specifically to you.

It’s a Small World After All

(Submitted by Skepticality listener  Chris Benson.)

I have two similar-ish stories:

1. In the fall of 1979 my family moved from Muscatine, Iowa to Kingman, AZ. It was the week before Halloween of my senior year and I was leaving behind a graduating class of 379.

On my first or second day at my new High School, I was walking down the hall and found myself looking at an acquaintance from my old High School class! We were both surprised, to say the least.

2. In the early ’80s I was at Arizona State and a friend of mine from our dorm needed a ride to the University of Arizona for an ROTC function. I had a friend from Kingman whom I knew was at U of A, but we had not spoken for a couple of years, and I had no other information, but figured I could go try to hunt him down.

I dropped my dorm-mate off at his ROTC thing and went to the Student Union to see if I could look my other friend up in a school directory. The fellow at the service desk in the Union said he couldn’t help me because they didn’t have a directory.

I knew driving down that it was a wild goose chase, but I was really disappointed.

Then I turned around trying to think of something else to try, and I’ll be damned if he wasn’t standing there. He was on his way to dinner at the Union’s cafeteria, and we spent a lovely evening together.

The population of that school was around 30,000 at the time, so I figure the odds were something close to that.

Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 258. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

1. This is probably impossible to estimate numerical odds. So many factors affect everything that happens. For example way back in 1979, what were the economics of Iowa and Arizona? In general there has been a movement of people in the US to the sun belt. If some specific economic or other conditions made making the move desirable, that would make the chances of meeting someone who made a similar move greater.

2. I’m glad that this story happened over 25 years ago. I did not notice at first that Chris said it was in the ’80s. I was about to criticize him for not doing a web search, or look for a friend on the face thing, or do an on-line criminal records search or something, to try to find his friend. But since it was a long time ago, he will be spared that criticism. If he should run into a similar situation in this decade, we know he will avail himself of the various internet tools to increase odds of success again.

We are sure that it must have been surprising to find his friend. Trying to estimate the odds of doing so is probably not really possible. But I think that as usual, there are some factors that make the odds much better than we might intuitively think at first. And it is worth thinking about them.

Let’s think about a few possible items. There may be a lot of odds reducers that he did not mention. For example, I suspect his friend lived in a campus dormitory and he happened, on purpose, or by chance, to go to the student union at dinner time.

I suspect that since it was a friend he was looking for, they may have gone to high school together. This means that his friend most likely lived in a dorm at the campus. If so, then it would actually have been a great plan to try to find a campus dormitory-living student by going to the student union cafeteria at dinnertime. Or breakfast time or lunch time.

Now if the population of the school was around 30,000 at the time, and half of the students lived in a dorm, then your odds of finding the person would roughly double. That would be about 1 in 15,000 chance, which is pretty long odds.

Obscure Actor Twice in One Day

(Submitted by Skepticality listener Vandy Beth Glenn)

Last Saturday afternoon, I was watching the TV show Fringe on Netflix streaming. In the guest-cast credits of the third-season episode, “Do Shapeshifters Dream of Electric Sheep?,” I saw the name “Marcus Giamatti.” I’d never heard of him or seen the name, and wondered if he was related to Paul Giamatti, one of my favorite actors. So I looked him up on the IMDb and saw that they’re brothers. “Cool,” I thought, and that was that.

Later that same day I got on my treadmill for my daily run. I watch TV while I run, and this time I had a DVD from CSI Season 10, also provided by Netflix.

The next episode on this disc was “Lover’s Lanes.” The guest cast for this episode included, you guessed it: Marcus Giamatti.

What are the odds?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 256.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

Once again it’s not a reasonable task to calculate these odds, but it is an opportunity to discuss what questions we should ask ourselves before getting too excited about the coincidence.

A look at IMDB tells us that Marcus Giamatti has a pretty long resume, but since many of the entries are guest spots on episodes of short-lived TV shows, we shouldn’t expect to see him when choosing something at random.

However, once we have paid attention to something, we are much more likely to notice the same thing or something similar or related afterward. This concept is called “priming”.

How many times has the author seen this actor in something and did not take note? Would she have noticed him in the episode of CSI if she had not looked him up earlier in the day? Had she seen this episode before and was not interested enough in who the actor was to look him up?

Also, how many times has the author seen an actor in two roles on the same day without noticing?

Another interesting question to consider: how much time would need to be between these two sightings to make the coincidence uninteresting (not a coincidence)? A day? A week?

Attention is really important when it comes noticing crazy odds.

The Man in the Arena

(Submitted by Skepticality listener, Skeptic Society blogger and Junior Skeptic Editor, friend of the blog Daniel Loxton)

I spent much of last summer preparing my speech for The Amazing Meeting 2014, a large skeptics conference in Las Vegas. It was totally nerve-wracking. I’m shy. I get stage fright. I’d never given a solo talk of that length in front of such an enormous crowd—1200 people! Many of my intellectual heroes would be in the audience. And, I was planning a very emotional talk about beauty and joy and meaning.

So I spent five weeks writing and obsessively polishing that talk, titled “A Rare and Beautiful Thing.” Its themes were built on discussion of skeptics of previous generations, including magician Harry Houdini. I said this:

When Rinn’s old friend Houdini finally did get into the fight, he arrived as a mighty champion. He brought skill and knowledge, and wealth and fame. Houdini studied and investigated and wrote books, and gave demonstrations.

He went to Congress to fight for tougher laws against fraudulent fortunetellers, at least in the nation’s capital. He fought with passion, and gravity of purpose.

And he lost.

There is a strange and heartbreaking beauty in that.

As I worked to cram two thousand years of scientific skepticism into half an hour, I was forced to make cuts. One of the last things I cut, very reluctantly, was this abbreviated quote from Theodore Roosevelt, which had accompanied the Houdini passage:

“The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again…but who does actually strive to do the deeds…and who at the worst, if he fails, at least fails while daring greatly…”

When I delivered the talk, the vast hall was silent. I had no clue whether the crowd was coming along with me. Then, as I finished the speech and stumbled off the stage in relief, I discovered that they had. Dozens of people rushed to talk to me. It was among the most amazing moments of my life.

One of those people was ‎a woman named Anna Maltese, who held a piece of paper in her hand. She wanted me to know that the talk had inspired her to share a favorite passage by her favorite American President. She felt sure I’d like it, so she had written it down for me. I looked at the paper. It said, “The credit belongs to the man who is actually in the arena, whose face is marred by dust…”

I was stunned. It was the final surreal touch to an unforgettable day.

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 255.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

The quote is not obscure, but it is not exactly “Four score and seven years ago,” either. It is seen rarely enough to make this feel like a crazy coincidence. And perhaps it was an unlikely event, but there are a few factors which increase the odds quite a bit.

The first thing that we must always consider is that the commonalities we know about (e.g., the Amazing Meeting) are usually related to things we might not have considered–something called confounding variables. Anna’s attendance at the event was not random. The subject matter that brought speaker and audience member together is somewhat academic in nature and those interested in it tend, on average, to be more educated than average. The odds that someone in the audience would be familiar with such a quote are higher than the odds that any random person would. Even the odds that an audience member would count that quote among their favorites are higher.

But I think that the most credit for this incident must go to the simple fact Daniel’s speech communicated his message so clearly that the quote he wanted to use to illustrate it was brought to the mind of an audience member who was intimately familiar with it. That’s a brilliantly crafted and delivered speech.

Monkey’s Uncle

(Submitted by Skepticality listener Brian Hart)

I’m taking college level courses at UCLA to complete my education. I was sitting, an hour before class, and reading in our Anthropology book, a chapter about primates. I had no idea there were so many species around the globe. Anyway, one of the Old World species I had never heard of before, the Vervet Monkey, native to Africa, was mentioned in the book along with it’s picture. The chapter I was reading was about sexual reproduction, populations, groups, etc.

I closed the book and headed on to my Anthropology class and put George Hrab’s skeptical show, The Geologic Podcast, episode #383. In the amusing segment called, Interesting Fauna, Geo started talking about a species of primate and it’s mating habits. Can you guess which species? Yep, the Vervet Monkey.

I’ll be a Monkey’s Uncle (or, I share about 96% of my DNA with my Monkey Uncle)!

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 254.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

It’s a cute story, but there is absolutely no way to calculate the odds of this happening. It’s highly likely that the author would read about vervet monkeys in an anthropology book, but the likelihood of the topic being discussed on a podcast is a pretty difficult thing to quantify. George is not an anthropologist, zoologist, or any other profession that would be expected to talk about primates. He is a musician by trade and his podcast is about science and skepticism. There are many potential topics for his show and while monkeys certainly aren’t a strange thing to discuss, it’s not exactly a commonly-discussed topic, either.

I think we just have to tip our hat to nature for this one and accept that this is one of those funny, unlikely coincidences that we just can’t quantify.

That and thank the coincidence gods or the opportunity for endless puns about monkeys.

Numbers Sometimes Lie

(Submitted by Skepticality listener  Stephen Hayko.)

I do clerical work for a company that uses part numbers that are six digits long and begin with either a 5 or 6. When we order parts, our ordering system generates a purchase order (PO) that is six digits long and sequential.

We’ve been using this ordering system for about a year, and throughout the company, we typically place about 45-50 orders in the system every week, in my branch. We’re one of 25 branches in the US that uses this system, and we are one of the higher-volume branches – most other branches use about 30-35 orders per week.

In March, I placed an order for part number 649384. This is a relatively common piece and we typically sell 8-10 of this part per week – so it accounts for 16-20% of our orders. Lo and Behold! The PO was 649384.

Given that information, what are the odds that PO 649384 was attached to an order for part number 649384?

Thanks!

Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 253. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary.

This problem seemed very straightforward at first, but on closer review it seems that there is something interesting hidden in the details Steve provided. Estimating the total number of POs generated company-wide using the average of the ranges you gave comes to about 780 POs per week. That’s about 3,586 per month, and 43,030 annually. Steve said the numbers generated automatically are six digits long, and are sequential. So if 43,030 are generated annually, it would take 649,384 / 43,030 years to hit number 649384, or about 15 years, one month. So barring any large increase or decrease in business, in about 15 years you may see this happen again. But wait, Steve also stated that the company has been using this system for a year. Something is fishy here. If the numbers are sequential, and they’ve used this for a year, then they must not have started at 000 001. They must have started somewhere around 649,384 – 43,030 = 606,354. That is, if the numbers Steve gave were close to correct. Starting to wonder if this is some sort of trick question here Steve. Something does not add up. Literally.

So either Steve submitted a trick question which he knows is impossible, or someone, for some reason, decided to covertly tamper with the automatic PO number generating software to make it start at some number other than 000001. Perhaps someone thought PO numbers like 000001, 0000002, etc. would make the company look like a startup, or just would look odd. PO number 606354 makes the company look like they’ve been in business for a long time, and/or process quite a lot of POs. So this great mystery deserves some investigation. Inquisitive minds want to know what was the first PO number generated, who determined what that number was, how did they determine it, and why? And was it part of a conspiracy, or did this mysterious person act alone? A reasonably thorough investigation is certainly in order. There must be a logical explanation.

A number starting in 60 does not look like someone used their birthdate, which would be weird anyway. Does Steve know the last six digits of the CEO’s social security number? Well, there could be a mundane explanation, like the numbers were sequential for many years, maybe kept on a clipboard or something, and only a year ago was it computerized. Let’s go with that, and forget the conspiracy theory. In fact, everyone please forget all conspiracy “theories.”

So back to the actual question. It seems that Steve already knows the answer to his question. He said that this common part accounts for 16 to 20% of their orders. So the odds of any one order having this part number on it should be approximately……16 to 20%! Grab any random order out of the pile (or computer system) and there will be a 16-20% chance that it has this part number on it. That goes for any PO number: 650000, 700000, 131313, and also for 649384. Steve knew the answer; he just did not know that he knew. This is certainly not a criticism. It is better to not know that you know something than to think you know something that you do not. The fallacy was that he thought the odds would be different for that one special PO number, but they are not. The odds are the odds. The odds, in this case, are perfectly rational – but not sequential.

Not by the Heir of my Twinny Twin Twin

(Submitted by Skepticality listener Misty Wegman.)

First of all, I do not believe in horoscopes or any such nonsense but in this situation it makes the story better. Feel free to take it out if it gets too messy.

I was born on June 2nd and my dad was born on June 3rd. This makes our astrological signs “Gemini” or Twins. He is an identical twin. I gave birth to fraternal twins. He is a twin-twin and I am a twin that had twins.

It gets better. My Aunt (father’s-sister) had identical twins. My mother’s Aunt had fraternal twins too (which is where I got them from). After my mother divorced my father, she married the boy of boy/girl fraternal twins. So I have twin second cousins, twin cousins, 2 twin dads and I’m an astrological twin that had twins.

What are the odds of more twins being born in my family?

Below are the extended notes provided by cognitive psychologist and statistician Barbara Drescher for use in Skepticality Episode 000.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own hilarious commentary. Also, visit Barbara’s blog ICBS Everywhere, and Insight at Skeptics Society.

Well, I would say that the odds of more twins being born might be pretty good, but not much higher than in anyone else’s family. Of course, one would have to define and learn quite a few things before even trying to come up with an actual number, including what is meant by “family” (siblings? offspring?) and the ages and intents of those involved.

But there are a few things to talk about nonetheless.

First, the author notes that two of the cases of twins are identical, and one case is a step-father. Identical twins occur as randomly as astrological signs and one has no blood ties to a step-father, so these factors are independent–they have no influence on whether twins will occur in a family. Fraternal twins, on the other hand, do run in families, as hyperovulation is a genetic trait, although one does not receive genes from aunts/uncles. If genetics are to blame, the author’s chances of having fraternal twins on a subsequent pregnancy is now double. In addition, the age of the mother is a factor–the older the mother is, the more likely fraternal twins will occur.

All of that said, fraternal twins can also be the result of fertility treatments. This introduces a controllable factor that can increase the odds of twins dramatically. If fertility treatments are involved, genetics can’t be blamed.

According to Babycenter.com and several other online sources, the most recent data shows about 1 in every 30 births today are twins (about 3.3%), with only a about 10% of those being identical. So, about 3 in every 1,000 births will be twins born under Gemini.

Having that many twins in a family depends on many factors such as the size of the family, but I do love the idea of introducing someone as a twin twin with twins (yes, I know author isn’t a twin herself, but I took some license).

(Submitted by Skepticality personality and friend of the blog Bob Blaskiewicz.)

What are the odds? I mean, they must be CrAzY!!!!
Bob 🙂
Two players die at world chess event in Norway
Competitor dies in the middle of a match during Chess Olympiad in Norway and another is found dead in hotel room

The most prestigious international tournament in chess, at which the world’s top players compete alongside amateurs to win honours for their country, has ended on a sombre note after two players died suddenly within hours of each other, one while he was in the middle of a match. Hundreds of spectators attending the 41st Chess Olympiad in Tromsø, Norway, and countless others watching live TV coverage on Norway’s state broadcaster, reacted with shock after Kurt Meier, 67, a Swiss-born member of the Seychelles team, collapsed on Thursday afternoon, during his final match of the marathon two-week contest. Despite immediate medical attention at the scene he died later in hospital.Hours later, a player from Uzbekistan who has not yet been named was found dead in his hotel room in central Tromsø. Norwegian police and the event’s organisers said on Friday they were not treating the deaths as suspicious.

“We regard these as tragic but natural deaths,” said Jarle Heitmann, a spokesman for the Chess Olympiad. “When so many people are gathered for such a long time, these things can happen.

The Olympiad involved 1,800 competitors from 174 countries, accompanied by more than 1,000 coaches, delegates and fans.

The event sees players compete in national teams over 11 rounds, often playing matches that last for up to six hours, and claims a worldwide online audience of tens of millions.

There were brief scenes of panic in the hall after Meier’s collapse, when spectators reportedly mistook a defibrillator for a weapon. Play was briefly suspended before his death was marked with a minute’s silence during the closing ceremony.

While the causes of the two men’s deaths are still unknown, they will raise questions about the mental and physical stress that tournaments place on players.

Meier is not the first player to die in the middle of a match; in 2000 Vladimir Bagirov, a Latvian grandmaster, had a fatal heart attack during a tournament in Finland, while in the same year, another Latvian, Aivars Gipslis, suffered a stroke while playing in Berlin from which he later died.

One of Australia’s leading players, Ian Rogers, retired abruptly from chess in 2007, saying he had been warned by his doctors that the stress of top-level competition was causing him serious health problems.

Tarjei J. Svensen, a reporter for chess24.com who attended the Olympiad, said the event had a reputation for heavy drinking. “There are two rest days during the competition, and particularly the night before the rest days there tends to be a lot of drinking,” he said.

A favourite attraction for delegates was the now-legendary “Bermuda party”, he added, hosted at each Olympiad by a member of the Bermudan delegation.

The Olympiad was big news in Norway, with the state broadcaster, NRK, carrying hours of live coverage each day, and the country’s government paying 87m kroner (£8.5m) for the privilege of hosting the event.

Last week the women’s team from Burundi were disqualified after failing to show up for their round six and seven matches; they remain unaccounted for, Heitmann said on Friday.

“It has been an eventful Olympiad, certainly,” said Svensen.

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Below are the extended notes provided by contributing editor Mark Gouch for use in Skepticality Episode 251. Mark is a wastewater treatment system operator and engineer living in Smithtown, NY (Long Island). He started to become interested in coincidences after recognizing the series of events that conspired to get him employment on Long Island many years ago. Two of Mark’s recommended books include “The Drunkard’s Walk: How Randomness Rules Our Lives” by American physicist and author Leonard Mlodinow, and “The Hidden Brain: How Our Unconscious Minds Elect Presidents, Control Markets, Wage Wars, and Save Our Lives” by Shankar Vedantam.

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A sad story, and surely it must have been a shock to those involved in the chess tournament. Well, we do not have a lot of information about the cause of death of the two men, so that limits what we might say about the probability. The best we can do is a very general estimate of the odds of the death of any person out of a thousand random persons. According to the ECOLOGY Global Network ™ web site, as of 2011 the global daily death rate was about 151,600 deaths per day. And in round numbers world population is about 7.3 billion.

So it would seem we should estimate the odds of one person out of a thousand at any conference, or any group of a thousand people should be somewhere around 151,600/7,30,000,000  * 1000= 0.0215, or about 2.15%. The odds of two persons in the group dying would be 0.0215 * 0.0215=0.00046, or about 0.046%. I think most people like to think of odds in terms of per million. So 0.0046% odds is 46,200 per million. This means that for every million conferences, meetings, etc. that have about a thousand persons in attendance, there would be over 46,000 of those events.