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Way More Than a Dozen

(Submitted by reader Becky Glynn)

My husband and I live in Monterrey, Mexico, most of the time, not that has anything to do with the story – per se.

Two months ago, we bought an 18-pack of eggs from our local grocery store. Regular store with regular eggs, or so we thought. Over the years, I have cracked an egg and have been surprised to see two yolks, or even a little red spot. So, when I cracked the first egg from the carton and saw two yolks, I wasn’t as surprised as much as I was amused. Then I cracked a second egg and there were two yolks. OK, I thought, what are the odds of that happening? The third, fourth, and fifth eggs also had two yolks. Now I know the odds are getting larger.My husband wasn’t quite sure I was telling the truth, maybe miscounting? I had hardboiled three eggs to make tuna salad, so I had my husband stand there while I peeled and opened the eggs. Yep, two yolks in all three. We are now at 8 eggs with double yolks from a pack of 18. As it turned out, there were actually 14 out of the 18 eggs that had double yolks.

We are “guessing”  they all came from the same chicken, but really, what are the odds of having that many double yolked eggs?  We will wait to see what you all come up with.


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 206. Take a look and leave your comments below.

[This] story is more interesting, maybe because I can actually calculate the odds of this happening–with a caveat. First I’ll explain the odds, then the caveat.
I consulted several internet sources and found the information pretty consistent, so I think it’s reliable. The odds of a double-yolk are 1 in 1,000 (.001). So, if these eggs were randomly selected, the odds of getting at least one double-yolked egg in a carton of 18 are 18 in 1,000. Once one has been removed, the probability of at least one of the remaining eggs being double-yolked is .017, and so on. All told, if these eggs were randomly selected, the probability of at least 14 double-yolked eggs in a carton of 18 is .000000000000000000000000000267 (there are 27 zeros).
Now the caveat: because they all came from the same carton, it’s highly likely that they share some factors that matter, so the odds of a second egg being a double-yolker are actually dependent on whether the first is. Perhaps they all came from the same hen or they were from hens which were housed near each other and exposed to the same environment, food, and other treatments. What’s more, the hens that laid these eggs may be around the same age, and young hens are the ones that lay nearly all of the double-yolkers. So, the odds that an egg from a hen that is 20-28 weeks old is double-yolked are about 10 times greater than if the egg were chosen at random.
Because we don’t know the source of the eggs for certain, it is difficult to calculate the real odds in this case. It may be as much as 10 times greater than if the eggs were randomly selected. However, at .0000000000000000000000000267 (that’s 25 zeros) that’s still rather impressive, don’t you think?

Check, Please!

(Submitted by reader Daniel Moyer)

In my youth I waited tables at a local diner. I worked the weekend early shifts, and referred to breakfast as the “meal of beverages.” There was always a huge variety of fluids (coffee, tea, milk, juice, water, etc…) at each table beyond the myriad assortment of breakfast foods. It happened one fateful day that I had two unrelated tables, both of them four tops.

As one could expect, each table had entirely different meals from the drinks down to the side orders. Eventually, table number one decided they were finished and ready to head out for their day, so digging through my pocketful of register checks, I handed them their bill, and they left, paying up at the register on their way out.

The second table remained active and decided they wanted additional food. When I went to add onto their check I realized to my dismay I had handed table number one the check for table number two, which was now closed out and paid for! I rushed up to the register to get the correct check to see how bad the situation was about to get for me. The hostess dug down through the cancelled checks to find the proper one and to our utter amazement, both bills were identical right down to the penny! Neither one of us could believe what we were seeing. With a great deal of relief and amazement, I explained the circumstance to table number two and showed them the proof, again, shock and awe.

I was able to add their additional food to table number one’s original check which they could now safely pay as easily as if the error had never occurred in the first place. The diner Gods were certainly smiling on me that day, and even though it’s hard to swallow, it’s the absolute truth and I enjoy recounting the story to this day. Is there any way to deduce these seriously crazy odds???


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 205. Take a look and leave your comments below.

Without knowing the possible combinations, it is extremely difficult to determine the odds of this happening. It might very well be high, especially if a number of items on the menu have the same price. Most restaurant pricing is a whole dollar amount with zero, $.50, or $.99 tacked on, but nothing in between. Furthermore, a diner’s breakfast menu is not likely to have items which vary a great deal in price and the per person total probably falls within a tight range most of the time. So, while I am sure that it felt shocking to the author, my guess is that the odds are not all that crazy.

A Key Question

(Submitted by reader John Meuser)

I grew up on a farm in a rural community in Indiana.

The high school I went to had been consolidated from several small town schools in the area, so almost all students were bused in being picked up from houses which were widespread. Even though our house was only about 15 miles from the school, it took about an hour for the daily commute. Pretty much all students get their driver’s license as soon as possible so that they don’t have to go through this lengthy process every day.

My younger brother is mentally handicapped so was unable to get his license at the same time all of his friends did, but my parents didn’t want him to miss out, so they allowed him to drive an off-road utility vehicle, best described as a large golf-cart, to school every day. The brand was Cushman, but I have no idea of the model. He probably had a longer commute than if he rode the bus, but my brother loved the independence.

He also had problems with the combination padlocks on the lockers, so the school allowed him to use a padlock which takes a key. This is a very rural area where no one locks their doors, so the only two keys that my brother ever carried were the key to his locker and the key to his Cushman. He was unlocking his locker one morning, and realized that he had accidentally gotten the two keys mixed up, but was surprised to find that both keys were completely interchangeable. His Cushman key could unlock his locker and vice versa. What are the odds that the only two locks in the world that my brother needed to use took the exact same key?


Below would be the extended notes provided by Barbara Drescher for use in Skepticality Episode 204. But as you may know from the podcast, the most Barbara could share is that she’s had a similar experience. This one’s just too tricky, and requires too much specialized knowledge, for her to assist.

So that’s where you, our faithful, generous, and brilliant readers/listeners come in. Do you know anything about the elements of this story that could help us solve this question? Are you, perhaps, a Cushman enthusiast? A locksmith? A trivia know-it-all who found a Cushman manual in a library and read it front to back in hopes that one day a Jeopardy answer would hang in the balance? Whatever the case, if you’ve got info, we want it. Please comment below the story and let us know what you think we need to know. There will be fame and fortune in it for you. Also, probably neither of those things.

The Randi Show

What are the odds that the incomparable James Randi would upload a video to YouTube about a crazy coincidence? Well, considering the source, I imagine quite high. Regardless, this is fun, so we just had to share it with you.

The Popes of Finnish Football

(Submitted by reader Brian Pope)

My name is Brian Pope I am an American and I have lived here in Vantaa, Finland for the past 5.5 years. I play football (soccer for my North American brethren) and am a goalkeeper. A few years ago I got a message from a teammate asking if I had given up on our hobby league football team and signed for a pro club in Vaasa, Finland (Vaasan Palloseura VPS).

Now I believe myself to be a decent keeper but by no means pro level. My teammate sent me a link that announced the signing of an American goalkeeper named Brian Pope to VPS.  I thought this was very entertaining. Through Facebook I was able to track down this other American Goalkeeper named Brian Pope and relayed the coincidence. He enjoyed the story as well.

During this same time, my wife’s cousin, who lives in Vaasa, happened by an apartment where the name on the mail slot said “Brian Pope” and snapped a picture. She thought it was pretty amazing to have another Brian Pope in Finland. She did not know that I knew there was another person by the same name living in Vaasa so I relayed the story to her.

What are the odds that there were 2 Brian Popes living in Finland at the same time both being football goalkeepers? Granted at different levels of football. The fact that my wife’s cousin happened by that mail slot is another set of odds all together.

For reference I was born in 78 and the other Brian Pope in 85.


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 203. Take a look and leave your comments below.

The odds of this are a little more difficult to calculate than most of the other “same name” stories that we get, mostly because the frequencies of names in Finland in past years are not easy to find. Both his first and last names are fairly common in the U.S., but I found myself impressed with the coincidences in the story and it is my own amazement, once again, that I think is interesting.

Soccer is an extremely popular sport, so even the fact that few soccer players are goalkeepers should not make this story so surprising. However, there is an aspect of this story that explains my feelings: distance and familiarity. Familiar settings provide frames of reference to anchor us. We are more confident with our estimates of everything from accident rates to salaries when the context is familiar. Finland is not a familiar place to most Americans. Numbers of Americans living in that part of the world are also not available, but who ever talks about moving to Finland? France, Italy, even Egypt are more likely. There is no Eiffel Tower, no pyramids, and no riviera. Finland does not seem exotic. It just feels foreign, and the
lack of familiar context seems to make the presence of such a common, American-sounding name feel more out of place than it probably was.

Nothing to see here…

This is a test post. You can safely ignore it. Or inform all your friends. Honestly, the choice is yours. But they’ll probably lose some trust in your advice if you do. Just sayin’.

In our never-ending quest to improve our site (remember the “under construction” text and images on old web pages, ignoring the fact that any good site should always be undergoing work?), we had to clean up a little issue with our Twitter extension that was posting junk links, presumably when we added or edited posts not ready for public view. Not sure why, but the fix was similar to the one we employed to improve our submission form: switch to the WordPress Jetpack feature that does the same. As WordPress grows and improves, it seems to slowly bring in some of the most valuable features we needed to rely on third-parties to achieve before, and often with its own advantages.

For this change, we’ve noticed that our Twitter updates now include a little “show media” link on them that will let you preview the post directly on Twitter. Pretty cool, huh? But don’t judge a book [blog post] by its cover [excerpt]. Click the link and read the whole story!

(Submitted by reader Jim Houston)

A few years after graduating from college in upstate New York, I returned to where I grew up in Pennsylvania and found a job about 20 miles away  from my hometown. The job wasn’t related to my major in Physics, but computer programming was something that was a bit more portable, and within a few months, I was asked to find other programmers for the project team.

Sifting through stacks of résumés is an exercise in looking for familiar experiences that would suggest someone can do the job you need done, so one morning I see a résumé that looks so familiar I could have written it myself. I realized as I read it that I must know this guy and so decided right away to call him in for an interview. He went to the same college as I, graduated the same year, and in the same major.  There were about 100 of us freshmen in the department and we all took the same intro courses for the first two years.  While 100 classmates is not a large group, I  may not have known many of their names, but usually recognized them if we passed each other in the halls.  So that I couldn’t place the  interviewee from the name on the resume didn’t strike me as unusual.

When my classmate walked in for the interview, I felt that I had never ever seen this guy before.  It was so unlikely that we could be in the same classes and not have recognized each other, that we actually spent a fair amount of time in the initial chat comparing notes on where we lived, who our professors were, who we knew etc…  Freshman year, he lived one dorm over in a complex of about 2000 students.  The next year, we both moved up to the newer North Campus dorms and again lived a couple of dorms apart, and for the remaining two years we both lived in apartments that were about three blocks from each other.

It turned out that we probably didn’t take classes together because we were six months out of sync on the prerequisites, but largely knew the same people and had the same professors.

What came next floored me. He not only grew up his entire life in my hometown, but I discovered he lived two streets away from where I had lived my entire life up to that point.  He had gone to a different school system and was on the other side of a major street that I had rarely crossed. He was as convinced as I was that even if we had somehow crossed paths, we had never seen each other before.

So when people bring up stories of chance encounters that demonstrate what a small world it is, I like to bring up my counter story of what a BIG world it is. For twenty years, I lived within two hundred yards of a person with very similar interests, went to many of the same playgrounds, stores, and parks and yet were still complete strangers.

(For the statistically inclined, college size was 16,000 students. Class sizes were about 40 people. The population density of my hometown is 15,000 people per square mile. The number of people who lived on the two streets in question is about 250. The rest is an exercise for the reader 🙂


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 201. Take a look and leave your comments below.

I love this story. There is, of course, nothing shocking about the coincidences except that the men did not remember each other at all. This should not be the case given the size of the school and the proximity of their childhood homes. And yet it is not surprising at all to me as a psychologist who has studied attention and memory.

The fact of the matter is that the author almost certainly interacted with the interviewee many times and simply did not notice or remember him. It is even more interesting that neither noticed the other while they were in college. I would expect at least that “I know you, don’t I?” feeling.

We all probably encounter many of the same strangers often, but without an interaction that is out of the ordinary, we don’t even encode their faces. If human beings were not so selective, we would be unable to function as we would need to sort through enormous amounts of information on a constant basis. Instead, we encode what we think might be important later and store it as connections to other bits of information.

To see this for yourself, try to draw the heads side of a penny–right now, without looking at one.  You have seen hundreds in your lifetime and you can probably recreate the gist of the coin and some of the details, but do you know where to put everything? Did you draw something that is actually on the tails side? Is the date in the right place? Which direction is Lincoln looking?

For some fun and interesting demonstrations of selective attention and memory, I highly recommend “The Invisible Gorilla” by Daniel Simons, a psychologist who has studied this phenomena.

Update and Apology

Dear wonderful people who read our blog and listen to our mini-podcast on Skepticality,

It’s been drawn to our attention recently that the reduction in story submissions we’ve noticed as of late isn’t due to some unique alteration in the earth’s magnetic field that’s caused our loyal fans to stop thinking to tell us every time something ridiculous happens to them but is, in fact, due to an unknown technical error that’s keeping us from receiving their stories. That’s right, apparently you’ve been sending us stories that we never received! The horror! The inhumanity! The fruit cake!

So with this in mind, we’ve switched our contact form from a third-party add-on to the newer form WordPress supports directly in hopes that we’ll get more reliable submissions. In addition, it allows for a much prettier, better-formatted submission page, so EVERYBODY WINS*!

Which leads us to a request: If in the last couple of months you’ve submitted a story to us and NOT received a personal thank-you from a member of our team (nearly always Wendy), please resubmit it now via the normal Submit page, or at least send in an inquiry to make sure we didn’t miss it. We’ll be eternally* grateful, and you’ll get your second shot at fame and fortune*.

Thanks as always for your support, and we look forward to your story submissions. Again. And sorry. Again.

*This claim has not been verified.

(Submitted by reader Cathy Smith)

My best friend in Jr. High was Lisa Butland.  We were both Air Force brats, stationed in Germany at the time.  By the time we graduated high school, our families were transferred to Texas, hers to Austin, and mine to San Antonio.  Afterwards, I moved to California, and we completely lost touch with one another.

Over ten years later I was back in San Antonio, and my boyfriend lived at the German House Co-Op, by the University of Texas campus.  One of the residents, Mark, looked vaguely familiar to me, but it took me a few visits to figure out why.  The kid with the Coke bottle glasses he reminded me of was only about twelve years old the last time I saw him.  As soon as I realized who he might be, I knocked on his bedroom door.

“Mark?” I peeked my head in the door.  The room was dark because the shades were still drawn.  Mark was in the top bunk, and his eyes were squinting because he did not have his glasses on yet.

“Yes?”  he said.

“Did you ever live in Germany?” I asked.

“Yes?”  he responded looking puzzled.

“Was your dad stationed at Hahn Air Force Base?”  I asked with a big smile.

He hesitated.  “Yes?”

“Is your last name Butland?”  I was getting excited.

“Yes?”  He sounded slightly disturbed.

“Do you have a sister named Lisa?”  I continued.  He obviously could not see the expression on my face.

He looked a little worried.  “Yes?”

“Do you remember a Cathy Sexton?”  I asked.

At this point, his eyes opened as wide as they could.  He took a big gasp of air and in an astonished voice exclaimed:  “You know Cathy Sexton?!!”

That was about twenty years ago.  As soon as he realized that I was Cathy Sexton, he gave me his sister’s number, and Lisa and I have been best friends ever since.


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 200. Take a look and leave your comments below.

I’m sure that you can guess what I’ll say about this one: it’s not so surprising, but it’s interesting nonetheless!

The most common coincidence stories seem to be related to meeting people with whom they had a past connection. They are very significant to the people who experience them, but the truth is that they are less interesting statistically than one might think.This case is no different; she met the brother of her long-lost friend not far from where she left them and they were probably close in age and socioeconomic status, increasing the probability of frequenting the same places.  As often is the case, I find the story about how they discovered the connection more interesting than the connection itself.
The majority of stories are either about someone the author clearly recognized or a conversation which leads them to realize that there is some deep personal connection, usually geographical. I have rarely heard stories in which the author’s memory is jogged after a few exposures to an individual.
We all meet people who seem very familiar and sometimes it takes us some time to put our finger on why. This is so common that it was used as a plot device (ever see the movie “The Arrival”?). But the vast majority of those cases involve a distinctive feature or mannerism which is shared by someone we know well rather than a person we have actually met before. For example, everyone with an underbite reminds me of a cousin I was close to while growing up.
But the fact that the author eventually figured it out and acted on it (and that it turned out to be someone she actually knew) makes this story unusual.

Similar Soldiers

(Submitted by reader Robert Wilson)

I joined the Royal Australian Air force in 1972. During the ’70s recruitment was high, so it was not uncommon to have  flights of 20(ish) trainees graduating each week or so. On my first pay parade (we all got paid in cash after a lengthy line up) we all stood at-ease awaiting our name to be called out.

When the paymaster shouted out our names, family name first, first name last, we would then snap to attention and march forward for our pay.

This is how it went:

“Wilson, Robert”…. two of us stepped forward!

No problem thinks the paymaster as he glances down at the pay slip and announces, “Wilson, Robert, William”

The both of us stood firm!

He then read out the 6 digit ID number, and we were separated by less than 100 numbers if memory serves (numbers are issued sequentially which just means we joined about the same time).

So, what are the odd of having identical names, and joining the air force within weeks of each other?


Below are the extended notes provided by Barbara Drescher for use in Skepticality Episode 200. Take a look and leave your comments below.

It’s not easy for me to put numbers on the probability of this happening because name frequencies in Australia were hard to find. However, I did find that the names “Robert” and “William” were as popular there in the 1960s (I assume that the author was between 17 and 25 when he joined) as the were in the U.S., where they took the 5th and 7th spots, respectively. As we’ve seen in past episodes, “Robert” is an enduring name; it was the #1 name for baby boys for decades and has not left the top 100 in more than a century. In the 1960s, “Robert” was the first name in 14,000 boys for every million born and “William” in every 10,000. There is no readily-available source to determine the probability that “William” would be chosen for a middle name, so the first name frequency will have to serve.

The surname name of “Wilson” is also a very common one, but it is difficult to determine just how common it was in Australia at that time. Today, “Wilson” is ranked 5th, occurring in 5,037.98 of every million people. This has probably changed a bit since the 1960s, but it’s our best estimate.
So, 140 of every million boys with the first name of “Robert” will have the last name of “Wilson”, and 1.4 of those will have the middle name “William”. This means that, for every 10 million men this author will meet around his age, 15 will probably share his full name.
The probability of joining the Air Force so close together adds a degree of complexity and to do it justice would require more accurate information about the distributions of these names across ethnic groups and as well as the distribution of ethnic groups in the military. Without that information, my best guess is the probability that another man in a selection of 100 will have this name, given that the author does, which is about 1 in a million.