What are the odds?

[Ivan Seeking]

Depending on how you break things down, it can be surprising how many seemingly highly unlikely events we can expect to occur in life. I became interested in this subject and once even tried to calculate the odds of a few amazing coincidences I've had in my own life.

Have you had any experiences that seemed to be a one-in-a-million or worse? Not to say they defy logic but might seem to do so.

One of the most unlikely experiences I've had occurred when I was a teenager riding with a buddy on a long-distance bicycle/camping trip, riding from Long Beach, Ca. to Hemet, Ca. and then up Mt San Jacinto. We had to ride on back roads (bicycles aren't allowed on freeways) and finally ended up in (what was then) the middle of nowhere; at least 60 miles or more out in the middle in the desert. It was very hot and we hadn't seen any cars or anyone or any buildings for a couple of hours or more. We had heavy packs to carry and it was slow going. We were really feeling the isolation! But then, in the distance we saw a figure approaching us. Before long we could see it was a rider on a horse...a female rider who began to look familiar as she got closer and closer. Finally we were face to face. She was a young lady I was friends with in school!

I don't know who was more shocked, her or me! It turned out her family had some property nearby. They often spent the weekends out there. This was at least 70 miles from my school, which was in a metropolitan area of 5 million people or so back then. This always struck me as one of the most unlikely events in my life. I guess the most unlikely fact of all is the fact that each of us exists.

 

[Baluncore]

Events that are not planned are unlikely, but there are a very great many possible unlikely events. The probability, that an unspecified unplanned event will occur, is a certainty.

Humour, is the arrival at the one point, via two separate paths, one obvious and normal, the second quite unexpected. A funny thing happened today, I bumped into ⋅⋅⋅ from ⋅⋅⋅ .

Once an unlikely event has happened, (the statistical path has collapsed), it is a certainty. Going back, to compute the probability of what is now a certainty, ignores all the coincidences that you did not predict previously, or you failed to recognise when they happened. What is the probability that you will recognise a coincidence?

I guess the most unlikely fact of all is the fact that each of us exists.

If you did not exist, then one could not notice such a self-referential coincidence.

 

[Ivan Seeking]

If you did not exist, then one could not notice such a self-referential coincidence.

The sperm that made me beat out 80-300 million competitors.

 

[Tom.G]

So what is the coincidence? With 300 million competitors there is virtual certainty that one would cross the finish line.

 

[PeroK]

Depending on how you break things down, it can be surprising how many seemingly highly unlikely events we can expect to occur in life. I became interested in this subject and once even tried to calculate the odds of a few amazing coincidences I've had in my own life.

Have you had any experiences that seemed to be a one-in-a-million or worse? Not to say they defy logic but might seem to do so.

I don't know who was more shocked, her or me! It turned out her family had some property nearby. They often spent the weekends out there. This was at least 70 miles from my school, which was in a metropolitan area of 5 million people or so back then. This always struck me as one of the most unlikely events in my life.

Let's say you know about 500 people as well as you know that old friend from school. We all know hundreds of people from school, work, hobbies and socially. If we allow that the person could have been any one of five million, that's only 10000-1 against you knowing them. That event in itself is clearly unlikely, but you should expect several such events in a lifetime.

PS I suspect that once you take into account your age at the time and the likelihood of people of your age being in such a location, the odds might be considerably higher.

 

[javisot20]

A highly improbable event is winning three consecutive times at European roulette (36 numbers + single 0, 1/37) by betting only on a single number, and not always the same number.

 

[PeroK]

A highly improbable event is winning three consecutive times at European roulette (36 numbers + single 0, 1/37) by betting only on a single number.

It makes no difference whether you bet on the same number each time!

 

[javisot20]

It makes no difference whether you bet on the same number each time!

I know, it's called the gambler's fallacy and the law of large numbers. In honor of the truth they cheated.

(It begins to be a more probable event when you place bets out of time practically seeing the ball fall into the box. Winning 3 consecutive times doing that is the perfect number of times to get kicked out of the casino for cheating...)

 

[PeroK]

Just imagine that on a given weekend of the NFL season, you had to guess the score in every game. There are 16 games every week, I believe. The odds against guessing them all correctly (assuming you can't fix the games in some way) are impossibly low. And, yet, every week there is a set of specific scores. So, every week the near impossible happens!

This should teach us that we have to be careful about the criteria we have for judging whether something truly unlikely has happened. In this case, it's probably quite simple to see why nothing remarkable has happened, but in other cases, the determination becomes a lot more difficult to see.

 

[pinball1970]

Just imagine that on a given weekend of the NFL season, you had to guess the score in every game. There are 16 games every week, I believe. The odds against guessing them all correctly (assuming you can't fix the games in some way) are impossibly low. And, yet, every week there is a set of specific scores. So, every week the near impossible happens!

This should teach us that we have to be careful about the criteria we have for judging whether something truly unlikely has happened. In this case, it's probably quite simple to see why nothing remarkable has happened, but in other cases, the determination becomes a lot more difficult to see.

I have had this discussion with people arguing the impossible happens for a reason (a topic we do not discuss here)
Your NFL game reminded me of an example I gave.
All the atoms in the rock that is mount Everest are real, exist and are in a certain configuration.
Adding all of those positions up would give a huge number in terms of odds that that atom would be there, in that specific location in the mountain on this day
Yet they are there, you can climb it and countless atoms are added every year as the mountain grows every year due to tectonic activity.
Each year, each day a slightly different configuration with gargantuan odds that will be the case every time you measure it (if you could)

Nothing special about Everest, it just sits there doing it's thing, no magic required and no odds to worry about.

 

[Baluncore]

Nothing special about Everest, it just sits there doing it's thing, no magic required and no odds to worry about.

I would like to thank Mt Everest and its statistics, for the mountainous part it plays each year, in selecting volunteers for the Darwin awards.

 

[pinball1970]

I would like to thank Mt Everest and its statistics, for the mountainous part it plays each year, in selecting volunteers for the Darwin awards.

Ouch! A little bit harsh. I am just glad that my passions do not require I put myself against the elements and obstacles.

Hand on heart and in the spirit of the thread, the one time I thought odds seem to be in my favour?

Walking with a friend I loved dearly, a female, attractive, on way back from the pub at night.
Both of us at a lowish point personally.
We stopped talked talking looked at the sky and saw a shooting star.
First time ever for her, second time for me.
We were together soon after and referenced that night.

I would have to break down each part to see the likelihood of each event.
Town light contamination, meteor occurrence. Not a miracle but I thanked my shooting stars.

 

[Ivan Seeking]

Let's say you know about 500 people as well as you know that old friend from school. We all know hundreds of people from school, work, hobbies and socially. If we allow that the person could have been any one of five million, that's only 10000-1 against you knowing them. That event in itself is clearly unlikely, but you should expect several such events in a lifetime.

PS I suspect that once you take into account your age at the time and the likelihood of people of your age being in such a location, the odds might be considerably higher.

I did try to break the problem down once. But it didn't take long to realize this is all terribly difficult to quantify.

Haha, I see that I started this thread 20 years ago!
https://www.physicsforums.com/threa...ble-real-life-coincidences-or-are-they.16317/

 

[pinball1970]

I did try to break the problem down once. But it didn't take long to realize this is all terribly difficult to quantify.

Haha, I see that I started this thread 20 years ago!
https://www.physicsforums.com/threa...ble-real-life-coincidences-or-are-they.16317/

My moments involve relationships. Not the bus that missed me by a few mm.

I am glad those moments happened.

 

[glappkaeft]

Have you had any experiences that seemed to be a one-in-a-million or worse?

I once walk up to a miniature gaming table just as a friend launched 12 missiles of some sort from his Warhammer 40K figures (Space Marine Dreadnoughts/Terminators/something like that, I don't play WH40K).

The missiles hit on 2 or more on a six-sided die and he rolled 12 dice in one go and all turned up ones. That is 1 in 2,176,782,336, the entire room of 15 or so on-lookers went silent.

 

[Ivan Seeking]

I once walk up to a miniature gaming table just as a friend launched 12 missiles of some sort from his Warhammer 40K figures (Space Marine Dreadnoughts/Terminators/something like that, I don't play WH40K).

The missiles hit on 2 or more on a six-sided die and he rolled 12 dice in one go and all turned up ones. That is 1 in 2,176,782,336, the entire room of 15 or so on-lookers went silent.

Don't you think it is more likely that you hallucinated the entire thing?

 

[glappkaeft]

Don't you think it is more likely that you hallucinated the entire thing?

If it wasn't for the fact that there where many of us there that remembers it, yes.

 

[Hornbein]

I once walk up to a miniature gaming table just as a friend launched 12 missiles of some sort from his Warhammer 40K figures (Space Marine Dreadnoughts/Terminators/something like that, I don't play WH40K).

The missiles hit on 2 or more on a six-sided die and he rolled 12 dice in one go and all turned up ones. That is 1 in 2,176,782,336, the entire room of 15 or so on-lookers went silent.

Is one the best number?

 

[Hornbein]

While playing bridge I once saw a suit play out like this.

JQKA
789T
3456
2

I'm too lazy to calculate the odds of such a thing.

At a supermarket the total was $77.77. The checkout lady said, the customer before you had the same.

 

[PeroK]

While playing bridge I once saw a suit play out like this.

JQKA
789T
3456
2

I'm too lazy to calculate the odds of such a thing.

We can do an approximate calculation by imagining that the cards in this suit get dealt at random, regardless of how many cards each player already has.

Someone has to have the Ace. The probability they also have the K, Q and J is approx $(\frac 1 4)^3 = \frac 1{64}$. The probability that someone else has the Ten is about $\frac 3 4$. And the probability they also have the 9,8 and 7 is again about $\frac 1 {64}$. The probability that someone else has the 6, 5, 4 and 3 is about $(\frac 1 2)(\frac 1 {64})$. Then, finally, the probability that the last player has the 2 is about $\frac 1 4$.

We can multiply this by 4 to cover all four suits.

That gives a probability of approximately $2^{-20}$, which is $10^{-12}$.

You must have played a lot of bridge!

 

[Hornbein]

I meant that the first trick was JQKA. Someone played the jack, the next player the queen, the third the king, and so forth. The second trick similarly was 789T, the third trick 3456 making the two a winning card on the fourth trick. Things get complicated because different players could have had the lead on each of the four tricks. Also there's a psychological factor : the players aren't required to "cover" the previous card, so that makes a serious estimate impractical.

I haven't played bridge for twenty years but I like logic so I follow an online group of expert bridge players. Last week one mentioned that in a tournament a computer dealt him a hand with twelve spades missing only the two. That's about fifteen billion to one. Or if you don't care which spade is missing then about a billion to one. If you also don't care which suit then a mere three hundred million to one.

Such probabilities are calculated by knowing that the possible number of bridge hands is about 640 billion and they are all equally likely.

 

[glappkaeft]

Is one the best number?

No, one is the only value that would cause a miss in this case and 2 or more would result in a hit so they would be equally good. The expected value from launching 12 of those missiles is 10 hits, he got none.

 

[Hornbein]

No, one is the only value that would cause a miss in this case and 2 or more would result in a hit so they would be equally good. The expected value from launching 12 of those missiles is 10 hits, he got none.

Aha, so it was the worst number. And the only bad number, so that made it more notable than any other number. All fives would have been pretty impressive, but not as much cachet.

 

[Ivan Seeking]

If it wasn't for the fact that there where many of us there that remembers it, yes.

I wasn't serious. It is a typical debunking dodge.
As for your paid witnesses.... :D

 

[Ibix]

The missiles hit on 2 or more on a six-sided die and he rolled 12 dice in one go and all turned up ones. That is 1 in 2,176,782,336, the entire room of 15 or so on-lookers went silent.

I used to do tabletop wargaming as a kid. My personal worst was a total miss with three twenty-sided dice needing 18 or less ($1/10^3$) and three needing 19 or less ($1/20^3$), a one in eight million chance. To add insult to injury (or lack thereof, considering I missed) I did it with three nineteens and three twenties.

 

[DaveC426913]

It makes no difference whether you bet on the same number each time!

I had a tough time convincing my (scientist) brother than you are as likely to win the lottery on the numbers 1 2 3,4,5 6,7 as any other set of seven numbers.

 

[gmax137]

“You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!”
― Richard P. Feynman, Six Easy Pieces

 

[gmax137]

I was visiting an old friend in Boston. We went to a local bar after dinner. A couple of seats down the bar two guys were talking.
"Where you from?" the first guy asks
"Ireland, County Cork"
"Why, I'm from County Cork! Near to Healy's Bridge."
"Me dear mum lives near Healy's. She goes to St. Katherines."
"I was baptized in Katherine's!"

My buddy and I were listening, unable to believe this coincidental meeting. We asked the bartender, didn't he think it was amazing? "Nah," he says, "That's just the Flanagan brothers getting drunk."

 

[Mondayman]

I've had two run-ins with police while quite intoxicated and probably should have ended up in the tank.

The first was years ago. I got taken home and given a ticket, with explicit instructions that I had to speak with the officer in person the next day. He wanted to talk to me about life choices (I was quite young).

Years later, I read a news article about dealing with public intoxication in a humane way and ensuring people who aren't a threat to others or themselves are able to get home or somewhere safe. There were two officers in the article. One of whom was the officer who took me home.

Fast forward a few more years, I got into an absurd kerfuffle at a work party. I didn't instigate anything but I definitely didn't do myself any favors (such as asking the constable for her number). I recounted how I was previously taken home by police to the constable who was questioning me, and told her about the article. She decided to look it up to see if I was being truthful. She laughed and said this is my ticket home. The leading sergeant on the scene was the second officer in that news article.

I was told that if you're drunk enough to ask for a cops number, you're drunk enough for the drunk tank. But in the end, the sergeant allowed me to get a ride home. With a warning that I'm probably not going to get that lucky again. I live in a big city with a large police force. Most would rather dump people off in the slammer. I ended up getting the two Mother Theresa's of dealing with public disputes and intoxication in seperate incidents 15 years apart. The chances were fairly slim.

Before anyone suggests it, I have quit drinking since then.

 

[Hornbein]

At a supermarket the total was $77.77. The checkout lady said, the customer before you had the same.

The odds against that are about one hundred million to one, if you think 77.77 is a special number. I say that no other number would have as much cachet.

I met a young lady from Toronto who had 1) been praying to meet a certain guy and 2) was working in a doctor's office. She called up a patient and left a reminder that they had an appointment. The wished-for man showed up instead. She had dialed a wrong number which happened to be his. At the time there were maybe a million telephones in Toronto so it isn't as unlikely as two $77.77s but it's more dramatic. On the other hand, what were the odds that anyone would show up for a doctor's appointment they didn't know anything about? I wouldn't.

The relationship didn't work out though. In her wishlist of requirements for the ideal man she had failed to specify that he shouldn't be on hard drugs.

 

[Hornbein]

Then there was the time the University of California at Santa Cruz statistics students dressed up as gangsters and showgirls and had a casino party. They had a roulette wheel with play money. Everyone but me bet wildly. They broke the bank [won all the play money] in about fifteen minutes.

And people think statistics is boring.

 

[nsaspook]

Unlikely but nice! Just dropped in a twenty to have a drink while sitting at the slot machine with 75 cent bets.

 

[Hornbein]

So what is the coincidence? With 300 million competitors there is virtual certainty that one would cross the finish line.

What? In humans conception occurs in about 1 in 50, uh, events.

 

[Ivan Seeking]

So what is the coincidence? With 300 million competitors there is virtual certainty that one would cross the finish line.

Regardless, the odds against my existence were 80-300 million to 1.

Put another way, when I was born, the world won the lottery.

 

[Ivan Seeking]

Okay, I posted this in the photos thread because it was such a nice example of Google stitching images incorrectly, This is a four door, not a six door.

What I didn't mention was the reason for me noticing this image in the first place. Another view reveals I owned the identical make, model, year, and color automobile. It is identical to my old car. It is about a 20 year-old vehicle in this photo.

It is parked in front of the home I lived in as a very young child.