The law of large numbers

On 11 November 2017 (11-11), I went to Groningen with my wife and son by car. While driving, I noticed the date and time displayed on the car’s clock. The date was 11-11, and the time was 10:35. It made me think, ‘Wouldn’t it be nice to look at the clock at exactly 11:11 today because it is 11 November (11-11).’ Within a second, I noticed the distance recorder standing at 111.1. It had been 111.1 kilometres since I last filled up. Peculiar coincidences can occur by chance. With eight billion people on this planet and so many things transpiring, these things happen.

An example illustrates this. Imagine you have five dice and make a throw. A remarkable incident is throwing five sixes. If you roll the five dice only once, it probably doesn’t happen. On average, it only occurs once every 7,776 times. But if you throw the dice a million times, it happens 128 times on average.

If a reset of the distance recorder occurs every 500 kilometres, the chance of 111.1 kilometres appearing on it is one in 5,000. The distance recorder was not far from the clock, so I would probably have noticed a peculiar number on it after seeing the date. The probability of the distance recorder being on 111.1 might have been 0.02%. The likelihood of the thought about 11:11 popping up on 11 November is difficult to establish, but in my case, it was not low.

The birthday problem demonstrates strange coincidences happen more often than we might think. If you share a birthday with another person in a small group, it might strike you as odd, but the chance of someone sharing a birthday with another person is already 50% in a group of 23. However, two people sharing a birthday is not a mind-blowing coincidence. It is not as remarkable as the incident with the distance recorder.

When you are a member of this group, the probability of you being one of the persons sharing a birthday is much smaller, namely 6%. Meaningful coincidences are likely to happen, but less likely to you. So, if many people experience the same and think it is merely a coincidence because coincidences occur more often than you might think, they suffer from what you might call a collective delusion. Imagine a group of 24 all sharing a birthday with one other group member, so they share 12 birthdays, and they all think, ‘Nothing exiting to see here. The odds of me sharing a birthday with another person in this group are over 50%.’

Taking a smaller sample reduces the likelihood of meaningful coincidences. If you randomly pick two people, the chance of them having the same birthday is only 0.3%. So, if you run into someone else who happens to share your birthday, and it happens again with the next person, it is noteworthy. If it happens another time with the following individual, you might wonder whether there is more to this universe than mere chance. The more elaborate a scheme, the less likely it is to transpire. The probability of three people sharing a birthday in a group of 23 is 1.3%, and for five, it is only 0.0002%. If your life is riddled with elaborate, meaningful coincidences, you might start to believe that you have a critical role in the universe.

Possible avenues to circumvent the law of large numbers

There may be a way to find out there is no such thing as coincidence. If some of the most significant historical events come with peculiar coincidences, that might be more telling for two reasons. First, there are only a few, so the law of large numbers doesn’t apply. After all, it is a small sample. Suppose no intelligence is coordinating events in this universe. In that case, it is less likely that meaningful coincidences will turn up in this sample, and elaborate schemes will be unlikely to emerge. Second, if the most significant historical events come with peculiar coincidences, it becomes more likely that history is scripted than when peculiar incidents transpire in someone’s personal life.

To make the argument, you need to answer questions like, what are the most important historical events, and what are peculiar coincidences? Events such as the sinking of the Titanic or the Kennedy assassination might not qualify, even though the coincidences surrounding them form a strange and elaborate scheme. The extent of these schemes might compensate for that, but it is hard to tell. The beginning and the end of World War I meet the requirements. D-Day, the fall of the Berlin Wall, and the terrorist attacks of 11 September 2001 are among the most important historical events.

And what should I think of the number of meaningful coincidences in my life? It is not possible to establish the likelihood of that happening. You can make assumptions to arrive at an idea. A highly unusual coincidence, such as the do-it-yourself store incident, could be likened to throwing five sixes with five dice. The chance of such an event happening in any year in any life could be one in 7,776. If something similar transpires again that year, it is like throwing five sixes twice in a row. The chance of that would be one in 60,000,000. On average, 120 people would experience something similar each year. But what if more similar incidents occur in one life? Or if 100,000 people have this instead of 120?

I have shared a few of my coincidence stories on the Reddit/SimulationTheory message board. Others also experience similar situations. Only the people on that message board are not a random group, but a select group of individuals who believe we live in a simulation, often because they have witnessed similar phenomena. Some of these stories are as remarkable as mine. I can’t verify these tales, but I believe most aren’t frauds because similar things happened to me. The question remains whether they have seen strange incidents occurring in the numbers I have seen.

There is a point where you must admit that these things are not merely coincidental. We can’t establish that point objectively. The number of possible unusual events is infinite, so the chance of something strange happening, such as the do-it-yourself store incident, could be higher than we intuitively think. It seems impossible to accurately estimate the odds. Still, without intelligence coordinating events in this universe, we should expect these incidents to be distributed more or less evenly across all people and time frames.

Even then, significant deviations from the average are possible. Lightning strikes only a few people. It happens to some people twice, which might seem odd, but there is nothing suspicious about that. If lightning strikes one in 10,000 people once, then one in 100,000,000 gets hit twice. But how would you explain if one person ran into lightning ten times, and this individual did nothing unusual? Statistically, it can happen. More likely, there is a cause, such as living in a dangerous spot. There is a point where we must assume these stories are evidence of us living in a simulation. We can’t establish that point precisely, but whether we live inside a simulation or not doesn’t depend on our assessment. We are, however, inclined to see causes behind remarkable situations or events, but they may be accidental.

The limits of our minds

We are good at attributing causes, but we do poorly at estimating the likelihood of an event. The psychologist Daniel Kahneman provided an example. It is a study of the incidence of kidney cancer in the counties of the United States. The research revealed a remarkable pattern. The incidence of kidney cancer was the lowest in rural, sparsely populated counties in traditionally Republican states in the Midwest, the South, and the West.¹ So what do you make of that?

You probably came up with reasons why kidney cancer is less likely to occur in these counties, such as a healthy rural lifestyle or low pollution levels. You probably did not think of randomness. Consider then the counties in which the incidence of kidney cancer is the highest. These counties were also rural, sparsely populated, and in traditionally Republican states in the Midwest, the South, and the West.¹

How can that be? Those counties all had small populations. And with smaller samples come more sizeable deviations from the average. Our intuition makes connections of causality, but our reason does not verify whether it could just be randomness. We like to think some cause makes unusual things happen, while they might be random accidents.

When we consider the most significant historical events, we run into problems if we use this small sample to establish that someone is ‘writing history’. On the other hand, comparing this sample to a sparsely populated rural county may not be apt. It is more fitting to compare this sample to the royal family, as it encompasses the most significant events in history. If a high incidence of kidney cancer were to turn up in the royal family, an experienced physician would tell you it is probably not a random issue.

I am a single individual, the smallest possible sample. Some people get struck by lightning twice. It could even happen three or four times, but the chance of it happening ten times is so insignificant that no one will ever experience that unless they live in a hazardous spot. Is the number of meaningful coincidences in my life enough to rule out chance? That number is extraordinarily high. It is not chance. The question arises: Am I just a random individual, or do I live in a dangerous location, or has destiny given me a unique role, such as proving that we live in a simulation? Others have this, too. And so, a lengthy series of peculiar incidents doesn’t suffice to believe the latter.

The things that could have happened but did not

In 1913, the ball fell on a black number twenty-six times in a row at the roulette wheel at the Casino de Monte-Carlo. Some people lost a fortune by betting the ball would fall on red the next time. They did not realise the chance of the ball choosing a red number never changed. The ball does not remember where it went the previous times. If we represent black with a B and red with an R and assume, for simplicity’s sake, there is no zero, we can write down falling twenty-six times on black like so:

B B B B B B B B B B B B B B B B B B B B B B B B B B

The probability of the ball falling on black twenty-six times in a row is one in 67,108,864. That is a long shot. What might surprise you is that the following combination of black and red numbers is precisely as likely to occur:

R B B R B R R B R B B R R B R R B R B B R R B B R B

You wouldn’t be thrilled if that happened unless you became a millionaire by betting on this particular series of twenty-six. And even then, you wouldn’t think of the 67,108,863 sequences that did not materialise. We tend to consider only the things that did happen, but we rarely think of all the things that could have transpired but didn’t. Events such as the ball falling on black twenty-six times in a row impress us. And I am even more impressed because twenty-six happens to be my lucky number.

This argument applies to meaningful coincidences but not to a prediction materialising, as such a feat may imply that all the other things couldn’t have happened. If I say with firm conviction that the coming sequence of black and red would be R B B R B R R B R B B R R B R R B R B B R R B B R B and it happens as I predicted, I may have the gift of prophecy. The chance of me being accidentally right was one in 67,108,864.

Imagine the probability of you sitting here reading this page on a tablet or a mobile phone, but as a prediction from 3,600 years ago. Imagine Joseph telling the Pharaoh: ‘I see (your name comes here) reading a pile of papyrus pages, not real papyrus pages, but papyrus pages appearing on something that looks like a clay tablet. Do not be afraid, dear Pharaoh, for it will happen 3,600 years from now. But if we do not set up this grain storage, it will not happen, so we must do it. And by the way, Egypt will starve otherwise.’

The chance of this prediction coming true was not one in 67,108,864, nor was it one in 1,000,000,000,000,000,000,000. Adding more zeroes doesn’t help. The chance is far smaller than any number you can ever write down. It is so close to zero that no one can tell the difference. Nevertheless, you sit here reading this text, perhaps even on a tablet. How could this happen? The answer to this mystery is that many things could have occurred but did not; however, something had to happen, and that is what transpired. In any case, Joseph couldn’t have made such a prediction by accident.

The licence plate number

What about the reference to the end date of World War I on the licence plate of Franz Ferdinand’s car? Few historical events are as significant as the start and end of World War I. And so, the law of large numbers doesn’t apply here. It is one of the most important historical events, thus part of a sample comparable to the royal family. A mere accident seems unlikely. The assassination could have gone wrong; cooler heads might have prevailed, or the war could have proceeded differently, ending on a different date.

It might have been possible to guess the end date of World War I once it had started. If you presumed that the war would not take more than twenty years, a random guess of the end date could be correct one in every 7,305 times. But something doesn’t add up here. Hardly anyone expected the war to last longer than a few months. The licence plate originates before the war. The assassination succeeded after a series of mishaps. If the licence plate number contained a prediction, that prediction included the assassination succeeding, Franz Ferdinand dying in this particular car, and this event being the trigger for the war.

That is hard to do. And so Mike Dash in the Smithsonian noted, ‘This coincidence is so incredible that I initially suspected that it might be a hoax.’² Only, it is not a hoax, so investigative minds could have probed other options, but they did not. Conspiracy theorists also ignored it, even though this incident agrees with their beliefs of a secretive plan being behind history.

In the conspiracy scene, a story circulates about a Freemason named Alfred Pike, who allegedly disclosed a secretive plan of the Freemasons to bring about the New World Order. Pike supposedly predicted both world wars with uncanny precision in 1871. Nobody had ever heard of this plan before 1959, when an ‘investigator’ ‘uncovered’ it. Contrary to the licence plate number, the story has no substance. It is a hoax. In the Netherlands, they would call it a monkey sandwich story.

Seeing meaning

Authors use symbolism, hidden meanings, themes, and stylistic figures. Events in their lives, as well as the writings of other authors, influence their writings. Literary critics look for those meanings. You can check out what experts wrote about the poem The Waste Land by T. S. Eliot. You will be surprised. Some authors marvel at what literature critics discover in their works. Apart from intention, there can be an unconscious influence. And so, seeing meaning is more like an art than a science. A scientist would argue there is no proof and that it is baseless speculation because science isn’t about meaning.

He spent a number of years at this project
And now he knows how an electron behaves

The Nits, Mountain Jan

You can’t understand intentions and meaning from investigating the conduct of electrons. Meaning in literature is often intentional. If someone wrote the script running the events in this world, the author might do what other authors do. And so, the licence plate number on Franz Ferdinand’s car could signal foreknowledge of future events or even control over them. The sceptics argue from a scientific perspective, while those who see meaning act like literary critics. Who is right about the meaning of AIII 118 depends on whether there is a script and, therefore, an author.

Sceptics might claim that AIII 118 is a random sequence of characters, but we see a reference to the end date of World War I. That is how our minds work. The argument is odd. If you take it to the extreme, this text is also a random array of characters, as is any book or report. And still, you read words and sentences that have meaning to you. Indeed, the licence plate number would have remained unnoticed if the war had not ended on 11 November 1918.

However, the war ended on 11 November 1918. AIII 118 is the car’s licence plate number that drove Franz Ferdinand to his appointment with his destiny. And destiny is the message the licence plate number radiates. It suggests premeditation concerning the assassination, the start of the war and its end on 11 November 1918. That is a meaning we can see without too much imagination. There are plenty of instances and locations where this sequence of characters could have turned up, so their presence in this particular spot is noteworthy. AIII 118 on a fish barrel in Vienna wouldn’t have attracted attention. Ditto for the licence plate number ABII 117 on that particular car.

Sceptics can also be fanciful. Austrians speak German. Armistice in German is Waffenstillstand. So why does it not read WIII 118? Or even better, W1111 1918? If someone sends you a message, you don’t quibble about such details. If I said ‘hello’ to you, you wouldn’t ask me why I didn’t utter the word ‘hi’ instead. That is, unless you are a philosopher with a lot of idle time and have a hobby of questioning everything. Great Britain, the United States and France were all major participants in the war. These countries all use the term armistice. And if the sceptics come with outlandish arguments, you have won the argument. Only, they disagree. Not seeing meaning is the art of being a moron. Communication with morons is, therefore, problematic.

Asking yourself which licence plate numbers were available in the Austrian-Hungarian Empire may be a better idea. You could check which combinations fit the purpose. There aren’t that many options. Perhaps, you end up with just one match: AIII 118. That makes it harder to believe that this sequence of characters is meaningless. This scheme became even more inconceivable because the war ended on 11 November (11-11), the most peculiar date of the year.

Only a few historical events are as important as the assassination of Archduke Franz Ferdinand and the Armistice of 11 November 1918. You can think of D-Day, the fall of the Berlin Wall, and 9/11. The coincidence scheme surrounding D-Day is extensive, and the recurrence of dates is intriguing. The involvement of Hans van Mierlo is also mind-boggling. It also relates to the Curse of the Omen, a film released on the anniversary of D-Day, as well as the untimely passing of Senator Robert Kennedy on 6 June (6/6) and Martin Luther King on 4 April (4/4) 1968. A historian correctly predicted the fall of the Berlin Wall in 1989, while the coincidences surrounding the terrorist attacks of 11 September 2001 are dumbfounding. In other words, this incident doesn’t stand alone.

A final argument may be that such extensive or peculiar coincidence schemes don’t appear in other historical events that are equally significant, such as the American, French, Chinese, and Russian revolutions. These events are marked by a few peculiar coincidences, such as Thomas Jefferson and John Adams having their appointments with the Grim Reaper on the same day, which happens to be 4 July, thus Independence Day. That is noteworthy, but perhaps not sensational. The parallels between Napoleon Bonaparte and Adolf Hitler might also raise some questions. Somehow, the licence plate number of Franz Ferdinand’s car is more exceptional, most notably because of it being so precisely predictive.

The Chinese Revolution of 1911 began on 10 October 1911. It marked the end of 2,000 years of imperial rule in China. The date, 10 October (10/10), is not as remarkable as 11 November (11/11), even more so because there are no related coincidences. The Russian Revolution led to the establishment of a communist empire that lasted for seven decades. A bad omen marked the coronation of the last Czar of Russia, Nicholas II. The communists later murdered him and his family. You can ask why these events don’t seem part of a coincidence scheme. It is like asking why several members of the Royal Family don’t have kidney cancer. Well, they haven’t. That’s all there is to it. Perhaps, it is not satisfactory to philosophers with a lot of time on their hands, but it will have to do.

Hindsight bias

And then there is the benefit of hindsight. Countless strange incidents could have occurred, but they didn’t. We notice only things that did happen and don’t think of those that didn’t. That is hindsight bias. The sample of the most significant historical events comes with the benefit of hindsight. There is a danger to that approach, and it is unacceptable in science. It is like selecting only the data that confirms your theory. You might have a theory about gravity, saying that all objects will fall to the ground. And you prove your theory by ignoring the heavenly objects and the birds in the sky, so everything you investigate falls to the ground. It later turned out that gravity works that way, and ignoring the heavenly objects and the birds in the sky put you on the right track.

With hindsight, you know things you can’t learn in advance. Hindsight knowledge is also a favourite tool of critics when something goes wrong. However, when you use hindsight to find evidence, your critics argue you can’t. That’s how the critics play their game. They might clip a bird’s wing feathers and then ask the bird to prove it is a bird by flying. But if you use clipped birds to prove your theory of gravity, they might criticise you for that as well. You can’t beat your critics in their game. No evidence will ever convince them. So I won’t try. This wasn’t science in the first place, but metaphysical speculation.

Using hindsight, thus, is the only way to conduct this investigation, as we can’t predict the occurrence of meaningful coincidences. If this universe is genuine, we can’t establish that it is authentic. However, if it is a simulation, we may discover it is a simulation. So, if there is meaning, we must look for it to find it. We should be careful, as we are inclined to see intent when it could have happened accidentally. With that in mind, it is still fair to say that meaningful coincidences related to the most important historical events are likely not mere coincidences. Combined with the other evidence, we can establish that we live inside virtual reality, probably a simulation created by an advanced post-human civilisation.

Latest revision: 24 July 2025

1. Thinking, Fast and Slow. Daniel Kahneman (2011). Penguin Books.
2. Curses! Archduke Franz Ferdinand and His Astounding Death Car. Mike Dash (2013). Smithsonian. [link]