#### Probability theory is a convenient oversimplification of the randomness of our universe, just as most cryptocurrency trading algorithms represent an oversimplification of the markets.

https://medium.com/media/203f229b2167225afdc4001b6eb67461/href

George Crowley was very good at any job, so long as the job never required him to look beyond the tip of his nose.

So it was no surprise then when he dropped out of high school and bounced from job to job before ending up as bricklayer.

Day in and day out, Crowley would trudge to new job site after job site, laying bricks with the precision and passion of a man who knew nothing else.

And in Crowley’s case, that was true.

Part of the reason why he had never been any good at school was because Crowley never understood what any particular subject was for, what was it’s practical purpose?

With bricklaying, at least things were clear, a wall not laid straight will collapse one day — it didn’t matter if it were a small council house in the suburbs of London or a 100-floor office tower in Canary Wharf.

So one day, when a co-worker noticed the degree of meticulousness with which Crowley was laying every brick, he couldn’t help but ask the hunched-over Crowley,

“Mate, is this necessary, you’re just laying a brick wall?”

Crowley, smiling, looked up and replied,

“To you I may be doing nothing more than laying a brick wall, but to me, I see myself as laying down a city.”

#### Snapshots of A Bigger Picture

Which brings us to probability theory.

Scientists have long used probability theory to make sense of an otherwise chaotic universe.

Like a bricklayer only sees each additional brick he or she lays, without probability theory, predicting the future is virtually impossible because all we have are snapshots of windows in time.

The bricklayer sees the brick, the cement, the trowel, but not the building, the neighborhood, or the city.

Which is why theoretical physics is possibly the most powerful tool we have as far as making predictions go, it’s sort of like handing the building plans to the bricklayer.

Because we can measure how the Universe behaves on cosmic scales, we can gain information about the laws and rules that it follows and its composition.

Using these measurements, scientists are able to apply the rules gleaned from them, use different compositions and wind the clock back using simulations to see what comes out of the atomic mix.

#### Cloudy With A Chance Of Meatballs

And for the most part, our observations sit well with what our simulations predict, but every so often, we get find phenomena that had very low probability of occurring — what statisticians refer to as “thin tails.”

But these “thin tails” have a possibility of upsetting everything we know about probability and that can often lead to some, well, misleading inferences.

To demonstrate, let’s take that most scientific of experiments — the coin toss.

Now all things being equal (*ceteris paribus* if you like), assuming the coin is perfectly balanced, the probability of the coin landing heads or tails is, one would assume 50/50.

Putting that data into a computer simulation, flipping as many imagined coins as many times as good husbandry demands, and recording all the possible results imaginable, you could choose how you’d divide the different flips up.

And as any statistician will tell you, size *does* matter, sample size in this case — but not how you’d imagine.

So whether it was a thousand flips or a billion flips in a row, with that data, you have your observations.

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Another way of course would be to simply calculate the probabilities based on the number of variables in a coin toss, and in this regard, the math is pretty straightforward.

In general, however, most physical processes that we’d simulate are far too complicated, and one would need to reduce errors further by making a more accurate or comprehensive simulation.

Now with all of the modeling out of the way, it’s time to play for all the marbles — by performing actual coin flips and comparing them against the simulations (comprehensive or otherwise) and the results can be quite extraordinary.

Let’s start with a manageable number of flips, say 10.

Even before we begin, most of us, instinctively at least, would anticipate that we’d get 5 heads and 5 tails.

But the odds of getting 5 heads and 5 tails in a 10-flip coin toss is only about 25%.

And the odds of getting all heads or all tails is in the region of 0.2%.

But as it turns out, the odds of getting 5 heads or 5 tails in a row isn’t as low as you would think, at about 10%.

Of course some of the discrepancies with our coin toss have to do with the sample size — a bigger sample size would make things clearer surely?

Not exactly.

#### More Observations More Ambiguity

While the odds of getting 100 tails or 100 heads in a 100-flip coin toss are comically low, the odds of getting 60 heads or 60 tails in that same 100-flip coin toss is a more realistic 5.7%.

But while there’s a 38% chance of getting at least 6 heads in a 10-coin toss, there’s only a 2.8% chance of getting at least 60 heads in a 100-coin toss.

https://medium.com/media/b3a4d8328a015695d27e9268c68bb584/href

And expanding that sample size to 1,000 tosses makes things worse, at a one-in-a-billion that 600 tosses are heads out of a thousand.

That’s the thing about sample sizes, bigger doesn’t always mean better — more data is only as useful as it can help to distinguish between a random fluctuation and what could be a meaningful flaw in a model.

Which goes some ways to explaining why a lack of data when trading cryptocurrencies hasn’t hampered the ability of well-oiled algorithms to deliver returns consistently.

#### It’s Mathematical

The mathematics that underpins something as seemingly simple as a coin toss can also be applied to many areas of science, from biology to particle physics, cosmology to astronomy and yes, even to cryptocurrency trading.

By taking the same laws and components, but randomly determined initial conditions, a simulated Universe can answer questions as diverse as the age of the Universe to what Bitcoin’s price will be in the next few hours.

And for the most part, many of the things that scientists (and traders) have simulated with regards to the Universe line up precisely as expected, just as on a balance of probabilities, successful cryptocurrency trading algorithms are more often right than wrong.

But there are also just as many observations in the Universe which are inconsistent with simulations, as there are cryptocurrency trading scenarios that don’t square with expected market behavior.

Take for instance temperature fluctuations in the Universe, where only 1 in 770 simulations are consistent with actual observations.

And when it comes to dark matter, our simulations can be off by as much as 1-in-a-billion.

https://medium.com/media/dbb25f40650cf83693dc21b06a598dc7/href

Which is why someone dissatisfied with current models may point to these inconsistencies and allege that our simulations of the Universe are completely broken.

Or when cryptocurrency trading portfolios swing wildly, that the algorithms must be broken — but that wouldn’t be quite right either.

When examining the Universe (or cryptocurrency markets), we’re deliberately looking for any deviations from our expectations, but our expectations are based on our *current* understanding of how the Universe and the market behaves, the composition and what the laws are as we know them today.

Similarly, when developing cryptocurrency trading models, many of the variables and assumptions are based on the market depth, trading volume and price action of what has *already* been observed.

If observations deviate from expectations, we have to consider the possibility that in some way, we may have gotten the laws, composition or initial conditions wrong.

And if a cryptocurrency trading algorithm loses money, we have to consider that the data, assumptions or the time frame selection may have been off.

But even assuming that there are no errors, there’s another altogether different possibility that our Universe or the market condition is simply a unique and highly improbable set of circumstances as we know them.

Or in the case of cryptocurrency trading — that there is market manipulation.

Looking at the Universe and testing it for anomalies in a million different ways, we’d expect to find at 45,500 of them at 2-σ significance, 2,700 at 3-σ significance, 63 at 4-σ significance and even 1 at 5-σ significance — what is considered the “gold standard” for any discovery in physics.

Despite that, sometimes the unlikely just happens by random chance and that’s just a reflection of the Universe we get.

https://medium.com/media/ba5f3dac19c36a5c52e3eb1574c15226/href

In the same vein, the cryptocurrency market sometimes can blindside even the most fervent manipulator.

If we had billions upon billions of Universes to observe, we could know whether ours was more or less par for the course.

We could know in what ways we were statistical outliers and we could reconstruct what the laws, composition and initial conditions of an “average” Universe truly are.

But just like any individual in our population, our observable Universe is bound to be typical in some ways, atypical in others, and to possess a few extremely rare properties.

Similarly for cryptocurrency trading, the vast majority of market conditions, especially as the number of participants has increased, is probably closer to average than most would assume.

Part of the challenge and why the behavior of cryptocurrency prices can be so unpredictable is that the average cryptocurrency doesn’t have a very long “observable period” of existence.

If we had billions and billions of cryptocurrencies, each with very long trading histories to observe, we could determine then with a relatively high degree of accuracy, any “reversion to the mean” and any deviation from that.

But we don’t, we have the data that we have.

An outcome that appears “unlikely” could be a hint that one of our assumptions about the properties of that cryptocurrency is flawed — but that isn’t necessarily the case either.

Even unlikely outcomes sometimes occur, and with more cryptocurrencies to observe than just Bitcoin, it’s impossible to know which outliers point to a real problem with our models versus which ones are simply due to a cryptocurrency’s particular uniqueness — sometimes manipulation — or what trading professionals call “market variance.”

Just like the Universe however, low probability events observed in the cryptoverse, must be viewed with suspicion because unlike the randomness that is the Universe, such outliers almost always suggest market manipulation.

Outside of these statistical “outliers” just like in the universe, most of the things that we do simulate with market behavior do happen — and really, that’s all you need.

Just like a cryptocurrency trading algorithm doesn’t need to be right 100% of the time to be profitable, scientists don’t need to model accurately 100% of the time to give us a good understanding of the Universe.

We just need to build on our understanding of the cryptocurrency markets and the Universe, by layering on our knowledge, one brick at a time.

We’re Probably Wrong About the Universe & Cryptocurrencies Too was originally published in The Capital on Medium, where people are continuing the conversation by highlighting and responding to this story.

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