Important NOTE: The term “bitcoin” in this article refers to BOTH bitcoin and bitcoin cash since at the writing of this article it is unknown which one of these crypto-currencies that in the future will represent the dominating chain (and hence in the author’s view should be referred to as bitcoin).  

Introduction

Forbes states that in year 2017 there exists approximately 2000 billionaires in the world measured in US dollar terms.

This is a very exclusive group of people compared to the total population of the world which currently is 7.5 billion people. Most people would probably like to be part of this exclusive billionaire club, but naturally this is not achievable for most people. However, most people would feel great just to climb the wealth ladder up to a fraction of a US dollar billionaire.

If we make a thought experiment that bitcoin in the future will play a dominating role in the world economy, the following interesting question arises:

       How many bitcoins do you need to own to reach a certain wealth level in the future?

This article tries to answer this question.

Wealth level definitions

To define wealth level we will make use of the famous pareto principle, first discovered by economist Vilfredo Pareto, which is a principle that is applicable in many areas of our everyday life. The pareto principle is also known as the “80/20 rule”, which means that 80 % of the effects come from 20 % of the causes. Vilfred Pareto discovered for instance that 80 % of the land in Italy was owned by 20 % of the population.

Assuming that the 80/20 rule can be applied on bitcoin wealth distribution we define the wealth levels according to: 

Wealth level 0 definition:

Wealth level 0 is defined as the average number of bitcoins hold by the 80 % of the population that will own 20 % of all bitcoins according to the 80/20 rule.

Wealth level 1 definition:

Wealth level 1 is defined as the average number of bitcoins hold by 80 % of the people that are not part of the population belonging to wealth level 0.

Wealth level 2 definition:

Wealth level 2 is defined as the average number of bitcoins hold by 80 % of the people that are not part of the population belonging to wealth levels 0 and 1.

...

Wealth level N definition:

Wealth level N is defined as the average number of bitcoins hold by 80 % of the people that are not part of the population belonging to wealth levels 0, 1, 2, …, N-1.

Wealth level calculation

With the wealth level definitions in place, let us now use the 80/20 rule to calculate how many bitcoins you need to own in order to be considerably richer than the average person (wealth level 0) in a future world dominated by bitcoin.

As input for the calculations we will use the following numbers:

• World population: 7.5 billion
• Number of bitcoins: 21 million

Wealth level 0 (the ordinary net worth person):

Applying the 80/20 rule we get that 0.8 x 7.5 billion = 6 billion people will own 0.2 x 21 million = 4.2 million bitcoins, i.e. on average 4.2 million / 7.5 billion = 0.0007 bitcoins per person at wealth level 0 (=the ordinary wealth level).

Wealth level 1:

Now to the really interesting part, if working with a large data set, which we do here (7.5 billion people) the pareto principle can be applied again to calculate the amount of bitcoins needed to achieve wealth level 1.

Applying the 80/20 rule on the population not belonging to wealth level 0 we get that 0.8 x (7.5 - 6) = 1.2 billion people will own 0.2 x (21 – 4.2) = 3.36 million bitcoins, i.e. on average 3.36 million / 1.2 billion = 0.0028 bitcoins per person at wealth level 1.

This is a quite eye-opening result meaning that to be 0.0028 / 0.0007 = 4 times richer than the average person in the future (given that bitcoin becomes a major part of the world economy) would require only 0.0028 bitcoins. At today’s bitcoins prices at about $5000 / bitcoin this translates into a modest investment of only $14!

Please note that in a global economy, a person with a net worth 4 times the average person has considerably better ability to invest in a higher living standard for example a house/car/holidays etc. 

Wealth level 2: 

Applying the 80/20 rule again on the population not belonging to wealth level 0 and 1 we get that 0.8 x (7.5 – 6 – 1.2) = 240 million people will own 0.2 x (21 – 4.2 – 3.36) = 2.668 million bitcoins, i.e. on average 2.668 million / 240 million = 0.0112 bitcoins per person at wealth level 2.

Please note that in today’s bitcoin prices it is still very cheap to acquire 0.0112 bitcoins (about $56), which would be sufficient to reach wealth level 2. Achieving this wealth level means additional possibilities to raise your living standard in a future world dominated by bitcoin, i.e. bigger house/better car/more holidays etc. 

Wealth level N:

We can see that each time we apply the 80/20 rule like this it corresponds to a big step up on the wealth (and social status) ladder, i.e. 4 times more wealth than the previous wealth level. So how many bitcoins would it require to join the exclusive US dollar billionaire club mentioned in the introduction of this article?

Here are the calculation results:

• Wealth level 0: On average 0.0007 bitcoins (held by 6 billion people = the average person)
• Wealth level 1: On average 0.0028 bitcoins (held by 1.2 billion people)
• Wealth level 2: On average 0.011 bitcoins (held by 240 million people)
• Wealth level 3: On average 0.045 bitcoins (held by 48 million people)
• Wealth level 4: On average 0.18 bitcoins (held by 9.6 million people)
• Wealth level 5: On average 0.72 bitcoins (held by 1.92 million people)
• Wealth level 6: On average 2.9 bitcoins (held by 384 000 people)
• Wealth level 7: On average 11 bitcoins (held by 76 800 people)
• Wealth level 8: On average 46 bitcoins (held by 15 360 people)
• Wealth level 9: On average 184 bitcoins (held by 3 072 people)
• Wealth level 10: On average 734 bitcoins (held by 614 people) 

As you can see from this data, wealth level 10 approximately matches the US dollar billionaire club, i.e. 614 people compared to the 2000 USD billionaires existing today. To reach wealth level 10 you need to invest in approximately 734 bitcoins today, which is beyond reach for most people, but do you really need to be on wealth level 10 to thrive; wouldn’t you be pretty happy to be just in wealth level 1-5? These wealth levels are still affordable to many people measured in today’s bitcoin prices.

Please note that the higher wealth level estimates are less reliable since the underlying data set used in the calculation is smaller (less people at the higher wealth levels).

Please also note that the wealth level estimates above are probably conservative since  

• The population is growing, i.e. there will be more than 7.5 billion people in the future, i.e. less bitcoins available for each person.
• Some bitcoins are not available since they have not been mined (yet).
• There will always be bitcoins lost forever due to people losing their private keys.
• A large amount of bitcoins are already owned by a very small group of people, here are two examples:
  • Satoshi Nakamoto potentially controls around 1 million bitcoins.
  • The MtGox Exchange robbers probably controls several hundred thousands of bitcoins.

Note that the 80/20 rule is sometimes also referred to as the 70/30 rule or the 90/10 rule, which one of these rules that best maps the future bitcoin distribution is anyone’s guess but the truth should be somewhere within the range described by these rule candidates. This article presented the results when applying the 80/20 rule but the calculation can easily be repeated applying instead a 70/30 or 90/10 rule.

The important take home message from this article is that the calculations in this article indicate that only a small amount of money invested today could bring you up considerably along the wealth ladder in a future dominated by bitcoin.

Disclaimer: Please note that this article should not be seen as investment advice, you are yourself responsible for your investment decisions.