The Math Behind $1 Million Bitcoin

Nik Bhatia (0:00)

I believe Bitcoin is heading to $1 million sometime in the early 2030s, and that is based on my belief in the Bitcoin power law. Today, I'm going to explain to you why I still believe in the power law and what it tells me about Bitcoin's future price.

Welcome back to The Bitcoin Layer, I'm Nik Bhatia. Today's video is about the power law. What is it and why do I still believe in it? And finally, what does it tell us about when Bitcoin might get to not six figures, but yes, seven figures and $1 million? We'll start here on the Bitcoin tab of TBL Pulse, our incredible data terminal available at the bitcoinlayer.com. And I will scroll down, we can see some of these charts that we have on our Bitcoin valuation section, but we'll focus here on the Power Law Quantile Chart. And I will expand this to show you Bitcoin's Power Law. We will go first to the entire price series of Bitcoin and its Power Law. Now, you will see Bitcoin's price is on a logarithmic scale here, the price history going all the way back to 2010 And you can see Bitcoin at $0 at that time. That's just Bitcoin at a few cents rounded down to $0.

And then by the time that we reached this point in 2013, Bitcoin had surpassed $1,000 for the first time. It surpassed $10,000 then in 2017

It surpassed $100,000 for the first time in 2025

And then the next big milestone to add another zero, or what we call another order of magnitude, when will Bitcoin get to $1 million? Well, between $1,000 and $10,000, it took Bitcoin about four years to get from $10,000 to $100,000. It took about eight years. So might we expect another 16 years, or eight years for Bitcoin to get from $100,000 to $1 million? I believe somewhere in that eight year time horizon to get Bitcoin to that $1 million mark. What is it based on? It's based on something called the power law. Now what is the power law? The power law is a mathematical relationship between two things. It shows how one thing grows in relation to another. With Bitcoin's power law, we're looking at Bitcoin's price in relation to time. These hold a power law relationship, which you can see represented by this curve. Now of course Bitcoin chops up and down above and below. Not only its power law, but some of these power law ranges. One standard deviation above and below the power law. On the bottom pane, you can see how Bitcoin has performed relative to its power law or where it sits relative to its power law. Sometimes when it's in red here, it's way above its expected level. And when it's in green here, that means it's way below green, meaning a good time to buy when Bitcoin is trading cheap to its power law. Now, the power law itself, the thing that I love about the power law is that the exponent, which is the variable that you try to solve for, to understand the relationship between Bitcoin's price and time, that exponent has been discovered by Dr. Giovanni Santostasi several years ago.

That exponent, when applied to Bitcoin's price history, it gives us this curve.

And so the relationship between time and price for Bitcoin essentially comes down to one exponent.

The input is time, the exponent is that variable, and the output is price. So Bitcoin's power law price is a very simple formula.

The basis for the math, it goes back to how things scale in nature and also in human civilization. One of my favorite examples is the education level of a locality will increase as the population increases, but not on a linear basis.

It increases with a power law of an exponent larger than one. This basically means that as the population of a city grows, the number of educated people will grow at a faster pace than the population growth. And that results from people being in one place and having the desire to make their society better, form schools, form universities, and then pursue a greater standard of living. If you want more information on this, I recommend Jeffrey West's book Scale, which was recommended to me by my two favorite Bitcoin mathematicians, Stephen Perrineau and Giovanni Santostasi. Dr. Santostasi recently published a book about Bitcoin called The Physics of Bitcoin. I strongly recommend people check it out if they want to understand a deeper overview of Bitcoin's mathematical properties. Back to the power law. We did several episodes this summer on the cold card incident, and a lot of you have been rethinking your setup ever since. My takeaway is that self-custody works, and it's best when no single device or vendor carries all the weight. CASA, today's sponsor, secures your Bitcoin with five keys instead of one, and it's held on hardware from different manufacturers plus your phone, and CASA holds one key for recovery. No single vendor can touch your funds and neither can CASA because moving funds takes three keys and CASA only has one. Their most popular offering, CASA Premium, they ship an onboarding kit right to your house with the hardware devices, the Faraday bags, and everything else that you will need. They pair you with an advisor who will walk you through the setup on a call, and the security advisory team is available for you for as long as you are a member. Check out CASA at casa.io and use code TBL for 10% off of your subscription. And I will zoom in here going to a trailing five-year time horizon. And now you can see this blue line, which is the power law line. This steady increase, it means that, or the reason that it looks like the steady linear increase is that the Bitcoin power law only has one input, which is time. So every day that goes by, the power law price goes up. That's the math of it. It doesn't chop around, doesn't go up or down. The power law just gradually goes up. Now I've done the math and I have my spreadsheet to show me that Bitcoin might get to a million dollars sometime 2031, 32, 33 That is when the Bitcoin price has essentially accumulated enough days that when we raise the exponent, the power law exponent and apply that to the number of days Bitcoin has been alive, you get to a seven-figure Bitcoin price. So is that possible? Is that likely? I do believe it is because I see Bitcoin adhering to its power law here over the last five years. Now, go back to the last two years and you might say, hey, Bitcoin is traded below its power law and even materially below some of the bottom bands of the power law expectation here for a lot of 2026 And I would say that that is a fair critique. But go back to five years. What did you see in 2022? You saw a similar level Bitcoin trading below this dotted green line. And for a long time too, it started trading below here in September of 22 and didn't truly recover it for good until October of 23 So over a year. What about this time? It first lost it around February of this year. So not that long ago. And are we back above this green dotted line? Not even. So Bitcoin has a lot of work to do. But if it can recover this bottom band of the power law, consolidate and then start to work its way back on up, that's another several year period where we can doubt whether the power law is going to hold or whether it actually has any magnetic force on the Bitcoin price or if investors think that that's what Bitcoin should be valued at.