I recently saw a headline about a "solo miner" successfully mining a Bitcoin block and receiving the coveted 3.125₿ mining reward. Actually, there's been a few of these stories in the past couple months. It always generates a bit of buzz in the Bitcoin community; it's proof that the Blockchain is truly decentralized and anyone can participate in it. All you need is an internet connection and a computer.

It's also sort of analogous to seeing a headline about someone winning the lottery. But does seeing a story like that ever entice you to go buy a lottery ticket? For most people, the answer is no, because it's common knowledge that the lottery is a bad investment and the odds are stacked against you.

But this made me wonder, is that the case for Bitcoin mining too? And what are the variables that will turn it from a bad investment into a good one, if so.

Mining Today

The reality of Bitcoin mining today is that it's become extremely centralized. Just 4 companies provide over 75% of the current global hashrate. And one company, Foundry USA, owns about 1/3 of the total hashrate. This is not ideal—a distributed network is fundamental for ensuring transactions in the ledger are authentic, censorship resistant, and correct. Too much centralization of mining makes the network susceptible to a 51% attack.

Therefore, it's important that Bitcoin mining continues to be accessible to the general public. And since the only real motivation for participating is financial, it's crucial for the investment to be profitable, somehow.

How does one determine the profitability of mining bitcoin? Mining the next block in the blockchain involves finding a specific random hash, so it's probabilistic in nature. A simple approximation for a probabilistic outcome is to calculate the expected value (EV) of participating in the network, and then compare that with the cost of doing so. This is straightforward to calculate with a few assumptions, which I will explain below.

The Expected Value of Bitcoin Mining

Expected Cost

I'm going to start with calculating the EV of running a single consumer grade bitcoin miner. This can be considered the "base case" that we can extrapolate from afterwards. There are several companies producing these mining units; I'm going to choose one popular and somewhat recent model: the Bitaxe Gamma 600 Series.

Here's the specifications we need:

• Energy consumption: 17 W
• Hashrate: 1.2TH/s
• Cost: $220 CAD

Source 1 Source 2

I'm based in Canada, so I'm going to use the average cost of electricity in Canada for this calculation. According to energyhub.org, the national average residential cost of power is $0.192 CAD/kWh.

I'm also going to assume you run the miner 24 hours a day for 3 years straight. This provides the time frame to amortize the purchase cost of the miner. It also makes the math easier because we don't need to consider the next bitcoin halving event in 2028.

Putting it all together, the cost of running a single Bitaxe miner per month is calculated as follows:

Expected Cost = Energy Cost + Amortized Purchase Cost
= ($0.192/kWh * 0.017kW * 720h) + $220 / 36
= $2.35 + $6.11
= $8.46

So purchasing and running a Bitaxe Gamma 600 Series will cost you $8.46 a month roughly.

Expected Income

Now let's calculate the amount of money you can expect to make. Lets start with the current global hashrate for bitcoin mining. According to CoinWarz, the current hashrate is sitting just below 1 ZettaHash per second (ZH/s). It's not often I get to use a unit prefix like zetta, so that's exciting. Zetta is a trillion billion.

Total hashrate
= 1 ZH/s
= 1000 EH/s 
= 1_000_000_000 TH/s

The hashrate fluctuates quite a bit and will likely keep increasing in the future, but for this calculation I will assume it's 1 ZH/s.

Source

The current mining reward, until 2028, is 3.125₿. At current prices, this equates to $367,900 CAD for every successfully mined block.

The Bitcoin network is designed to produce a block every 10 minutes. It will adjust the difficulty level for mining blocks based on the recently seen hashrate, algorithmically, to ensure the network maintains a steady production rate of blocks. Therefore, we can expect roughly 4320 blocks to be mined every month.

The expected value calculation is simply the chance you will successfully mine a block multiplied by the value of that block's reward. We can approximate the probability of that happening by dividing the hashrate of our Bitaxe by the total hashrate in the network.

Expected Income
= 1.2 TH/s / 1_000_000_000 TH/s * 4320 * $367_900
= $1.91

So, according to the math, you can expect to make $1.91, while spending $8.46 a month, mining bitcoin with a single Bitaxe Gamma 600 Series, in Canada. This equates to a return on investment of -77%.

The Expected Value of Playing the Lottery

Now, just for fun, let's compare this to buying a lottery ticket. Fortunately someone on GitHub already did the necessary calculations for me (Thank you keitchchhh!).

Source

This analysis is specifically for the lotteries available in Ontario, Canada, where I live.

The expected values here are based on a single $3 play and is dependent on the jackpot value. Even the low end, $1.40, your expected return on investment is only -53% so it's already a better investment than solo bitcoin mining.

So in conclusion, buying a single consumer grade Bitcoin miner is probably not going to make you rich. You'd be better off playing the LottoMAX. But this begs the question, what do you need to do to make mining profitable?

1. Mine Bitcoin 2. ???? 3. Profit

I asked an LLM to make a calculator based on all these variables so you can play around with the numbers and see what sort of changes can turn the ROI positive.

Next, I made some graphs showing how all these different variables affect the overall ROI. The data visualization code is available on my GitHub here.

For all these graphs, I kept all the other variables the same as our "single-Bitaxe-miner-running-for-3-years-straight-with-average-energy-prices-in-Canada" example above. I just varied one input at a time to see the effect on the profitability.

First, here's the effect of the global hashrate.

At the current levels of ~ 1000EH/s, the profitability of your single Bitaxe is basically bottomed out. But it exponentially increases as total hashrate decreases, reaching profitability around the 225EH/s mark.

Next, let's look at how the cost of electricity affects the ROI.

It doesn't affect it much. Even if electricity was free, the ROI would still be -68%, which suggests, in this Bitaxe example, most of the cost is coming from the hardware itself and not the power it consumes.

Next, what if we suddenly time travelled back to 2008 when the mining reward was 50₿? And let's pretend it still had the same exchange rate it does today. Would we be profitable then?

Yes, we would be. In fact we'd only have to travel back to 2012 to receive an awesome 84% return on our investment. Of course, this example is pretty baseless since the mining reward and the overall price of Bitcoin are highly correlated.

Speaking of the Bitcoin price, how do changes in its exchange rate with fiat currencies (like the Canadian dollar, in my calculation) affect our ROI? Let's see.

It has a positive linear relationship, which might have been obvious to the more statistically inclined readers. If we entered a bull market where the price of 1₿ exceeded $500,000 CAD, our single Bitaxe miner would be looking like a good investment all of a sudden.

But yet again, the price of Bitcoin is not entirely independent of all the other variables in our equation. Namely, the total hashrate in the network would likely increase as Bitcoin's price rises. That's just how a free market works.

Here's the ROI compared against the number of years you keep your Bitaxe miner running. Let's just pretend the mining reward stays the same.

Even if you kept your single Bitaxe running for 20 years straight, and thus were able to amortize the cost of the hardware over that entire period, you'd still be sitting at a -40% ROI. I guess it's not about how long you play the game either.

So what is in our control? Obviously, it's how big of a mining setup you have! Instead of 1 Bitaxe, lets buy 100!

Huh...I guess it's going to help much. In fact, it wouldn't help our ROI at all. Even if you owned a million Bitaxe Gamma 600 Series and ran them 24/7 for 3 years, your return would still be -77%.

What I've learned is that what really determines your mining profitability are 3 things:

1. How much your energy costs
2. How much the mining hardware costs
3. How energy efficient the miners are, calculated in Joules per Terahash computed (J/Th

The first one is entirely dependent on how you source your electricity for mining. The last two are based on the miner you choose and can be compared nicely using this site: https://www.asicminervalue.com/efficiency

For example, if we look at the #1 rated miner for efficiency on that site, the Bitmain Antminer S21 XP+ Hyd—it boasts a hashrate of 500Th/s while consuming 5.5kW of power, which results in an efficiency of 11J/Th. Compare that with the Bitaxe Gamma, which has an efficiency of 14J/Th. Admittedly, that doesn't sound like much more. But when you scale to computing 1000s of Terahashes per second, all that energy saving makes a difference.

For instance, if we could lower our energy cost from the national average of 0.192 $/kWh down to 0.05 $/kWh, then mining with the Bitmain Antminer S21 XP+ Hyd would result in an ROI of 9%. If we bought a lot of them and got a bulk discount of 15% on the hardware too, suddenly our ROI jumps to 23%. And if we could keep them running for 5 years instead of 3, our expected return on investment is now 71%.

So there's an example of a way to make mining profitable.

Conclusion

This was a highly simplified analysis. There was a bunch of things I didn't consider:

• Hardware maintenance cost
• Cooling cost (lots of miners generate an insane amount of heat)
• Bulk discounts or buying used hardware
• All the correlations between these variables

So don't take this as financial advice to go buy 100 Antminers and put them in your basement. But I hope you learned something.

Let me know in the comments if I made any egregious statistical errors in my analysis, or didn't account for something else important! Feedback is always appreciated. Thanks for reading.