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I went to Bitmain's home website one day when I saw the S21 Hyd. I ran calculations on that and found out it could pay for itself every 4 months (after power bills). So, how come Bitcoin mining operations don't double over a specific time period e.g. every 4 months? Assuming you have a good paying job, and you just want to get a lot of miners until a point, after only three years, you have 1023 miners, making 25,000 dollars per day. And then in another 3 months this turns to 50k, and so on. What controls the growth of Bitcoin mining operations?

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That is exactly what is happening: Bitcoin’s hashrate is growing exponentially, except that the growth is limited by the speed at which new hardware is produced and deployed. (A line with a positive slope in a logarithmic chart indicates exponential growth.) A chart of Bitcoin’s overall hashrate on an exponential scale.
via bitcoin.sipa.be

The network’s hashrate has increased by 37% since May with 11 adjustments increasing difficulty and only three adjustments reducing difficulty.

Difficulty adjustments since May
via btc.com

As long as mining is profitable, miners invest in additional hashrate to corner a larger share of the entire mining reward. Hardware manufacturers come out with more efficient models that replaces prior models. Miners with less profitable operations go out of business or shut down their less profitable hardware.

I would be a naïve miscalculation to expect that your hardware will pay for itself in four months, though. Just as you are deploying your new hardware, so will your competitors. Your profitability will decrease significantly in the coming four months compared to today’s network outlook, and you will need to adjust your expectations accordingly.

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I ran calculations on that and found out it could pay for itself every 4 months (after power bills).

I'm rather skeptical of that. My first Google result was here. As of 27 Nov 2023, it's listed as having a gross yearly income of $9,444.62, electricity costs of $5,557.25 at 0.12/kWh, and net of $3,887.37. The lowest price listed is $5,368.73, for 497 days or 16.5 months to pay back.

And this is based on spot prices. Just because the numbers at the moment work out to be profitable, doesn't mean that they will be in the long run. And 16.5 months is a somewhat long run to be depending on profit/expense numbers to be holding steady. And this website it's not available yet, so if it really is profitable, then once it does become available, the hash rate, and hence the difficulty will spike upwards. Furthermore, I suspect that there are costs that aren't being factored in. The nature of the difficulty mechanism means that absent a breakdown in basic economics, the net risk-adjusted profit is driven towards zero.

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