# Is this the truth about mining?

## Cross-checking bitcoin mining data

### SHA256 ASIC Mining vs Cloud Mining, bitcoin mining efficiency, and more.

Cloud miners barely taking a cut. The upper limit of mining per GHS. And the most exact mining calculator yet.

Scientific Modelling, Problem Solving, Optimization, Bitcoin, Cloud-Mining, Mining

September 25th, 2014

Perhaps you were thinking the same I was thinking: do the cloud mining providers take a big % of your profits? Apparently not. I've had the pleasure of receiving some data from another cloud mining service (MegaMine.com), and some ASIC mining. Since the data I received was from an interval of about a month and a half, I was not very happy to start inferring a formula about it. So I decided to check its numbers against mine, and to my surprise, they almost matched.

Cloud Mining BTC/GHS deviates, on average, 4% from ASIC Mining

In the sample, it deviates more times above than below the average. Aside from that, I believe this has implications that go beyond mere comparison of hashing power. Now I can estimate how much to spend per GHS, on every mining solution, in one formula.

### How much will I earn per GHS?

If you've got a savvy eye, you might have seen that one of the constant coefficients of the earnings formula in the previous article is very close to Phi, the golden number. Although this might be only a coincidence.

y = (x - 1.61913159457706) / (12340.5916664742 + 81.1765090417067*x)

1.61803398874989 / 1.61913159457706 = 99.93% of phi

Specifically, this function represents what you can expect earning from an investment in one GHS, after X days starting from April 13th 2014, with an average absolute deviation of 0.00000739. Since it is very likely that one of those constants is phi itself, I ran the inference one more time with that constant fixed. This modified the other two constants a bit, but the average absolute deviation stayed the same.

y = (x - 1.61803398874989) / (12340.5406806778 + 81.176332636651*x)

Those two constants come from the abstract entrails of an AI, but the model works. Let's say for instance that you bought mining power at 0.0064 BTC/GHS, on April 13th 2014. You want to know when are you going to be on break-even, so you do:

0.0064 = (x - 1.61803398874989) / (12340.5406806778 + 81.176332636651*x)

(12340.5406806778 + 81.176332636651*x) * 0.0064 = (x - phi)

78.97946035633792 + 0.5195285288745664 x = (x - phi)

78.97946035633792 + phi = 0.4804714711254336 x

80.59749434508781 / 0.4804714711254336 = x

167.74 = x

And that's precisely when break-even is achieved: September 27th 2014. I had mine arrive a bit sooner because of some referral GHs that were free, but this is exactly on point: 5 months and 17 days.

What really surprises me of this equation is that I thought it only applied to cloud mining providers. By checking what scarceâ€”but relevantâ€”data was provided to me today, I found that its returns correlated just fine to regular SHA256 ASIC mining. Given some conditions, this has implications that I didn't take into account before.

For instance, no GHS mining since April 13th 2014 will produce more than 0.01231886 BTC, no matter where they come from. That is the positive horizontal asymptote of this function, and remind yourself that this figure accounts for mining earnings from transaction fees. If that portion of earnings increases, the function will change for the better.

### How long will my mining equipment be profitable?

This has a lower bound: the cost of electricity. Which its fair to say that varies between 0.08 and 0.4 USD per KWh around the world. The ASIC that provided my new data is a Rockminer R-Box (34 GHS) that coupled with its Raspberry Pi controller consumes about 48 watts an hour, or 1.152 KWh a day.

For the sake of argument we'll have this R-Box running until it can't produce more than it consumes, and we'll fix the electricity costs at 0.08 USD per KWh and 450 USD/BTC. Given the above function this would be:

f(x) - f(x-1) = electricity cost = 0.09216 USD / 34 GHS = 0.00020480 BTC / 34 GHS

electricity cost = 0.00271058 USD/GHS = 0.00000602 BTC / GHS

A = 12340.5406806778, B = 81.176332636651, PHI = 1.61803398874989

f(x) - f(x-1) = (x - PHI) / (>A + B*x) - ((x-1) - >PHI) / (A + B*(x-1))

f(x) - f(x-1) = (A + B*PHI) / (A + B (x -1)) (A + B * x)

0.00000602 = (A + B*PHI) / (A + B (x -1)) (A + B * x)

x = 409.189

If you tried to solve this with 0.00020480 instead of 0.00000602, you already know that there is no solution in which x is a positive value; and since those values are out of the question in this model, there's no solution in which that value is profitable enough to pay its electricity. However, this is not the case here.

According to this model, that R-Box will keep producing until 1 year, 44 days, 4 hours, 32 minutes and 9.6 seconds pass. In that time-frame it will have made 0.30417744 BTC, which is about 72.62% of the asymptote. That little miner's productive life would end on May 27th 2015. However its profitable life barely started, since its capital costs are about 142 USD (~0.31 BTC), and its maintenance costs about 37.71 USD, which gives us a net loss of about 42.83 USD.

All of this takes into account that the R-Box started on April 13th 2014. If it were plugged right now, you would have to start from a position further into the future. Should you begin today, you would have to start from x = 163, doing f(x) - f(163).

### What if efficiency does not rise in the future?

Let's assume a mild scenario, BTC price stays the same, hashing efficiency stays the same and transaction volumes (and fees) stay the same. The most efficient miner listed is about 3.33x times more efficient than the R-Box analyzed, this would make it last 871 days.

On day 872 mining would no longer be profitable. Lots of miners would quit, which would lower the network difficulty until some miners start to see a profit. Less efficient miners are left out of the business, and the equation above won't be useful anymore.

### I'm too lazy to do the math above. Now what?

Don't worry, just play with the fields below and let JavaScript do the rest.

### Conclusion & Credits

Certainly this is only a model, a change in transaction fee volume or mining reward can alter the landscape, the results must be taken at face value. The code of the calculator is freely available (I did not want to encrypt it), and I used binary search on a decreasing function to get a very exact value in no-time; the interval of this function is 50 years (18250 days).

What's very curious to me is that my AI found Phi as a constant, I haven't found any special thing about the other two constants rather than they are the squares of 111 and 9; they are not primes or anything that I know of. Should you have a lead regarding that, it would be most appreciated. And, as of always, more data would be very welcome.

Special thanks to Mr. Clive Warwick Koen for his mining data. And that's it. Hope you liked it!