*If you have any questions about this process, you can contact me with the form below! Happy mining. *

In general, the profit margin for miners becomes slimmer through time as the competition to break into bitcoin mining increases and the barriers to entry are higher than ever. Customers have in general had poor experiences with ASIC manufacturers who have delivered the mining products late, making the hardware purchase a net loss for the investor. The situation is not so grim for the miner, however, because the bitcoin price and price velocity are as high as they have ever been, and are not showing signs of flinching.

Despite the apparent victory for the miner when the price rises, it is a common misconception that a positive return of investment can be saved for a poor mining hardware purchase if the bitcoin price rises enough. This is not actually true – well, not exactly. The truth is, if the only way to make ROI is if the price of bitcoin rises, then you should have simply bought bitcoins, rather than the miner.

The question of when a “good” time to sell your miner is complicated. What you have is a machine that prints money. But it prints money at an ever decreasing rate. When do you sell it? You need to first make a few back of the envelope calculations.

**Calculate your miner’s daily performance today**

First you find the number of bitcoins your miner will earn you per day at the present time. There are many online calculators for this. You can do it by hand in a number of ways; my favorite way is the following:

• Get an estimate online of the total network hashrate (at the time of writing it is about 4200 TH/s).

• Figure out what fraction of that total hashrate is your contribution; this is

Fraction = (your hasrate)/(network hashrate)

• That’s the fraction of all bitcoins per day which will belong to you (it’s a generous estimate because of mining pool fees which we disregard).

• The total number of bitcoins generated per day is about:

(25 BTC) / (1 block) * (1 block) / (10 minutes) * (60 minutes) / (1 hour) * (24 hours) / (1 day) = 3600 BTC per day

• Your expected Bitcoins/day is then just

My BTC/day = Fraction * 3600 BTC/day

For example: if you own a 576 GH/s KNCMiner Jupiter…

• Your share of the network hashrate is 576/(4200*1000) = .00013714

• This is the fraction of daily bitcoins produced by everyone, which is always 3600. You generate about 3600*.00013714 = .4937 BTC/day

• This estimate is roughly true when taken for the period of 2 weeks over which the difficulty is adjusted, and is a central tendency. You actual daily rake will differ day to day due to the nature of Bitcoin. However this way of estimating is surprisingly accurate, if you get a good Hashrate estimate.

**Calculate the expected return of your miner from now on**

This can be in principle extremely difficult. I will present an extremely over simplified model that can be used to roughly calculate the expected return of your miner given market trends by invoking the approximation of a geometric series for the difficulty.

• Divide the last difficulty by the current difficulty.

• This is the value *r* or the common ratio. *r* must be between 0 and 1, or you have have a mistake.

• If you can, find *r* for the previous diff change or previous 2 or 3 and average them.

Once you have the *r* you want to use, the number of bitcoins your miner will EVER produce is approximately

Bitcoins from now to eternity = (number of bitcoins I’ll produce this 2 weeks period)/(1 – r)

For today the difficulty is 510 million. Prior it was 390 million. That gives an *r* = .76 which we will proceed with, though you can go back a few steps and average the result if you like by checking a chart like this.

Anyway, once we have *r*, we find

Bitcoins ever = (number of bitcoins I’ll produce this 2 weeks period)/(1 – r)

= (14 days)* (.4397 BTC / day)/ (1 – .76)

= 25.6 BTC

**Decide when to sell **

Snce I love to disregard complications, let’s assume you can liquidate your Miner instantly, without any problems/costs/risks for a “market price.” You should sell your miner precisely when the market price of the miner will allow you to buy more bitcoins than the total number left your miner will ever create.

Let’s do this analysis again with KNCMiner (for no real reason other than consistency at this point) as an example. Here is some data from ebay.com on sales of “knc miner” equipment over the past 7 days:

Because there is some variance here and not too many data points, let’s calculate some quantities for only one of these examples – the one on 11/3 which went for $8100.

On 11/3 let’s assume the expected return for the Miner was 25.6 BTC just as it is today. The price of bitcoin – that is, the bitcoin to USD conversion – is a far (perhaps infinitely) more volatile quantity than the expected return of Mining hardware when returns are stated in BTC. So a quick search of data on coinbase.com for example shows the price that day was, on average, 218.24 USD. So if this seller collected precisely 8100 USD for this sale (he didn’t because of ebay and paypal fees) he could have turned around about bought

BTC earned by selling = (8100 USD)/(218.24 USD/BTC) = 37 BTC

That’s a pretty good sell, IF the seller turned around with his money and bought BTC immediately. This is true regardless of the future price of bitcoin because this is a bitcoin to bitcoin comparison (in general, by staying within bitcoin when calculating, it is easier to extract information from the market data).

**Limitations of this model**

This model is completely invalid if the difficulty is not increasing in a pretty particular manner which it seems to be for now. Specifically, this model will completely fail if the difficulty is increasing but in smaller increments each time. This model will fail even more massivly if the difficulty is stable or decreasing, which is not the case presently, but has happened before. A stable difficulty will also almost certainly occur one day again – but I will not digress as to why this is the case in this post.

Furthermore this model assumes bluntly that the network difficulty takes *geometric* steps upward, which would be the result of a purely exponential hashrate plot. Simply put, the network difficulty is not geometric in general, but only approximates geometric behavior in a sufficiently short period of time. In fact, it is a mathematical certainty that in an appropriate time scale, any relationship at all will trace an exponential curve quite closely and it is this universal principle that I have exploited in this model.

But the difficulty really cannot really be geometric – not only because the ratio of two consecutive difficulties is pseudorandom, but rather because the network hashrate displays kinks, corresponding to generations of ASIC technology.. However, it can be seem empirically that the difficulty function is approximately geometric within 3 to 5 difficulty increases, over which the ratio r does not deviate strongly from a central value. Luckily, 4 increases of difficulty amounts to 8 weeks. Since the advent of ASIC architecture, 8 weeks has been, perhaps consequently, the approximate lifetime of a mining device (some devices has an even shorter lifetime).

This is congruent with the intuition which says if your mining income rate falls off faster than a geometric series, you don’t have much time left before your mining income will be quite literally zero; though an old pentium 4 CPU can “mine” a bit, there comes a point when you will simply *die* before you mine an amount of bitcoin that exceeds standard transactions fees. Whether this is the case today is left as an exercise for the reader.

Because of the probabilistic nature of the the bitcoin network’s protocol, there is a fundamental limit on the accuracy one can hope to have predicting short term trends. bitcoin is also a financial instrument, and being such lends itself poorly to any model with long term accuracy. Thus we must be sure of the time scale over which a particular model has any validity. This empirical rule of geometric increases in difficulty is merely a model, so use it with caution. If you plan on doing such a calculation, it would be wise to trace the difficulty back a few steps and see if something else is going on in the bitcoin economy. If that is the case, it is time to make a new model.

This week I will make a detailed mathematical analysis of the geometric approximation to network changes. This will come with a post to generalize the fit to longer times through the use of more complicated models resembling statistical mechanics of physics. If I forget to do this remind me, seriously.

– Altoidnerd