ASICs - which should you choose?

[Xfinity]

I've written a short post detailing how to estimate an ASIC device's yearly earnings, the time it will take to recoup the initial cost, how long you can can expect to mine profitably with a given device and more. I won't repeat the entire post here, but I've posted a teaser chart below.  Post your own analyses and chart, and help fellow miners figure out which device they should purchase. I look forward to your comments and suggestions either here or at the blog.

Good work organofcorti and nice blog

[Jutarul]

A more intuitive graph would be a ROI graph, with the x-axis being the time of operation. the y offset is the initial hardware cost, and the xoffset is the break even point... I didn't see one.

Post a link to an example and an explanation of the calculations you're talking about and I'll try to make one. Otherwise I've provided a method to calculate the data - go for it!

Gladly.
it's a 2d graph with follows: y = a*x+b. It should be denominated in BTC since this compensates for opportunity cost. In that case we assume the miner holds on the the mined BTC till the break even point (at which point the exchange rate matters).

y = profit per day in BTC
x = day
a = mined BTC per day
b = (negative) initial hardware costs in BTC

a itself is a function of x, since the efficiency of the mining changes with time, thus: a=a(x)
a(x) can become negative since mining operation include an upkeep (electricity cost), thus the price of electricity matters:

a(x)=a1(x)-a2(x)

a1(x) = generated coins
a2(x) = upkeep

a1(x) depends on difficulty (D), hashing power (H) and reward (R)
a2(x) depends on electricity costs (EC), consumption (W) and exchange rate (ER) (since the graph is denominated in BTC)

a1(x) converges against zero with time since difficulty is supposed to increase and rewards drop according to the schedule.
a2(x) may fluctuate a lot around an average value. It is supposed to decrease in short term (increasing exchange rate) but increase in long-term (higher electricity costs).
The lifetime of the hardware is characterized by the time (x) at which a1(x) intersects a2(x).

To provide an example I use your data from your post for BFL (some simplifications used):
b= -100 BTC ($1299 with $12.99 per BTC)
a1(x)= [ 60 Ghps / ( 90 Thps * (1 + 0.05 * (x/14) ) ) ] * ( 25BTC * 6 * 24 ) = [ 60 / 90000 ] * [ 1 / (1 + 0.05 * (x/14)) ] * 3600BTC = 2.4BTC / (1+0.05*(x/14))

(1.05 derived for your 5% increase in total hashing power per difficulty period, 14 days per difficulty period, neglecting compounding)

a2(x)= [ (60 * 24 Wh)*(0.1 USD/kWh) ] * [ 0.1 BTC/USD  ] = 0.0144 BTC

The graphs look something like:

[bitboyben]

Def donation worthy.

I've learned lots and I hope you don't mind me using some of this.
I'd like to project some possible difficulty curve increases. Yes, it will be full of assumptions.

Was there any reason why you chose 5% per diff change or was it just a reasonable assumption used to evaluate your original analisys of "Which ASIC to choose?"

[DoomDumas]

Thanks a lot organofcorti for all this info, charts, blog.. very nice

[organofcorti]

Thanks for taking the trouble to write a helpful, clear and thoughtful post, Jutarul. I followed your explanation well enough to have a few questions which I'll post one at a time.

a1(x) depends on difficulty (D), hashing power (H) and reward (R)
a2(x) depends on electricity costs (EC), consumption (W) and exchange rate (ER) (since the graph is denominated in BTC)

....

a2(x)= [ (60 * 24 Wh)*(0.1 USD/kWh) ] * [ 0.1 BTC/USD  ] = 0.0144 BTC

a2(x) what what I was trying to avoid. I think btc exchange rates will continue to be much more volatile than I'm happy to attempt to model. So by calculating the fiat to btc conversion once and using the the exchange rate as an independent variable, I don't have to be concerned with long term exchange rate volatility affecting a model's outcome.

Have I misunderstood any of this so far?

TIA

[organofcorti]

Def donation worthy.

I've learned lots and I hope you don't mind me using some of this.

Of  course, go ahead and use what you need. It's why I wrote the blog post.

I'd like to project some possible difficulty curve increases. Yes, it will be full of assumptions.

The challenge for you will be modeling the initial change in difficulty until it reaches steady state. After steady state it's likely to increase by some arbitrary average percentage, but until steady state is reached the increase in hashrate will be a function of the hashrate and number of sales of the devices over time. At a very uninformed guess, I would expect the cumulative increase in hashrate over time to be something like an exponential or pareto CDF.

Once you have your model for the hashrate increase, you need to model the increase in difficulty. To do this properly you'll need to include difficulty increase by a maximum of 400% per difficulty period, and also that the greater the increase in hashrate, the shorter the difficulty period will be (in terms of time elapsed).

You've probably already thought of all this, but if not I hope it helps. I'll be interested to see the results you get.

Was there any reason why you chose 5% per diff change or was it just a reasonable assumption used to evaluate your original analisys of "Which ASIC to choose?"

It was based on the average percent difficulty change since the start of the year, and assumes that difficulty has reached a steady state after the bulk of the ASICs have been introduced. It is an assumption that may not be at all warranted, but it's likely closer to be more accurate than trying to model the exchange rate.

[creativex]

3) We dont have exact power numbers for the bASIC, but 300W is a little high. That number about the 1000W PSU being able to drive 10 bASICs doesn't clarify whether that's the 27 or 54GH/s units, but I'm inclined to think the second. I'm guessing 1000W will power either 10 27GH/s units, or 5 54GH/s units.

Hot off the presses

I personally use these on my fpga rigs - one of these 1000 watt babies will easily power 8-10 54Gh/s bASICS

I believe that should send that debate to it's final resting place.

https://bitcointalk.org/index.php?topic=79637.2060;topicseen

[Jutarul]

Thanks for taking the trouble to write a helpful, clear and thoughtful post, Jutarul. I followed your explanation well enough to have a few questions which I'll post one at a time.

You're welcome. Since you took the time to create a nice post, I thought I'll take the time to give you some feedback. Also gave me an opportunity to re-evaluate some aspects about mining profitability.

a1(x) depends on difficulty (D), hashing power (H) and reward (R)
a2(x) depends on electricity costs (EC), consumption (W) and exchange rate (ER) (since the graph is denominated in BTC)

....

a2(x)= [ (60 * 24 Wh)*(0.1 USD/kWh) ] * [ 0.1 BTC/USD  ] = 0.0144 BTC

a2(x) what what I was trying to avoid. I think btc exchange rates will continue to be much more volatile than I'm happy to attempt to model. So by calculating the fiat to btc conversion once and using the the exchange rate as an independent variable, I don't have to be concerned with long term exchange rate volatility affecting a model's outcome.

Have I misunderstood any of this so far?

TIA

Yes. a2(x) is a bitch. And in reality it's not a constant and does not resemble an average.

Rational miners should mine as long as a1(x)>a2(x). However, that disregards other factors, like resale value of the hardware, protection of the network, etc.... That's why I used the term "upkeep". It's the expense you have for generating new coins and "protecting" your investment.

The thing about a1(x)>a2(x) is also that it may trigger some people to hold on to their hardware for latter use, when the exchange rate becomes high enough again... It's a very dynamic system.

[organofcorti]

Have I misunderstood any of this so far?

TIA

Yes. a2(x) is a bitch. And in reality it's not a constant and does not resemble an average.

That's pretty much what I thought. What have I misunderstood?

Rational miners should mine as long as a1(x)>a2(x). However, that disregards other factors, like resale value of the hardware, protection of the network, etc.... That's why I used the term "upkeep". It's the expense you have for generating new coins and "protecting" your investment.

The thing about a1(x)>a2(x) is also that it may trigger some people to hold on to their hardware for latter use, when the exchange rate becomes high enough again... It's a very dynamic system.

Since I'm not attempted to create an accurate model for mining but a comparison between devices, I'd thought that evaluating a1(x) - a2(x) at the point of evaluation only (ie as if no electricity bills are paid until the evaluation point, and no btc are spent until then). In this case isn't the denomination of the graph immaterial? Whether it's denominated in btc, local currency or % ROI the results should be equally valid. Is this right?

I'm just asking this because I'm working on an ROI chart like yours, but as a tile-plot, the third dimension as the exchange rate at evaluation point. I don't want to post it if there's a glaringly unforgivable error in doing so.

[organofcorti]

3) We dont have exact power numbers for the bASIC, but 300W is a little high. That number about the 1000W PSU being able to drive 10 bASICs doesn't clarify whether that's the 27 or 54GH/s units, but I'm inclined to think the second. I'm guessing 1000W will power either 10 27GH/s units, or 5 54GH/s units.

Hot off the presses

I personally use these on my fpga rigs - one of these 1000 watt babies will easily power 8-10 54Gh/s bASICS

I believe that should send that debate to it's final resting place.

https://bitcointalk.org/index.php?topic=79637.2060;topicseen

Ah crap. Another update is due, I believe. Once I've hashed out the ROI curve details with Jutarul, I'll update.

[creativex]

Sorry. Ummm...sharing is caring?

Looking forward to your updates.

[Jutarul]

That's pretty much what I thought. What have I misunderstood?

nothing?

Rational miners should mine as long as a1(x)>a2(x). However, that disregards other factors, like resale value of the hardware, protection of the network, etc.... That's why I used the term "upkeep". It's the expense you have for generating new coins and "protecting" your investment.

The thing about a1(x)>a2(x) is also that it may trigger some people to hold on to their hardware for latter use, when the exchange rate becomes high enough again... It's a very dynamic system.

Since I'm not attempted to create an accurate model for mining but a comparison between devices, I'd thought that evaluating a1(x) - a2(x) at the point of evaluation only (ie as if no electricity bills are paid until the evaluation point, and no btc are spent until then). In this case isn't the denomination of the graph immaterial? Whether it's denominated in btc, local currency or % ROI the results should be equally valid. Is this right?

I'm just asking this because I'm working on an ROI chart like yours, but as a tile-plot, the third dimension as the exchange rate at evaluation point. I don't want to post it if there's a glaringly unforgivable error in doing so.

Technically you can easily renormalize the denomination at the break even point with the above assumption. Personally, I prefer the BTC denomination, because it provides information on how much BTC can be "generated" with the device (production-cost). If you denominate in $, you should always have two graphs: the value increase of your mining investment, and the missed opportunity of holding on to your BTC. The difference provides true information on the ROI.

[organofcorti]

.....

Technically you can easily renormalize the denomination at the break even point with the above assumption. Personally, I prefer the BTC denomination, because it provides information on how much BTC can be "generated" with the device (production-cost). If you denominate in $, you should always have two graphs: the value increase of your mining investment, and the missed opportunity of holding on to your BTC. The difference provides true information on the ROI.

I'm not sure about the opportunity cost as it applies to mining since converting either from local currency to btc or btc to local currency means you have to hold on to one or the other. So, assuming you're correct - and I guessing here - but is there no opportunity cost for local currency because you're spending it and not earning it?

[Jutarul]

.....

Technically you can easily renormalize the denomination at the break even point with the above assumption. Personally, I prefer the BTC denomination, because it provides information on how much BTC can be "generated" with the device (production-cost). If you denominate in $, you should always have two graphs: the value increase of your mining investment, and the missed opportunity of holding on to your BTC. The difference provides true information on the ROI.

I'm not sure about the opportunity cost as it applies to mining since converting either from local currency to btc or btc to local currency means you have to hold on to one or the other. So, assuming you're correct - and I guessing here - but is there no opportunity cost for local currency because you're spending it and not earning it?

Mmm, I am a bit confused now. Would you please restate your point?

AFAIK it's simple: assume you have an initial amount of $1000. You decide to buy mining equipment which generates 100 BTC before it blows up in your face (we neglect the electricity cost for simplicity). Alternatively you could have bought 100 BTC from your initial $1000 at $10 per BTC. Assume in 1 year BTC is $1000 a piece. Now your mining equipment generated $99000 profit.
Correct? No - because the profit is an outcome of the value appreciation of BTC. Your device just made it barely to break even.

[monstrs]

Very nice graph and good article, keep up the good job 

[quasarbtc]

Interesting. Thanks for posting.

[ldrgn]

Good effort but putting such a large range on BTC price only hurts your presentation.  You should be tackling mining profitability with the mindset of "Hey, let's see how profitable this is given that BTC stays at $11 or thereabouts."  There is absolutely no point in even peeking at mining return over ~$10/BTC (A crueler man than I would call it masturbatory).  I recommend a range of $11/BTC and down if you insist on having exchange rate as a variable.  Otherwise, I'd just stick to a constant $11/BTC.  It is much more useful to show a wide range of difficulties and difficulty prediction functions as that is the true unknown variable here.

[organofcorti]

AFAIK it's simple: assume you have an initial amount of $1000. You decide to buy mining equipment which generates 100 BTC before it blows up in your face (we neglect the electricity cost for simplicity). Alternatively you could have bought 100 BTC from your initial $1000 at $10 per BTC. Assume in 1 year BTC is $1000 a piece. Now your mining equipment generated $99000 profit.
Correct? No - because the profit is an outcome of the value appreciation of BTC. Your device just made it barely to break even.

I follow you - it's about buy and hold vs invest in mining equipment, yes? I'll try to think of a way to show that not involving using a btc denominated chart.

Good effort but putting such a large range on BTC price only hurts your presentation.  You should be tackling mining profitability with the mindset of "Hey, let's see how profitable this is given that BTC stays at $11 or thereabouts."  There is absolutely no point in even peeking at mining return over ~$10/BTC (A crueler man than I would call it masturbatory).  I recommend a range of $11/BTC and down if you insist on having exchange rate as a variable.  Otherwise, I'd just stick to a constant $11/BTC.  It is much more useful to show a wide range of difficulties and difficulty prediction functions as that is the true unknown variable here.

I'd like to point out that my sexual fantasies rarely involve bitcoin.

That said, there is a very good reason I increased the x-axis to US$40/btc in the chart you refer to, and that is to enable comparisons. If one device at one locale can get you to the break even point at 12 months at starting difficulty = 30 million and an exchange rate of US$10/btc, and the same device will reach break even at 12 months at starting difficulty = 30 million  and an exchange rate of US$30/btc, then you know it's time to move to a state where electricity is cheaper. I'm not expecting btc to reach maximum of the x-axis, but if I didn't include up to US$40/btc then some of the chart would have been blank.

With those points in mind, and with the aim of producing an ROI like chart, I made the following:

Chart 1: (new) In order to read this group of charts, find the intersection of a percentage ROI and number of difficulty periods (eg. % ROI after one year is at ~ 26 difficulty periods). The colour of the tile is an indicator of the exchange rate required to meet this %ROI after the given number of difficulty periods. The faint white line along the middle of each plot indicates the break even point. Click on a chart for enlargement.

More charts and more detail at http://organofcorti.blogspot.com.au/2012/11/93-more-on-asic-choices.html

[bitboyben]

I want to make that chart 3d... mmm 3D....

[organofcorti]

I want to make that chart 3d... mmm 3D....

I did a 3d version, not as easy to understand as the tile plot and a bit uglier. I can post it though if you want.