ASIC Difficulty Curves

[bitboyben]

I was tinkering around with the current difficulty increases say 0.2% to 0.6% per day and plugged that in to the forecast increase of ASIC hardware.
Came up with some interesting numbers.
Then I decided at what point would electrical consumption come in to play. I was a bit surprised as to how quickly the GH/W would come in to play with ASICs.
I wasn't expecting it to be an issue for at least a few years.

I made a quick chart and decided to share it.

This is weekly increases and the Total Hash rate.
The dashed lines represent at what total hash rate a ~$1400 ~60G/h ASIC would after power consumption provide at least +5% return on top of the price of the equipment within a year.

There's a lot I don't take into account.
Starting with the fluctuating price of bitcoins. Assumed $12 here.

Comments?

[Cablez]

I did something a little similar looking at the earning tack a few days ago.

Here is a quick little representation of the mining income upon ASIC release.

The only assumptions are 2 BFL SC singles and a linear rate of difficulty adjustment per day. Not completely realistic but close.

[bcpokey]

My eyes hurt quite a bit trying to look at the tiny numbers of the first image. I'm not sure what you mean when you say current increases, that you are referencing, but it seems clear at even a cursory glance that only the .2% / day rate is within sensible tolerances.

You are already starting your curves at 200TH/sec, when asic rates are close to parity with current GPU rates (that is to say the $ value of buying an asic in that world is similar to the $ value of buying a GPU in our current bitcoin world). Even the .4% curve, over the course of 30 days, increases from 200TH/sec to 400TH/sec, or using your values: 3,333 singles at a cost of $4,700,000 of hardware has been brought online that month. Possible I suppose, but let's not forget that the incentive to buy asics is much lower at this point, with supply potentially still far more limited than the current GPU market, and for comparison the entire GPU / FPGA mining set up running now is probably closer to $7m in value. Something to bear in mind I suppose, but seems very unlikely.



For the second graph, I would think for that to be helpful to yourself and others, you would want to use the step-function change that occurs with bitcoin rather than linearity, as it will certainly impact the results quit a bit. Difficulty takes a step after every 2016 blocks, based on time over expected time. If you were to luckily hop on that early, you drastically under-represent your first 5 day earnings, which would of course account for the majority of your first 30 day return. This would also be closer to the mark on reality, as the change of hashing power will almost certainly be far more accelerated than the even distribution you are working with.


Admittedly somewhat nitpicky, but I figure for usability these are low-hanging fruits.

[creativex]

I believe the unit of time referenced in the first chart to be weeks and not days. It is a bit difficult to follow, but interesting just the same. Thanks for sharing the work that went into these guys.

[bcpokey]

I believe the unit of time referenced in the first chart to be weeks and not days. It is a bit difficult to follow, but interesting just the same. Thanks for sharing the work that went into these guys.

That would indeed make more sense (guess my smarting eyes missed the word weekly in the OP), and allow for numbers to be more sensible. I still question a doubling of hashing power in 30 weeks, but it's certainly possible.

Power consumption definitely changes the name of the game quite a bit.

[creativex]

As stated many variables are left out. Sentiment is one, and it's obviously a biggie. Miners as a group tend to be fairly...not dumb, so they're unlikely to just blindly walk off the cliff of indefinite ROI by the hundreds. If and when the profitability of mining with ASICs becomes marginal then sales will fall. If these fellers instead invest in bitcoins directly then prices are likely to rise.

I don't see electricity costs as playing a large role in ASIC mining profitability for some time to come. I believe you can safely chuck the top and bottom lines as the presumed efficiency leader(BFL) will still require something to tether to and even a little tablet will use 20w or so. The 480w mark is probably more power than any of the currently announced ASIC units will consume to reach 60Gh. Average is probably right around the 500Th mark on that chart and I don't see us reaching that for some time. Even then with the huge increase in efficiency ASIC has over GPU mining I don't see it as the determining factor for some time, though obviously in areas with high power costs that time will arrive much sooner than for others.   

[MrTeal]

You'll be better off just adding the first couple months manually and then try to use a function after that.

I'd actually recommend using at most a linear increase after the initial batches of ASICs hit, with it more likely we'll see a sqrt(x) or log(x) increase. Look at the graphs of hashrate historically.

In the 3 months between May and August 2011, hashrate increased by a factor of 10 as everyone started GPU mining. It was then basically flatlined until for a year until this summer when the price jumped. Given the assumption that people are making about price staying constant, I'd say it's much more likely that we'll see an initial huge surge as all of 6-12 month payoff slack is taken up, and then a tapering off of hashrate growth.

[bitboyben]

Thanks for the feed back so far. I'll get back to it tomorrow.

[bitboyben]

So here's my shopping list of proposed changes:

Revised power prices: I based the electricity costs on my current costs. I think I'm in the lower third. I'll take a look at some of the rates others are be paying by looking up local costs on the forum as posted.

Clean up "weeks"

Make larger: Size suggestions

Add resistance to difficulty increases. Log(x)/historical charts: Thanks for the input on that. It will of course become less favourable for miner to continue to invest in hardware as difficulty increases. I'm thinking of making a poll asking what levels of minimum reveue people would be comfortable with.

Other difficulty data sets: I realize that I went basically straight to 200Ths. I based that on my earlier poll on Hash rate. From the sounds of it BFL will ship 150Ths in the first shipment/batch. I don't have order numbers on other ASIC producers. Any info on that would be helpful.
I also had some stepped (two week) difficuly rates using other rate increase theories.
I picked 0.2%-0.6% based on the daily change charts over the last  6-7 months. I suppose FPGA shipments have lead to steady increases over that time period and the CPU to GPU hash increases maybe more realisic.

Predicting shipments- So much has been already written on this. I guess I'm looking for the rate of deliveries not exact dates. I don't think the manufacturers could even say at this point.

Predicting reinvestment:  Not sure how much revenue miners will be reinvesting. Seems silly not to do some. but who wants to put 100% revenue into more hardware.

Reexamine underlying revenue calculators: need to double check the unerlying math makes sense

Thank you all for input

[MrTeal]

I believe that the first batch of bASIC units is about 50TH/s, and there's been two 300 piece preorders of 66GH/s Avalon units.

I really don't know what an acceptable level of expected ROI for ASIC units are. For me, it's much shorter than it would be for something like a GPU rig was. With GPUs, a 12 month ROI would have been acceptable for a whole rig, since you have a value floor because of the inherent general purpose value of the hardware.

With ASICs, there is no secondary market outside bitcoin mining. If you pay cash expecting a 12 month ROI and the price goes to $5 you basically have to hold your coin or accept that you might take 5 years to pay off the unit. If for some reason countries legislate or regulate BTC enough to kill the price, your investment might just be a writeoff. It's much riskier than CPU or GPU mining was, and even more risky than FPGA mining.

[bitboyben]

Thanks MrTeal I hope you had a chance to check out the ROI poll I put on the board as well. Maybe I need to tweak that to reflect the greater risk will require higher ROI for those exact reasons. maybe +20% is the new break even point for some because of the specific nature of ASIC hardware. In my case it was easy to get the GPU bc I wanted one any way. But if potential newcomers have to get mining specific hardware and the returns are low they may not bother. Which would be good for established miners and potentially good for the price of btc if newcomers directly invest in btc.

[bcpokey]

Since I enjoy charting and numbers, I thought I'd throw my hat in the ring.

I did a lot of hand calculation, since I feel that for certain periods of time, formulas are not applicable (just as for certain periods they are). So this is my view of what will happen if and when BFL hits the market with their projected quantities and dates.

Assumptions: 20,000 fully functional ASIC chips, at 7.5GH/sec a piece, arriving ~Nov 25th, being shipped in 1/3rd installments roughly once per week to their pre-orders and post-orders (so 50TH delivered in chunks each week, coming online at roughly the same time).
Rounding: A fair amount, but nothing critical to the numbers.
The columns you see are: Total Network Hashing power (in GHash/sec); Difficulty; Date; BTC Generated (for 60GH/sec per day); USD equiv (@$10.5USD / BTC); Cumulative BTC generation.

The graphs are ugly but self-explanatory. I believe this area of time (it can be translated to any point in time until the other producers begin to ship, so dates don't matter) is the most interesting and graph worthy. Early adopters will make out like bandits, but once the 150TH has been rolled out, things are much less interesting, and begins to mirror the GPU world, for generation/ROI and so forth, and the trend becomes easy to see (the top isn't easy to predict, but I'm figuring ~200-250TH/sec as the initial goldrush surge fades). Thoughts and comments, and criticisms welcome, within reason.

[bitboyben]

Great stuff, thanks for sharing.

I've seen spread sheets of the historical hash power/ difficulty out there I was, as suggested, going to slap the percentage difficulty change on to some of these exisiting numbers and see where that takes us. I just ned to find it, and not get tied up so much with work so I can actually work on this.

[kjlimo]

Thanks for putting this together.  I agree with what you've done.

Exciting to think that we could make $1k per unit in Dec and still have a rate of over $3k for 2013.  Obviously something will change before then, but still fun to think about.

Getting excited!!!

[Xfinity]

interesting stuff, thanks for sharing!

[bitboyben]

Looking for some feedback on my assumptions.
On the initial jump in Hashing power I got BFL 150Th and bASIC 50THs and Avalon ~40THs I'm thinking will take about 6-12 weeks to be delivered? Initial delivery dates and Delivery times seem to be getting closer and closer between the various manufacturers. Agree close enough? y/n?

I should double check to see where about the GPU profitability will become negative and see where that would happen on the graph. I may be able to subtract the current ~25TH network at that point in time.

I still like the 0.2%, 0.4% and 0.6% difficulty per day increases. I calculated 5% per difficulty period falls in between those numbers and smarter guys than me seem to be happy with that number.

I'm looking to project the next year in difficulty per week.

I won't factor for BTC-> fiat exchange(yet).

I'm trying to determine a range of numbers(dates/difficulty) where a given ASIC hardware unit has a ROI of 1 year -5% to +30% and include electrical costs of 0.1-0.3USD/KWhr and the missing 100W for a host.
As the difficulty approaches this range I can reduce the change in difficulty as miners are assumed to be purchasing less hardware as the ROI decreases.

Bit off topic but does the price of BTC increasing only ~140% over the last year but the difficulty increasing 220%->340%? mean anything to any one?

[MrTeal]

Looking for some feedback on my assumptions.
On the initial jump in Hashing power I got BFL 150Th and bASIC 50THs and Avalon ~40THs I'm thinking will take about 6-12 weeks to be delivered? Initial delivery dates and Delivery times seem to be getting closer and closer between the various manufacturers. Agree close enough? y/n?

Sounds about right

I should double check to see where about the GPU profitability will become negative and see where that would happen on the graph. I may be able to subtract the current ~25TH network at that point in time.

GPU Mining will become unprofitable pretty much as ASICs hit for everyone that doesn't have free power. Not all of the current 25TH/s is GPUs though, a bunch is FPGAs. The BFL Singles would be profitable at the current exchange rate and $0.10/kWh until about 150TH/s, while the Spartan based ones like the ModMinerQuad would be profitable until about 300TH/s under the same conditions. It's hard to tell how much FPGA hardware will not get traded in though.

I'm trying to determine a range of numbers(dates/difficulty) where a given ASIC hardware unit has a ROI of 1 year -5% to +30% and include electrical costs of 0.1-0.3USD/KWhr and the missing 100W for a host.
As the difficulty approaches this range I can reduce the change in difficulty as miners are assumed to be purchasing less hardware as the ROI decreases.

I'd include maybe 50W for a host. For one, even my desktop with a bunch of case fans, an overclocked i5-2500k and two 6970s doesn't idle over 100W. Anyone building a mining system can easily have much lower draw than that.

Idle power consumption for something like an i3-3220 is under 60 watts, and that's with a high performance Z77 MB (ASUS Maximus V Gene), 4 sticks of RAM, and a high power GPU. Even under load encoding x264 it only drew 80W.
Second, the average number of devices per host is likely greater than 1.
Using too high a host computer power draw will mask differences between different ASICs.

Bit off topic but does the price of BTC increasing only ~140% over the last year but the difficulty increasing 220%->340%? mean anything to any one?

It hasn't, the price of BTC this time last year was under US$3.

[organofcorti]

I still like the 0.2%, 0.4% and 0.6% difficulty per day increases. I calculated 5% per difficulty period falls in between those numbers and smarter guys than me seem to be happy with that number.

An increase of 1.0035% per day isn't the same as an increase of 5% per difficulty period - the latter is a step function, and also increasing the percentage increase decreases the length of time for which the difficulty implies, since an increase in difficulty of 5% means 2016 blocks were solved 5% faster than expected.

Depending on what you want to do with the data, I think you might be better off measuring time in difficulty periods. A difficulty period is then converted to days as follows:

Code:

days = difficulty periods * 14/(1+average percentage increase per difficulty period)

For example, 10 difficulty periods where the difficulty increases by 5%:

Code:

days = 10 * 14/1.05 = 133.33 days

HTH

[bitboyben]

Ok thanks guys.

MrTeal: Thanks again for the numbers. I agree that 100w is conservative. I'm personally hoping to run my ASIC on the RPi or a laptop which uses a about 35w when I last measured it. And you are right if people are going to buy more hardware the share of the host's power draw diminishes. Also the host can be used for other operations while it is mining if someone so chooses, so how do we calculate for that? Maybe I'll stick with 50W as a fairly conservative number. I was just going to stick with organofcorti's numbers because he has done so much work already.
As for the bitcoin price YTD, I got it off here http://www.bitcoinmoney.com/post/34853623626/october-2012-results and you are right. 137% is the price rise since the start of Jan 2012 so not a full year.

organofcorti: http://organofcorti.blogspot.ca/2012/11/93-more-on-asic-choices.html
I saw your new maths on your blog there and much of it contains data that I was trying to get for myself. Props on doing that.  I found that your charts are awesome because they cover so many different possibilities. However, I'd like to use certain sets of assumptions to come out with my own set of numbers and start to affect the difficulty curves as miners approach stated max difficulty goals.

By max difficulty curves I would like to assume that a percentage of revenue will go in to reinvesting until such time that difficulty approaches a miner's preferred min ROI. That min ROI is -5% to +20% ROI over one year including electrical use and the cost of hardware. This is not to be confused with Profitable in the sense that the mining equipment is producing more BTC than it is using in electricity. And of course you have a formula for that in your latest post. (I think I'm repeating myself again, again)

I've been using THs, USD$ and days/weeks/months for my calculations not BTC, difficulty and difficulty periods so I'll have to switch over.

Good points and thanks for the help.

[2GOOD]

organofcorti: http://organofcorti.blogspot.ca/2012/11/93-more-on-asic-choices.html

Very good stuff. Thank You