linearity in profitability calculations

[nFast]

Hello,

I'm just planning to start mining and trying to do the maths before it.
While I was trying to figure out my future profit, I realized that I use
a few assumptions that are not necessarily true.  Two of them:

1) I've measured that with X Mhash/s speed I earn Y BTC/week.  Now
I'm not sure that if I can double, tripple, etc. my speed, then my
earnings will double, trippe, etc. of Y.  Is that true, that if I would
have been mining with k*X speed, k*Y BTC have been earned?

2) When difficulty doubles, half as many BTC can be mined.

Well, these are the basics of my calculations, but I'm not sure of them.
I would like to know your opinion on the above two points.

THX

[bcpokey]

The amount of BTC you earn depends on the method of mining you choose, are you doing Solo mining? Are you mining on a pool? Is the pool PPS, is it proportional? Is there a fee? Etc.

Pay-per-share is the only one where you can say that your BTC earned doubles when you double your mining speed (until they change the amount they pay per share of course). Other methods typically depend on what proportion of the mining power you generate (and some luck as well). For most small time miners however, doubling your hash power will effectively double your earnings, assuming other factors remain the same.

When difficulty doubles, you will earn roughly half as many BTC, that one is more cut and dry.

So the answer is "yes" with a buncha caveats. Difficulty changes constantly, as others in the mining game add or subtract their relative hashing power.

I suggest that you pay close attention the the ASIIC discussions going on, as that has a huge impact on profitability, whether you are GPU farming, or jumping on the ASIIC bus as well

[creativex]

Good post ^. I'd also caution the OP to heed the reward halving coming early next month. It's likely to lead to changes to the fiat/BTC exchange rate and mess with everyone's profitability models.

[jwzguy]

Definitely a good post. It's very refreshing to see a new poster asking for potential flaws in their calculations instead of proudly describing their 12 month projections.

The short answers to your questions are yes to both.

The real questions are:

1) how are you going to double your speed? I would discuss all the difficulties involved with scaling up GPU mining operations, but since it's about to be completely irrelevant, I won't bother.

2) Are you aware of how much difficulty has been increasing over the last 5 months? While not any kind of ceiling on future difficulty increases, it should at least expose you to some issues in making profit projections any farther than 12 days into the future.

When ASIC machines start being delivered, they will make all our recent difficulty increases look trivial.

[bobitza]

1) I've measured that with X Mhash/s speed I earn Y BTC/week.  Now
I'm not sure that if I can double, tripple, etc. my speed, then my
earnings will double, trippe, etc. of Y.  

No it won't. Assuming you're mining in a pool, double-ing your hash rate will only double your earnings if someone else takes the same amount of power offline in order for the total hashrate to remain constant. Think of it like this: in a day your total BTC = YourHashrate / TotalHashRate x daily mined BTCs. Since the daily mined BTCs are pretty much constant ... you got the idea. This happens because the difficulty adjusts to total hashrate.

2) When difficulty doubles, half as many BTC can be mined.

Yes. I would phrase it like this: half as many BTC can be mined in a given time period (i.e. 24h). There will be some variation until difficulty adjusts to the ASICs, but once the diff stabilizes ... you got the idea.

[bcpokey]

1) I've measured that with X Mhash/s speed I earn Y BTC/week.  Now
I'm not sure that if I can double, tripple, etc. my speed, then my
earnings will double, trippe, etc. of Y.  

No it won't. Assuming you're mining in a pool, double-ing your hash rate will only double your earnings if someone else takes the same amount of power offline in order for the total hashrate to remain constant. Think of it like this: in a day your total BTC = YourHashrate / TotalHashRate x daily mined BTCs. Since the daily mined BTCs are pretty much constant ... you got the idea. This happens because the difficulty adjusts to total hashrate.

2) When difficulty doubles, half as many BTC can be mined.

Yes. I would phrase it like this: half as many BTC can be mined in a given time period (i.e. 24h). There will be some variation until difficulty adjusts to the ASICs, but once the diff stabilizes ... you got the idea.

Well, that's not really right, which is why I phrased my answer as I did earlier. To explain why your explanation isn't wholly appropriate think of it as follows:

Imagine a pool has 100 Hashing units, you control 1% or 1 hashing unit. You then double your hashing power, to 2 hashing units, giving the pool a total of 101 hashing units. 2 / 101 * 100 = 1.98% or essentially 2%.

It only breaks down when you are a significant fraction of a pools total hashing power, at which point it is quite unlikely you will be doubling your hashing power at any rate.

[bobitza]

Pay-per-share is the only one where you can say that your BTC earned doubles when you double your mining speed (until they change the amount they pay per share of course). Other methods typically depend on what proportion of the mining power you generate (and some luck as well). For most small time miners however, doubling your hash power will effectively double your earnings, assuming other factors remain the same.

With your 1.98% example, aren't you contradicting yourself? Doubling your hash power does not double your earnings because a) 1.98% is not the same as 2.00% and b) the difficulty will increase to "match" the new total network hash rate.

2) When difficulty doubles, half as many BTC can be mined.

I fast read / misread this as "When the reward is halved, ..." and gave a response to that question. It just happened that the correct answer is also Yes, but for different reasons.

[nFast]

Thanks for the answers for everyone.


I think I've got it.  What really matters is my relative hashing power to the hashing power of the whole world.

If I mine in a pool and I double my hashing speed, I end up with a bit less than 2% (1,98% as bcpokey showed us in his example) of the hashing power of the pool.  On the other hand my pool's hashing power is now bigger (it is a little bit more likely to mine a whole block for my pool with my doubled power), so we all in the pool share a bit larger portion of the pie, so I will earn more than 1,98%.  I think it shouldn't matter that I mine in a pool or solo because of this.  So at the end of the day what really matters is my relative power to the whole world's power.  (...and not my relative power to the pool.)

To answer my own question:  I won't earn exactly double amount of BTC when I double my hashing speed, and the reason is the same why 1,98% is 1,98% and not 2%. The whole world is just a much larger pool than my mining pool.  What matters is the ration of my hashing speed to the whole world's hasing speed, but if I double it, it'll be still a bit less that double.  For instance if I would have 0.00001% of the hashing power of the whole world, and I could double it, I would have 0.00002 / 100.00001 (that is ~ 0.000019999998%).  The smaller my initial speed is before doubling, the closer I will be to the double income.

That'a why I stopped extrapolating difficulty and such things.  The base of my new calculation is that I must extrapolate the overall hashing power of all miners on the Earth (it should be an exponential curve because of the improving technology and improving popularity of bitcoin mining).

Code:

    r  :=    my hashing power  /  the overall hashing power

gives me a ratio that is easy to use to calculate the amount of BTC I can earn. (I must calculate it as a monthly, weekly, maybe daily average.) If X is the amount of BTC that can be mined in, for instance, 24 hours, and r is the average ratio for that day, then r*X is the average amount of BTC I'm gonna earn on that particular day.  (Of course it's not exactly the amount I'm going to earn because of fluctuation in the earnings, luck, etc., but the sum of these amounts over a future period should be quite correct in the long run, as long as my guess is good and the overall hashing power used in the valvulation is close enough to the real.)  The value of X is an easier one.  Suppose the world can mine a block in every 10 minutes, and the block reward is 25 BTC on that day, so the daily maximum is 24 * 60/10 * 25 BTC = 3600 BTC, and it will be 3600 in the next 4 years.

What I want to say is that I think there's no need to calculate anything else for a future period that the overall hash rate of the world.  That's the only value worth guessing for profitability calculations.  I would like to know if you see it in another way.

[jwzguy]

You can't "calculate" what the total network power will be in the future. You can only guess.

[nFast]

You can't "calculate" what the total network power will be in the future. You can only guess.

Okay, you are right.  I'm sorry for my English.  ...but fortunately you've guessed what I wanted to say.

That would be an estimation. A guess. Extrapolation. Lottery numbers. A subjective opinion. However, there are things that I *can* calulate.  The average increase in percentage in the past month by month or week by week.  The cca number of sold ASIC devices multiplied by their avg hashing power. Or the average of the guesses of others.

BTW you can't calculate the future difficulty either, just make guesses on it.  What I wanted to say is that you don't need to do so. It's enough to guess the overall hashing power, nothing else is needed.

[MrTeal]

Correct nFast. All other things remaining equal, the only thing that matters is your hashrate relative to the network hashrate. Unless you are a huge miner, doubling or trebling your hashrate will not significantly affect the network.

Even if you had say 100GH/s right now (~0.4% of the network assuming 25TH/s) and tripled that, you would now be ~1.19% of the network which should be a 2.976x increase in earning assuming the rising difficulty doesn't cause someone else to drop out. If you're in the single or 10s of GH/s right now your increase won't noticeably differ from linear.

[jwzguy]

Fine, but the real questions are ones I already asked, which you didn't answer.

You said you were interested in these calculations because you were about to start mining. So - how are you going to go about that now? What estimation are you making of future network power and how far in the future are you projecting?

[nFast]

You said you were interested in these calculations because you were about to start mining. So - how are you going to go about that now? What estimation are you making of future network power and how far in the future are you projecting?

Okay, the story is that I've started things just with about 6 Mhash/s and 10 days later with 30 Mhahs/s using CPUs. Yes, I know that it's ridiculous. The purpose was to measure the amount of BTCs that belongs to the hashing speed.  My initial assumption was that I can scale it up to a BFL Single 'SC's speed, but now I know that I was wrong.

I don't want to jump into GPU mining.  The plan is to get money from investors (actually we are already talking about it and I'm working on the financial plan part of the business plan) for this and skip the GPU level and jump directly to the Ghash level.  But before this I have to do an honest calculation about the profitability for the investors.  At this point I have an estimation for the overall hash rate for 2013 H1, which starts with an average of 33,2 Thash/s in January and goes up in June to 70,6 Thash/s in the last month.  These are totally subjective numbers, there's no science behind them.  It's just a guess.  But everything else in the calculation is real:  hosting prices, electricity, salary for the crew, taxes.  I'm struggling with the cost of capital a bit, but it'll be fine.  The critical part is the future hashing power...  (I'd like to know if you think these numbers are too low... and if so, why... and what do you think what would be a suitable method to somehow guess these values better - in a bit more scientific way)


The answer to your questions is:

1)  How to double the hashing power...  Well, in my case I have virtually no hashing power now, so it's not a big deal to double it. (The 30 Mhash comes form 3 HP servers, but it's just an own measurement, just for myself, just to see how mining works, and see a few real numbers. 6 servers woluld just double the hashing power, but the plan is something else.) In case of spending venture capital for mining hardware it does not look so hard to achieve a few hundreds of Ghash/s speed.  At his moment bASIC01 and BFL's Mini Rig seems to be a good solution, and scaling such a system up is just not a problem. If we need double power, we'll double the number of devices. The bASIC device needs an erhernet switch to go online, the other type has USB connector, and all I need is a relatively cheap PC.  Scaling up to the right size at the beginning is just a number:  how many devices will we buy, how much money will the investors bring in.  Scaling it up later will be another challenge.  What I do in my calculation is that I keep back money for that event.  I think after N months all the devices should be replaced with new ones that are the most efficient (I mean speed/price is the highest on the market) available at that future time.  I know that I won't be able to sell the old ones later.  The N month period unfortunately depends on the investors too, I would say 6 to 10 months would be real (yet another guess), but it depends on the amount of money they want to get back monthly.  (The larger this amount is, the later I can afford to upgrade the system.)

2)  Yes, I'm aware of the historical data, and I straggle to project it to the future. That's the weekest point of the whole thing. That's why I try to simplify everything to just project one single variable (the overall hashing rate) to that 6 months.  If the above method in my prev. post is correct, my next exercise will be to guess the future hashing speed as good as I know, somehow in my mind that ASICs will be switched on, most of the GPUs will probably go off-line, and after a few months faster devices can come to the market driving up the overall hash rate faster.

[MrTeal]

You said you were interested in these calculations because you were about to start mining. So - how are you going to go about that now? What estimation are you making of future network power and how far in the future are you projecting?

Okay, the story is that I've started things just with about 6 Mhash/s and 10 days later with 30 Mhahs/s using CPUs. Yes, I know that it's ridiculous. The purpose was to measure the amount of BTCs that belongs to the hashing speed.  My initial assumption was that I can scale it up to a BFL Single 'SC's speed, but now I know that I was wrong.

I don't want to jump into GPU mining.  The plan is to get money from investors (actually we are already talking about it and I'm working on the financial plan part of the business plan) for this and skip the GPU level and jump directly to the Ghash level.  But before this I have to do an honest calculation about the profitability for the investors.  At this point I have an estimation for the overall hash rate for 2013 H1, which starts with an average of 33,2 Thash/s in January and goes up in June to 70,6 Thash/s in the last month.  These are totally subjective numbers, there's no science behind them.  It's just a guess.  But everything else in the calculation is real:  hosting prices, electricity, salary for the crew, taxes.  I'm struggling with the cost of capital a bit, but it'll be fine.  The critical part is the future hashing power...  (I'd like to know if you think these numbers are too low... and if so, why... and what do you think what would be a suitable method to somehow guess these values better - in a bit more scientific way)

Your numbers are incredibly optimistic. Butterfly Labs' first run of chips is 20,000 units, most running at 7.5GH/s. They look poised to deliver most of 150TH/s by the end of December, with the rest probably online by the end of January. BTCFPGA has preorders for approximately 50TH/s worth of bASIC units that should be delivered some time in December. Avalon should deliver ~40TH/s in January. Blockerupter plans to start with 12TH/s shortly.

By the end of January, it's quite probable that the network hashrate will be over 250TH/s

[nFast]

Your numbers are incredibly optimistic. Butterfly Labs' first run of chips is 20,000 units, most running at 7.5GH/s. They look poised to deliver most of 150TH/s by the end of December, with the rest probably online by the end of January. BTCFPGA has preorders for approximately 50TH/s worth of bASIC units that should be delivered some time in December. Avalon should deliver ~40TH/s in January. Blockerupter plans to start with 12TH/s shortly.

By the end of January, it's quite probable that the network hashrate will be over 250TH/s

Hi,
Thanks for those numbers!  Could you please tell me what is the source of them?

[Unacceptable]

So that = a diff of about 33,108,768 with a network hashrate of 252 TH.

30,000 mh (30gh) @ 33,108,768 with BTC price @ $11 = .91BTC per day

About the same income I have with 3 gh today  

Now you need to set a goal,how many BTC/$ do you need per day  

Opps,forgot about the halving in early dec,cut that BTC in half  

[bobitza]

Here's a thing to think about it ...

If everybody thinks the same, then everybody will double the hash power, then you need to double your hash power just to stay at the same level of BTC gained.

[thoughtfan]

...I straggle to project it to the future. That's the weekest point of the whole thing.

@ nFast,  I am also a newbie so please don't take anything I have to suggest as having any authority.  I am quoting the above back at you because that's where I suggest you put your focus then keep it there for some time.  You have correctly identified that ascertaining the figures for the future is the weakest point of your (and everybody else's) models.  Even the soundest of guestimates may be out by an order of magnitude and the difference this make to the potential profitability of your proposed venture is immense.

Remember that the starting point with anything to do with Bitcoin is that it is not impossible that the exchange rate could drop to the floor tomorrow and take years to recover.  It is not improbable that it could do something like halve and hover there for a while before going...(?).  So if you're buying your gear with fiat money that needs to be taken into consideration.  I happen to believe Bitcoin's utility is such that it will continue to rise overall for some time.  But having that belief is a different kettle of fish to using it as an assumption upon which to make any investment that risks more than I can easily afford to lose.

So to put some of your money into Bitcoin with your belief of what the market is or isn't going to do is fine if you acknowledge there is a risk involved.

To put all your own money into Bitcoin would be even more risky.

To put all your own money into Bitcoin mining gear at any time is riskier still.

To put all your own money into Bitcoin mining gear right now with all the unknown variables is riskier still.

To put all your own money into pre-orders of Bitcoin mining gear where you don't know when in relation to everybody else's you'll be able to plug it in, that's assuming the company won't run away with your money is riskier still!

It is my opinion that multiplying each of these risks gets us to the stage where even attempting calculations about return on a serious fiat investment is a waste of time.

There are many threads and huge numbers of posts with back-of-the-envelope calculations on them.  Some people such as yourself are wise enough to know the assumptions upon which the numbers you start with are sketchy at best.  The problem I see is that once we put our beliefs into a formula and explain it all in this great newly-learned terminology of gigahashrates and difficulties I think we're making it very difficult to keep ourselves focused on how unreliable any results we are likely to come up with are¹.  'It's a number that comes after the equals sign.  Of course its the right answer!'

I don't want to be one of the doom-and-gloomers saying it's all finished and not to bother.

But as humans it is far too easy for us to blind ourselves with the $$ signs and refuse to let go of our belief that what we want to see happen in the future is quite likely not to happen.  It's the same reason 9 out of 10 businesses fail.  Most don't even look at the possibility of failure other than as a precursory exercise to put in the 'business plan' and of those who do look at it more seriously many still fail to allow the reality of the risk being taken to take its appropriate place in considerations of whether to proceed.  Optimism and a preparedness to continue in the face of adversity are great entrepreneurial traits.  But they go against us when we're trying to be realistic about risk.

If you've got some money of your own, would like to be part of this and acknowledge the significant risk you might have lost it forever then why not join the party as I'm doing myself

But I get shivers when I see happy hopefuls talking about borrowing money or getting investors involved in mining operations.  Of course if it's a bank you're borrowing from, ifyou have other means of repaying and or you were honest about what you were borrowing for then go bust it's their lookout.  In a way if it's investors it is their risk to take but your responsibility, as you rightly pointed out, to give them a realistic idea of what they can expect.  The problem is I don't think you or anyone else here who has really thought this through and taken all factors into consideration can give ourselves let alone investors an honestly 'realistic' idea right now.  I would highly recommend you don't risk the friendship you have with your potential investors and at least wait until things settle down in six months or so when calculations might give you some useful figures before involving anybody else.

All the best with your decision making

¹ It is one of the reasons I attempted to write a piece explaining mining dynamics with no terminology or calculations.  Don't get lost in the detail.  Make sure you thoroughly understand and accept the reality of the big picture before making decisions that involve any more than money you can afford to lose.  I also look at it from a different angle when asking whether mining will become more or less centralised

[jwzguy]

Great post, thoughtfan.

To people who want to get into mining now,  I applaud your decision to support the network. It seems very unlikely you'll break even on your equipment for a long time. If you do, it will be because you didn't cash out until the exchange rate went up significantly.

I think a lot of new miners (assuming they've read enough to understand what's going on) are counting on this eventuality. However, if your motivation is profit, it makes a lot more sense to buy directly and hold than to put yourself into a hole and hope the price goes up enough so that you get back to 0.

[bcpokey]

Great post, thoughtfan.

To people who want to get into mining now,  I applaud your decision to support the network. It seems very unlikely you'll break even on your equipment for a long time. If you do, it will be because you didn't cash out until the exchange rate went up significantly.

I think a lot of new miners (assuming they've read enough to understand what's going on) are counting on this eventuality. However, if your motivation is profit, it makes a lot more sense to buy directly and hold than to put yourself into a hole and hope the price goes up enough so that you get back to 0.

I agree with thoughtfan and to a limited extent your post. However, as a "long-time" member of bitcointalk (really 1.5 years isn't that long when you think about it), I can say that all this rubric sounds mightily familiar. When the network was expanding at a healthy clip alongside the expansion of BTC price the boards were filled with thread-wars about the barrels of cash that would be flowing in, vs. the people decrying how sorry they felt for the poor fools who would soon be selling their svelte bodies on the streets in attempts to repay their ill-considered mining purchases.

Both were right and both were wrong, some folks got in over their heads in their gleeful bitcoin lust (I remember one gentleman who claimed he spent $30k retrofitting his house with high-current lines), and some people made a mint off high-power farming rigs (some of the folks running 70+GH/s to this day on GPUs, eek). I myself was a middle of the roader, I expanded myself until I was limited by my household power capacity, and I made out well enough. I had to terminate my operation due to Californias high power costs before the evil times of the $2 coin set in, but I had repaid all my equipment, made a profit, had some fun, and happily move on.


So, I certainly understand both sides having their place, and I urge considered-enthusiasm, rather than dark gloom, or unbridled gorging.