Present Value of a your miner income as a Geometric Series

[ricksta]

So with all these discussion on if mining is profitable or not, I decided to do a quit analysis.

Assuming each day, you will make 4% less bitcoin due to difficulty increase. You have a 1GH rig. That will yeild 0.66BTC daily.

Assume you need 500W of power for 1GH rig. for the simplicity of this calculation, lets assume your electricity is free.

So now we have a simple geometric series problem, assume you will run your rig forever.

where Present Value = (Today's income/(1+DifficultyIncrease))/(1-1/(1+DifficultyIncrease))

Today's income is 0.66BTC, DifficultyIncrease is 4%

So the total income you will make from a 1GH rig is 16.5BTC. At today's exchange rate, that is $280

Which is well below the cost of a 1GH machine(about $1000), which makes your investment a negative present value of $720 if you paid $1000 today for a 1TH rig.

If you have a hard time seeing how the calculation come about,

Here is a simplified version:
Day   Income
0   0.66
1   0.6336
2   0.608256
3   0.58392576
4   0.56056873
5   0.53814598
6   0.516620141
7   0.495955336
8   0.476117122
9   0.457072437
10   0.43878954
11   0.421237958
12   0.40438844
13   0.388212902
14   0.372684386
15   0.357777011
16   0.34346593
17   0.329727293
18   0.316538201
19   0.303876673
20   0.291721606
21   0.280052742
22   0.268850632
23   0.258096607
24   0.247772743
25   0.237861833
26   0.22834736
27   0.219213465
28   0.210444927
29   0.20202713
30   0.193946045
31   0.186188203
........

If keep going until infinity, the sum is 16.5

Now if you factor in electricity cost, the present value will be even worse.

Now for those of you wondering, what if the price of bitcoin go up? So how high does it take for you to break even? So if present value of $1000 rig is 16.5 btc, that means the exchange rate should be 1000/16.5 = $60 to break even.

in another words, don't sell until btc is at $60, or you will never make your money back!

Personally, I think I bought into bitcoin too late to make any money, but I like the concept and I like to be a part of it just  because.

Feel free to tare this analysis apart, it is a very simple analysis.

[mmortal03]

Instead of 4% increase per day, shouldn't you use the percent increase per length of average difficulty period?

[Synaesthesia]

Well the difficulty won't increase indefinitely ... it's unpredictable actually.

[SlipperySlope]

I also believe that a more accurate model would be to apply the difficulty increase over an average duration - not daily.  The log charts at http://bitcoin.sipa.be/speed-ever.png are especially helpful in visualizing the steady, yet step-wise, increases.

Leaving aside speculation on when ASIC technology supersedes today's GPU technology, I assume that the difficulty will level off when a substantial number of miners quit due to high power and air conditioning charges due to their mining rigs. 

Worldwide, there is a large disparity in what miners pay for power.  For example, in Austin, Texas, USA, I pay about .13 USD per KWh.  My rigs are located in the crawl space under my house and operate without air conditioning.  They draw a total of 850 watts from the power socket.  That costs me about 2.63 USD daily.  I suppose that sometime in the next few months I'll be mining coins paying about 4 USD per day, and that difficulty will level off until the technology changes or BTC prices dramatically increase.

[ZombieDeity]

I hope this is as wrong as it sounds.  I just started mining with a 2 Gh/s rig yesterday.

[AngelusWebDesign]

Good luck; that's all I can say.

I hope your rig didn't cost you much.

[BombaUcigasa]

Next difficulty jump will be around 10% for 12 days. How did you calculate 4% per day?

You can never correctly estimate the real difficulty or bitcoin price in the future!

[bcpokey]

There should just be a bot for the forums that comes in to another thread with one of these "Future bitcoin mining" predictions, and just says "you assume you know the future therefore your analysis is wrong" and then closes the thread.

Yeah I have fascist leanings, sue me.

Anyway, a geometric series and a stepwise function will not at all yield the same thing, hence why you were wrong from the start. Additionally looking at merely the very first step in the more accurate stepwise function your progression falls apart. Rather than .404 on day 12 we are looking more like  .63

A model is only as useful as it is accurate, and yours misses the boat completely.

But you were doomed from the start by tackling an intractable problem, so it's not totally your fault.

I will admit however that A) You should not build a 1$/Mhash machine and B) You should not expect to make much profit in the current price/difficulty regime. We will see where difficulty heads however.

[mmortal03]

Well the difficulty won't increase indefinitely ... it's unpredictable actually.

That's true, but you are actually making my point for me.  It would be smart to assume, just as a rule of thumb, that it WILL increase indefinitely, however, assuming it will go up 4% daily doesn't seem to be the right way to conservatively estimate this.  It's got to be more like a weekly step pattern (unless my knowledge of calculus is waning, and you CAN accurately estimate a comparable area under the curve with the daily 4% estimate you are plugging in).

[BombaUcigasa]

Well the difficulty won't increase indefinitely ... it's unpredictable actually.

That's true, but you are actually making my point for me.  It would be smart to assume, just as a rule of thumb, that it WILL increase indefinitely, however, assuming it will go up 4% daily doesn't seem to be the right way to conservatively estimate this.  It's got to be more like a weekly step pattern (unless my knowledge of calculus is waning, and you CAN accurately estimate a comparable area under the curve with the daily 4% estimate you are plugging in).

EVEN if the difficulty and bitcoin numbers in the OP were exactly becoming reality, there is another variable that can't be predicted correctly in the future: BTC value.

Thus the OP conclusion that you're stupid to buy a 1000$ 1GH rig can't be verified at the moment, and could be or could not be true depending on how the price varies.

I recommend that the OP checks the evolution charts from mtgox, the difficulty charts, the cycle graphs and the approximation functions and do a better calculation.

[rearwheels]

Actually I don't mind reading about such modelling.

Of course he cannot be right (now). Why 4%? Why not 4.23567%?

4% increment to infinity vs X% difficulty increment every Y days.

It's just all hypothesis.

Everyone have their own view and parameters that they want to take into account in running their mining "business".

[gmaxwell]

That's true, but you are actually making my point for me.  It would be smart to assume, just as a rule of thumb, that it WILL increase indefinitely,

So I should start investing in heavy lifting spacecraft businesses because it would be smart to assume that in ten years, given your figures, we'll be at a factor 1.6e62 than now than now thus requiring us to construct a dyson sphere in order to power bitcoin mining?

Every exponential is a logistic in disguise.

I may not have much of a clue what the future hashrate will be— but I can easily predict a few things: It won't require us to capture the complete energy output of the sun, so any continued exponential projection is wrong beyond short time frames, and it won't become significantly unprofitable against power consumption for the most efficient operators. I can speculate about what efficient means in the future, but without knowing the exchange rate isn't useful. And anything thoughts about the future exchange rate will just be guesses.

[nebiki]

Every exponential is a logistic in disguise.

quite true. in fact, i expect the bound to be near what we're currently at. the "most efficient operator" is probably somewhere around 20cents/kwh (incl. maintenance cost and a minimum of profit to motivate him to keep his business going).

[rograz]

What mainly has been driving difficulty (during the past months) is prices increase of BTC and not the other way around like some ppl seem to believe (and hoping, wishing their BTC should be worth 100USD etc). Add 2-3 weeks for difficulty lag and you start seeing where the 40-60% increases we have seen for some jumps are coming from, if price stagnates or starts declining long term we'll go back to much smaller jumps in the 10-30% area until ppl start dropping out due to low profits.

[ZombieDeity]

No, no, guys... OP is right!  The sky is falling!  Quick, everyone sell me your rigs for next to nothing before they become literally worth nothing tomorrow!!!1!

[mmcgehee]

This is very on target discussion, but the data is old:

"in another words, don't sell until btc is at $60, or you will never make your money back!"  Hello??!?  It's over $600 now

And of course, difficulty continues to creep up.  So few, can hold their nerves calm, and calculate what's best.  Present value of an annuity is the right way to calculate, but do you calculate using dollars, or bit coins?

[goose20]

This is very on target discussion, but the data is old:

"in another words, don't sell until btc is at $60, or you will never make your money back!"  Hello??!?  It's over $600 now

And of course, difficulty continues to creep up.  So few, can hold their nerves calm, and calculate what's best.  Present value of an annuity is the right way to calculate, but do you calculate using dollars, or bit coins?

Unfortunately fiat aint going to die off as quickly as we'd like - so you be calculating using dollars still.