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Rannasha

hero member

Activity: 728

Merit: 500

Quote from: kthejung on April 03, 2014, 04:48:11 PM

Quote from: Rannasha on April 03, 2014, 04:53:55 AM

If you earn X per day and you assume a difficulty increase of D every adjustment (D being between 0 and 1, with 0.1 meaning a 10% increase), then the total amount mined by the device will be at most:

14 X / D

So using your numbers, that's $204.13. The derivation of the formula mentioned above is fairly straightforward using the expression for the sum of a geometric series and some highschool algebra.

Of course there are number of assumptions that limit the accuracy of the prediction (constant difficulty increase each adjustment, constant Bitcoin-price), but the math is accurate.

The resulting solution seems decently a accurate estimation; easy to use as well. How did you come about this formula? Why does this work?

I derived it. The nice thing about a constant difficulty-increment is that you obtain a so-called geometric series for the mining income. And geometric series have (in this case) a very simple sum. I've posted the derivation once or twice here on the forum, so you can dig through my post-history. But I also just wrote a blog-post on the subject, so you can read more about it there: http://bitcoin.rannasha.net/?p=40

Quote from: ?? on ??

Quote from: Rannasha on April 03, 2014, 04:53:55 AM

If you earn X per day and you assume a difficulty increase of D every adjustment (D being between 0 and 1, with 0.1 meaning a 10% increase), then the total amount mined by the device will be at most:

14 X / D

So using your numbers, that's $204.13. The derivation of the formula mentioned above is fairly straightforward using the expression for the sum of a geometric series and some highschool algebra.

Of course there are number of assumptions that limit the accuracy of the prediction (constant difficulty increase each adjustment, constant Bitcoin-price), but the math is accurate.

Would you please give an example of this calculation? I couldn't reach the $204.13 by myself! What does 14 mean?

You mentioned a daily income of $3.0197 by the time you start mining and assumed a difficulty increase of 20.71% per cycle. Plug that in my formula and you get:
14 * $3.0197 / 0.2071 = $204.13
(note: You need to calculate costs and income in Bitcoin, not USD or any other fiat currency)

The significance of 14 is that it is the number of days between difficulty adjustments in the limit case where the difficulty changes by 0%. See the link I posted above for a full derivation of my formula and why the 14 stays in until the end.

J_Dubbs

sr. member

Activity: 322

Merit: 250

Quote from: teresaejunior on April 02, 2014, 05:20:40 PM

Please, I need urgent help with some math on the mining profit for some 120 GH/s rigs I bought, to be shipped in the beginning of May. According to CoinWarz, today I would earn US$5.31 a day on each one of them, without counting electricity costs.

Considering the difficulty goes up around 20.71% every 11 or 12 days, and it is going to adjust around the 5th of April, I would be earning around US$3.0197 a day by the 11th of May, which is about the time I would get them in my hands, right?

So I made a small bash script to calculate what I would earn in one year, based on my understanding, and still discarding electricity costs:

* First we multiply US$3.0197 by 12 to check what I would earn in the first 12 days: x = 12*US$3.0197 = US$36.2364
* y means all the money I have earned in the year, it starts at 0.
* One year has around 30 "groups" of 12 days: 365/12, which becomes the loop {1..30} below.

Code:

x=36.2364
y=0
for i in {1..30}; do
  x=$(bc -l <<<$(echo $x/100*82.85)) # x is reduced in every loop interaction
  y=$(bc -l <<<$(echo $x+$y))        # y = x + y
  echo $x dollars earned in this group of 12 days.
done
echo --- You will earn $y dollars in one year. ---

For me the result is 174.43 dollars in one year, which is less than what I paid for them. Also, in just a few weeks, I would be earning just a few cents a month, and I have totally ignored the electricity costs here.

I would be very grateful if I had some light shed here, and would be very happy, actually, if my math is totally screwed Wink

Thank you!

The further out you go the less accurate your forecasting will be due to the volatility of BTC. Kudos on the code but you really need to understand you are mining one thing and calculating your return in an exchange format, doesn't work that way. The math might not be screwed but the market is, if this were predictable we wouldn't bother.

kthejung

full member

Activity: 210

Merit: 100

Quote from: Rannasha on April 03, 2014, 04:53:55 AM

If you earn X per day and you assume a difficulty increase of D every adjustment (D being between 0 and 1, with 0.1 meaning a 10% increase), then the total amount mined by the device will be at most:

14 X / D

So using your numbers, that's $204.13. The derivation of the formula mentioned above is fairly straightforward using the expression for the sum of a geometric series and some highschool algebra.

Of course there are number of assumptions that limit the accuracy of the prediction (constant difficulty increase each adjustment, constant Bitcoin-price), but the math is accurate.

The resulting solution seems decently a accurate estimation; easy to use as well. How did you come about this formula? Why does this work?

precrime3

member

Activity: 84

Merit: 10

PM for journalist,typing,and data entry services.

Quote from: ?? on ??

I hoped to achieve at least a ROI, but it seems that won't happen Cry

It IS possible. Just mine till your close enough to break even, then resell. Many people buying antminers at normal price even used!

Rannasha

hero member

Activity: 728

Merit: 500

If you earn X per day and you assume a difficulty increase of D every adjustment (D being between 0 and 1, with 0.1 meaning a 10% increase), then the total amount mined by the device will be at most:

14 X / D

So using your numbers, that's $204.13. The derivation of the formula mentioned above is fairly straightforward using the expression for the sum of a geometric series and some highschool algebra.

Of course there are number of assumptions that limit the accuracy of the prediction (constant difficulty increase each adjustment, constant Bitcoin-price), but the math is accurate.

Meman

member

Activity: 92

Merit: 10

Quote from: ?? on ??

Thank you for the answers! The 0.0013 rate is more reasonable, but it still won't cover the expenses for the own miners, and in just a few months the miners won't be able to pay for their own electricity costs... Sad

Yes, but only if the difficulty rises with the same rate (as it did over the last 12 months) and the Bitcoin price stays where it is now (or even worse: continues to fall). I think, the difficulty will rise more slowly, once the next generation ASIC's are shipped out (that's just a speculation). It may even decrease at some point, but i think the chances for that are not very high (another speculation). You're welcome.

Meman

member

Activity: 92

Merit: 10

Yes. You can calculate it by yourself by entering the difficulty one year ago (ProfitDecline = CurrentBTCperDay/BTCperDay1YearAgo).
You can find historic difficulty data here (at the bottom of the page): https://bitcoinwisdom.com/bitcoin/difficulty

kthejung

full member

Activity: 210

Merit: 100

Quote from: Meman on April 02, 2014, 09:49:30 PM

Quote from: ?? on ??

The value 0.61 for "Profitability decline per year" really seems out of date, among other things in the list below.

To get a more realistic result, use 0.0013 (it's the btc gain decline from Mar 24 2013 to Mar 24 2014).

If you've mined an amount of 1 BTC each day in Mar 24 2013, you would mine 0.0013 BTC each day today (with the same hardware).

are you sure about the 0.0013 decline rate?

Meman

member

Activity: 92

Merit: 10

Quote from: ?? on ??

The value 0.61 for "Profitability decline per year" really seems out of date, among other things in the list below.

To get a more realistic result, use 0.0013 (it's the btc gain decline from Mar 24 2013 to Mar 24 2014).

If you've mined an amount of 1 BTC each day in Mar 24 2013, you would mine 0.0013 BTC each day today (with the same hardware).

kthejung

full member

Activity: 210

Merit: 100

According to this http://www.bitcoinx.com/profit/ using a difficulty of 6,500,000,000 that first month you should make about $100 per unit after electricity costs; I guessed the power consumption of your units to be about 200watts. I'm going to take a guess and say that revenue after that month will be about $70 and then $50 after that month; bringing the 3 month total to about $230. But mining is not really about the fiat profit, unless you plan to pay bills with monthly profit. Mining is about having more coins in the end than what you started with. If I have 3 btcs now and start mining and after a few months I have 4 btcs, then that's 1 more btc that I earned for doing minimal work. The price at the end of the year could be anything so I'm not concerned about the fiat revenue or profit until I sell the coins.

teresaejunior

newbie

Activity: 20

Merit: 10

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