Theoretical limits, given 14 days per difficulty and 50% increases in difficulty

[[Coins!]]

So there is a way to calculate a theoretical limit of a given operation, given diminishing returns.

Right now hashing power is way too high, the next retarget is basically 8 days away (check out block explorer's eta function).

Retargets have been 50% for the last few bits.

We are at the 131,000ish block level right now.  210k - 131k = 79k.  So 79k blocks to complete before only 25 btc's are rewarded instead of 50btc's.

79k blocks / 2016 = 39 difficulty increases.

Assume a single miner is rocking 1.0Ghash, and thus generating 1 BTC per day.

They will generate 14 coins over 14 days, and then there will be a retarget adding 50% difficulty.  This will repeat every 2016 blocks until we hit the 210000th block, at which point generation is halved, so that will be my end-time.

So the limit, as x approaches 39, of 14 +14*(2/3)+14*(2/3)^2 +...+14*(2/3)^39 can be represented by a limit of some kind (math gurus jump in here):

I just used excel and calculated out the sums by dragging a simple formula for the coins per day, and each subsequent cell was 2/3 of the previous value.

I basically got 35 coins, maximum, for each 1.0Ghash by the 39th difficulty increase, assuming it actually does take 14 days per difficulty. If it takes less than 14 days, then obviously each 1.0Ghash is worth less than 35 bitcoins.

For me, at 330mhash, I mine 0.33 coins per day (4.6 coins in a 14 day difficulty right now).  My maximum output is therefore ~11.5 coins, theoretically, over the next 39 difficulties.  But really, once I get to the 6th difficulty, I'll have already created ~11 coins.  So I will drop out in 6 difficulty increases, as I don't see much point in spending another 33 difficulties to get 1 coin.

So for those of you investing in mining rigs.  I'd take a look at these #'s.

[1714880393]

1714880393

[1714880393]

1714880393

[1714880393]

1714880393

[1714880393]

1714880393

[Beremat]

All of these analyses don't take into account the price of bitcoins, which is pretty much impossible to predict.

[MoonShadow]

Interesting analysis.  Can't say that I would agree with your premises, though.

[Yuvea]

models suck if the assumptions are not valid!

in your case, these are the issues I see after a quick glance:

-no model for fluctuation of BTC prices
-assume exponential growth of total network hashing power for the next 40 increases
-difficulty increase is not based on a model for expected hashing power but rather on a static +50% increase
-no link between price of BTC and difficulty
-where is the time period?  39 difficulty increases is more than a year's worth of mining...

[bcpokey]

Please stop making these threads. There is a "beginners" that links to a thread that makes the exact same "analysis" pinned to the top of this forum.

First things first, 14 days difficulty requires ZERO increase in difficulty. Difficulty increase occurs when block rate occurs faster than predicted average should be. 50% difficulty increase requires ~7-9 days between difficulties.

Next, the fact is that these analysis make no sense because a static difficulty increase makes 0 sense. Retargets have been at 50% for... 1 difficulty change. Before that it was a 25% retarget. Before that 65-75%, before that 40% before that 30ish%.
Not to mention a static PERCENTAGE increase means an exponential numerical increase (of difficulty/hashing power). This is completely unfeasible unless price continues to rise at a similar rate.

In fact, in 2 difficulties it is likely your analysis will fall through like a brick on a wet paper napkin. Next difficulty is set to bump over 1million difficulty, but price has just fallen through the floor to around $13 (probably end at $10 or so). This makes mining a complete flip of the $30 / coin 500k difficulty point at which all the machines that are coming online now to bump the hash rate up were bought. Some people will try to stick it out because they sunk their money in so foolishly, many people will run up a massive sell-off to try to recoup the losses they suddenly find themselves taking.

Anyway, that's all short term, long term no one knows, which is why I don't like these threads. The future is not a line on a chart.

[[Coins!]]

All of these analyses don't take into account the price of bitcoins, which is pretty much impossible to predict.

This is true, but the bulk of people in this forum are in here for the long haul, I believe.  All the GPU's pointed at the network aren't going anywhere until mining starts to suck (6 difficulties from now).

Interesting analysis.  Can't say that I would agree with your premises, though.

Which ones? Why not?

models suck if the assumptions are not valid!

in your case, these are the issues I see after a quick glance:

-no model for fluctuation of BTC prices
-assume exponential growth of total network hashing power for the next 40 increases
-difficulty increase is not based on a model for expected hashing power but rather on a static +50% increase
-no link between price of BTC and difficulty
-where is the time period?  39 difficulty increases is more than a year's worth of mining...

As long as BTC are over $1USD, I would say my predictions are valid.
I do indeed assume exponential growth.  WHy wouldn't I, given that it has been exponential recently, and more and more media attention is bringing in new miners?
Yes, the static 50% is an assumption (Based on exponential growth, which isn't guaranteed, but it is part of my model).
See point #1 above.
Time period is based on now until the 210,000th block, at which point 50 BTC reward becomes 25, and people drop like flies.

[[Coins!]]

First things first, 14 days difficulty requires ZERO increase in difficulty. Difficulty increase occurs when block rate occurs faster than predicted average should be. 50% difficulty increase requires ~7-9 days between difficulties.

7-9, days. Ok : )  So could be that 6 difficulties pops up in early August.

Next, the fact is that these analysis make no sense because a static difficulty increase makes 0 sense. Retargets have been at 50% for... 1 difficulty change. Before that it was a 25% retarget. Before that 65-75%, before that 40% before that 30ish%.
Not to mention a static PERCENTAGE increase means an exponential numerical increase (of difficulty/hashing power). This is completely unfeasible unless price continues to rise at a similar rate.

I agree price is a factor, but there are a lot of GPU's out there with bored users, that don't need a lot of incentive to just point unused cycles at the network.  Users like me for example. Widespread media attention (the hacking of the 25k coins, the acceptance of BTC by wikileaks, MtGox articles, etc) will only bring new users onboard who don't need to invest much if any capital to continually double the hashing power of the network.  I am not saying it is bad, but I completely disagree that it is unrealistic.

In fact, in 2 difficulties it is likely your analysis will fall through like a brick on a wet paper napkin. Next difficulty is set to bump over 1million difficulty, but price has just fallen through the floor to around $13 (probably end at $10 or so). This makes mining a complete flip of the $30 / coin 500k difficulty point at which all the machines that are coming online now to bump the hash rate up were bought. Some people will try to stick it out because they sunk their money in so foolishly, many people will run up a massive sell-off to try to recoup the losses they suddenly find themselves taking.

Yes, foolishly.  I agree, given my analysis and your input that doublings/retargets could occur in 7-9 days instead of 14.  Unless 1.0Ghash mining 20-35BTC breaks even in terms of USD, those mining rigs don't appear to be the greatest investment.  Right now (15 USD) 35BTC recoups $475 or so.  At $20 USD they recoup $700.  At $30, might be break-even. Hopefully price rises, and more people discover bitcoins.

[MoonShadow]

I agree price is a factor, but there are a lot of GPU's out there with bored users, that don't need a lot of incentive to just point unused cycles at the network.  Users like me for example. Widespread media attention (the hacking of the 25k coins, the acceptance of BTC by wikileaks, MtGox articles, etc) will only bring new users onboard who don't need to invest much if any capital to continually double the hashing power of the network.  I am not saying it is bad, but I completely disagree that it is unrealistic.

Hmm, maybe.

Care to make a wager?

[k]

50% difficulty change means exactly 9.3333 between difficulty change (2016 blocks, meant to take 14 days, 14/9.33333 = 1.5)

[smell]

So the limit, as x approaches 39, of 14 +14*(2/3)+14*(2/3)^2 +...+14*(2/3)^39 can be represented by a limit of some kind (math gurus jump in here):

14*(1/(1-(2/3)))=14*3

It's a geometric series: http://en.wikipedia.org/wiki/Geometric_series

Or use my calculator: http://bitcoinstuff.appspot.com

[[Coins!]]

Hmm, maybe.

Care to make a wager?

Perhaps good sir.  What are the terms ?

50% difficulty change means exactly 9.3333 between difficulty change (2016 blocks, meant to take 14 days, 14/9.33333 = 1.5)

Ooh ok.  9.3 days then, instead of 14.  I'll leave my original post alone, but redo the calculations down here.

14*(1/(1-(2/3)))=14*3

It's a geometric series: http://en.wikipedia.org/wiki/Geometric_series

Or use my calculator: http://bitcoinstuff.appspot.com

Ah ok.  So given my premises above (which may not be correct, of course) then we basically have:

N*3

As the theoretical maximum, where N is the number of coins you're mining right now in this difficulty.  N becomes 2/3 of its value each difficulty increase, given 50% increases

If difficulty increases every 9.3 days, and adds 50%, then my theoretical maximum # of coins is:

Coinsperday = .33
# Days = 9.33
Coins at current Difficulty = .33 * 9.33 = 3.07  (This is N)

N*3 = 3.07*3 = 9.23

Our theoretical 1.0Ghash miner will get 9.3 for his value of N.

9.3*3 = 27.9 maximum coins over the next 39 difficulty increases (given 50% increases in difficulty)

At $20/coin I make $180 or so.  

At $20/coin our theoretical miner makes $558.

By the 6th Difficulty I'll have mined up 8.4 coins, and by the 39th I'll have mined up an additional 0.8 coins.  

Provided of course that people do keep hearing about Bitcoins, and that people are willing to continue adding hashing power to the network by a factor of ~2 each 9 days for the next 6 difficulties (45 days).

[MoonShadow]

Hmm, maybe.

Care to make a wager?

Perhaps good sir.  What are the terms ?

A simple over/under straight bet.  Based on your calculations, at the calculated date.  If the difficulty is, say 98% or higher of your projected amount, you win.  If lower than 98% or your projected difficulty, I win.

Five bitcoins is the wager.

[[Coins!]]

A simple over/under straight bet.  Based on your calculations, at the calculated date.  If the difficulty is, say 98% or higher of your projected amount, you win.  If lower than 98% or your projected difficulty, I win.

Five bitcoins is the wager.

Well as you can see here I do not have 5.0 bitcoins : p  (That is the address in my signature too, by the way).

I may only end up with 5 bitcoins just as the 2016th block is hashed in this current 877k difficulty round. Based on my calculations I'll only end up mining a grand total of 9 bit coins in the next 6 difficulties (55.8 days at the 9.3 days-per-difficulty at 50% increases from above).  So wagering more than half my projected wealth seems a bit too steep for me : (  15 days worth of hashing!

What projected date, though.  

Block explorer lists the next difficulty at 1200518.48071190, which is a 36% increase.   To be 50%, it would need to be 131k.  Obviously the lower the earlier difficulties, the less likely it is that my 50% calculations hold up by the 6th difficulty round~

[MoonShadow]

A simple over/under straight bet.  Based on your calculations, at the calculated date.  If the difficulty is, say 98% or higher of your projected amount, you win.  If lower than 98% or your projected difficulty, I win.

Five bitcoins is the wager.

Well as you can see here I do not have 5.0 bitcoins : p  (That is the address in my signature too, by the way).

I may only end up with 5 bitcoins just as the 2016th block is hashed in this current 877k difficulty round. Based on my calculations I'll only end up mining a grand total of 9 bit coins in the next 6 difficulties (55.8 days at the 9.3 days-per-difficulty at 50% increases from above).  So wagering more than half my projected wealth seems a bit too steep for me : (  15 days worth of hashing!

What projected date, though.  

Block explorer lists the next difficulty at 1200518.48071190, which is a 36% increase.   To be 50%, it would need to be 131k.  Obviously the lower the earlier difficulties, the less likely it is that my 50% calculations hold up by the 6th difficulty round~

The wager can be any amount of bitcoins that you wish to commit.  It's not about the amount for myself, but the fun of it.  

9.3 days * 6 difficulty adjustments = 55.8 days.  So make it 60 days from  tomorrow, Sunday June 18th at noon Eastern time is when the bet is final.

Bet starts with the next difficulty setting the bar, but I'll lay out the difficulty over/under based upon the estimate presently on bitcoinwatch.com.

((((((1,052,445 next difficulty, estimated) * 1.5) * 1.5) * 1.5) * 1.5) * 1.5) * 1.5) * .98

11988006.328125 * .98 = 140838049808701.7442626953125, or over 130 million times higher hashing power than the next estimated difficulty?  Wow, did I do that right?

So the over under difficulty would be 140,838,049,808,701 dropping the decimals, assuming that the estimated difficulty is the actual difficulty.

Feel free to check my math, please.


EDIT: I definately did something wrong here.  Yup, decimal screwup.  11748246.2015625 is 98% of 11988006.328125.  So the over under would be 11,748,246.  About ten times the next estimated difficulty.  That sounds more like it.

[bcpokey]

Yay! Another difficulty bet! The last one was awesome, I think Cyde came out by like 1000 difficulty which was amazing. I don't expect this one to be as interesting, but I enjoy watching these nonetheless

[Mageant]

I think there is a very simple lower limit you can calculate mining regardless of price of future BTC in dollars.

With a certain set of hardware figure out how many bitcoins you will be able to mine with that hardware. Since the returns diminish they will approximate a certain number of bitcoins.

Then calculate how many bitcoins you could purchase for the price of that hardware at the current price.

If you can buy more bitcoins with the money then do that instead of buying hardware. That will certainly be more profitable because this calculation does not even include the price of electricity.

[[Coins!]]

The wager can be any amount of bitcoins that you wish to commit.  It's not about the amount for myself, but the fun of it.  

9.3 days * 6 difficulty adjustments = 55.8 days.  So make it 60 days from  tomorrow, Sunday June 18th at noon Eastern time is when the bet is final.

Bet starts with the next difficulty setting the bar, but I'll lay out the difficulty over/under based upon the estimate presently on bitcoinwatch.com.

((((((1,052,445 next difficulty, estimated) * 1.5) * 1.5) * 1.5) * 1.5) * 1.5) * 1.5) * .98

11988006.328125 * .98 = 140838049808701.7442626953125, or over 130 million times higher hashing power than the next estimated difficulty?  Wow, did I do that right?

So the over under difficulty would be 140,838,049,808,701 dropping the decimals, assuming that the estimated difficulty is the actual difficulty.

Feel free to check my math, please.


EDIT: I definately did something wrong here.  Yup, decimal screwup.  11748246.2015625 is 98% of 11988006.328125.  So the over under would be 11,748,246.  About ten times the next estimated difficulty.  That sounds more like it.

Well, a) Including the next difficulty, which I think will be higher than 1.05m btw, I only plan to stay in 6 more difficulties, not seven. So we'd have

1.05m * (1.5^5) = 7,992,004  +/- 2% (which is prettty precise).  

So the point is 7,992,004-2% if I assumed I was going to be accurate within 2%, an accuracy that would earn me some kind of psychic award : )  

b) Since we're waiting the next 6 days for the next retarget, we only need 5 * 9.3 + the 5 days so ~45 becomes ~50 given your generous +10% days.  So it would be 50 days after the next retarget.

c) Give me a slightly larger variance, say 10%, and I'll stick with your premise of 1.05m and 50% increases over the next 50 days.  I realize that if the retargets are under 50% that the days will be completely off (14 for example instead of 9.3 with a zero increase in difficulty).  Sound good? And since I don't have an awful lot of btc, how about a whopping 0.5BTC !  

d) Final #'s : 1.05m * 1.5^5  = 7,992,004 variance of 10% (which is 799200). Bottom range being: 7,192,803

50 days from the next retarget which is due in 6 days (June 25) is August 14th.

Bet: 0.5 BTC

I think there is a very simple lower limit you can calculate mining regardless of price of future BTC in dollars.

With a certain set of hardware figure out how many bitcoins you will be able to mine with that hardware. Since the returns diminish they will approximate a certain number of bitcoins.

Then calculate how many bitcoins you could purchase for the price of that hardware at the current price.

If you can buy more bitcoins with the money then do that instead of buying hardware. That will certainly be more profitable because this calculation does not even include the price of electricity.

Without knowing what BTC's are worth, though, that is hard to predict in that fashion.  For me, I wanted a GPU for gaming, so I am just a bored user waiting for the next big MMO adding my GPU to the network's hashrate.  As word grows, people like me will likely be the bulk of the miners, since it costs us virtually nothing and we'd be buying the hardware anyway.

[nebiki]

well, i am considering buying a second 6950 for my gaming computer. because under normal circumstances i wouldn't pay an extra 200eur for an additional card, it would still be an investment. my calculations tell me that if i mined for the next few weeks, the card would have cost me about 100eur. it's a hard decision for me. maybe if i find a card with a pre-installed EK block for ~210, i'd do it. luck could still get me some more profits, if the rate would align with the difficulty any time soon. i'm definitely out in 4 weeks, though. european electricity cost is just too much.

[Lars]

The idea that we will see a 50% jump in difficulty every time for the next 39 adjustments is VERY unreasonable. Let's do the math here.. 1.5^39=7371554 and change. Basically you are assuming that the hashing power of the network will increase by ~7.5 million times it's current value. At the systems current level of maturity I seriously doubt that.

Let's do some more estimates around this figure.. Assuming 15000 GPUs make up todays network. (I'm probably off by quite a bit, but not by any significant order of magnitude) For your assumption to hold true, in about 2 years we would be having 15000*7371554=110573310000 GPUs in action. Or about 20 GPUs per person on the planet. I'm not even sure if we have enough power on the planet to run that many cards.

If you truly beleive this then I suggest you go out and put all your money in AMD stock on whatever exchange they are being traded. For everyone else I suggest you just keep your miners running. Growth in computing power/increases in difficulty will at the end of the day be connected to the profitability of this kind of operation. Right now the profits from mining are insane, and we have lots of people moving in to take advantage of that fact. Eventually we will get to a point where you need a full year or so to break even, and at that point people will probably stop adding more power to the network. But as long as we are seeing crazy profits (like less than 3 months to completely pay off a rig) we will keep getting more and more rigs set up at the rate we are seeing now.

[[Coins!]]

The idea that we will see a 50% jump in difficulty every time for the next 39 adjustments is VERY unreasonable. Let's do the math here.. 1.5^39=7371554 and change. Basically you are assuming that the hashing power of the network will increase by ~7.5 million times it's current value. At the systems current level of maturity I seriously doubt that.

Let's do some more estimates around this figure.. Assuming 15000 GPUs make up todays network. (I'm probably off by quite a bit, but not by any significant order of magnitude) For your assumption to hold true, in about 2 years we would be having 15000*7371554=110573310000 GPUs in action. Or about 20 GPUs per person on the planet. I'm not even sure if we have enough power on the planet to run that many cards.

If you truly beleive this then I suggest you go out and put all your money in AMD stock on whatever exchange they are being traded. For everyone else I suggest you just keep your miners running. Growth in computing power/increases in difficulty will at the end of the day be connected to the profitability of this kind of operation. Right now the profits from mining are insane, and we have lots of people moving in to take advantage of that fact. Eventually we will get to a point where you need a full year or so to break even, and at that point people will probably stop adding more power to the network. But as long as we are seeing crazy profits (like less than 3 months to completely pay off a rig) we will keep getting more and more rigs set up at the rate we are seeing now.

39 times was to the 'endgame' where 50 BTC -> 25BTC for blocks.

In reality, as you can see doing the math, 6 30-50% increases over the next 50 days is enough to push me out of the market.  

Your argument that 39 consistent increases of 50% is improbable is fine.  However, try to prove to me that 6 more 30-50% increases are improbable.  It only takes 6 big increases in a row (including the next one which I think will put the difficulty in the neighborhood of 1.4M) to make the next 33 negligible to me.