Hi xhomerx10. I'd be interested in the specifics you used in your calculations. A couple of observations. First, difficulty has been going up by more than 2.5%/day and the next increase looks to continue this trend. Secondly, don't forget to factor in the cost of powered USB hubs to operate your satoshi sticks.
Cheers.
Hi Creativex,
I was calculating a compounded rate on diff and if you take 2.5% compounded daily over 10 days (which is as long as the Bitcoin network took to finish the last 2 sets of 2016 blocks) it works out to just shy of a 30% and I think the last two changes were right around there. I didn't factor in electricity costs - I am merely trying to show the
maximum number of coins you can generate. If you can't mine at least as many bitcoins as it would take you to buy it at today's exchange rate, it is simply not worth buying the device. The bitcoins would be a better purchase for your money.
Essentially, I calculated the current reward and used a power series to factor in the rate of change of difficulty hence the declining reward.
Consider h is hash rate in hashes per second, t is time in seconds, D is difficulty, the probability of generating a block is 1/(2^32*D) and the current block reward is 25 BTC
reward = 25*h*t/(2^32*D)
now substitute 86400 seconds for the time to represent one day's reward for each subsequent day, increase D by 2.5% (so D*1.025) of the previous day and as you can see we have a convergent power series: 1 + x + x^2 + x^3... whose sum can be calculated using the formula [x^(m-1)-1]/(x-1) for m iterations OR to simplify further, we can use an infinite number of iterations which gives us the sum 1/(1-x)
x will have the value 1/1.025 (because D is in the denominator) if we consider the 2.5% per day compound increase so the sum of this power series is 1.025/.025 or 41
Simply multiply the initial reward by 41 to get the total number of coins you can mine in an infinite number of days.
So total reward (@ 2.5%/day increase in difficulty) = [h/d] * [(41*25*86400)/2^32] which you can use for any device. If you want to use a different percentage increase, substitute 1/(1-x) for 41 (so for your 3% assumption we would get 34.3)
Right now I have 13.6 GH/s in USB miners and my total reward will be 4.26 BTC if the network hash rate continues to increase at this pace. I realize there is actually a step change in difficulty every 2016 blocks but even if I use a 10 day period (which is how long the last 2016 blocks took) and 30% compounding instead, the result is only slightly larger ~ 4.5 BTC. I don't even want to say how much I spent to get them but I can't make an argument without it so... about 22BTC. Now if those 4.5 BTC I can ultimately generate are worth as much as the 22 BTC I spent to get them, then I'm good but imagine what those 22 BTC would have been worth if I had saved them instead ;( Live and learn!
Take care
PS based on the 2.5% increase, a 2 TH/s miner received 90 days from today would mine 1.65 BTC/day so you're right, at 14k, it's still only worth a wait-and-see!