"Let's also suppose that the difficulty continues to increase at about 50% per month as it has for the past few months. That means that starting now your USB Block Erupter will mine no more that 0.41 BTC over its lifetime."
How can this statement be true if you leave it plugged in it will mine and it will make money no matter how small the amount? So you mean to tell me if i ahve 500 block erupters and i just leave them going for 5 years I'm only gonna make .41 bitcoins? I find this false. Please show me the math and dont give me no shit about power cost.
If you have 500 miners running at 336 MH/s, then you will mine at most 500 x 0.41 = 205 BTC, if the difficulty increases 50% per month every month for the next 5 years. However, 500 miners are going to cost you 350 BTC up front.
It is an interesting bit of math. Here's a simple example: Let's say that you are paid a certain amount of bitcoins every week forever. The first week is 1 BTC and each following week is 1/2 of the previous week.
You would get this many bitcoins:
S = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ...
This is called a "power series", and without going through all the math, I'll just tell you that you will receive 2 BTC total even though you will be receiving bitcoins forever.
In a more generic form, a power series looks like this:
S = 1 + r + r
2 + r
3 + r
4 + ...
and the result when 0 <= r < 1 is this surprisingly simple expression:
S = 1 / ( 1 - r )
In the example above, r is 1/2, so S is 1/ (1 - 1/2), or 2.
Now, let's talk about mining. If the difficulty increases by 20% every difficulty period, then a miner mining at a fixed hash rate will mine 83.3% of the coins it did during the previous period. This is a power series in which r = 1/1.2!
So, with a difficulty increase of 20% each period, then
S = 1 / (1 - 1/1.2), or 6
This means that if the difficulty rises 20% every period you will mine will up to 6 times the amount you mined in the first difficulty period. Your miner currently mines 0.06327 BTC every period, so the total your miner will ever mine from now on in this case is 0.3822 BTC.
If the difficulty increases by 10%, then the total will be 11 times the amount mined in the first period. Your miner will mine 0.696 BTC
Of course, the difficulty can't increase at 20% or even 2% forever, so you are technically correct. The difficulty will flatten out someday. However, the reality is that you will not mine forever, and also with the difficulty increasing so quickly these days, the small amount you mine this year is going to be 100 times what you mine next year.
The best thing to do is to avoid paying more for a miner than what it will mine, but if you can't do that, then the next best choice is to just buy the bitcoins outright now, and then use them to buy a miner when the difficulty finally flattens out.
