The difficulty has been increasing more-or-less exponentially since the first increase 30/Dec/09, see
http://forum.bitcoin.org/index.php?topic=43.0http://forum.bitcoin.org/index.php?topic=1918 In this thread I calculated the expected number of blocks you can ever generate, assuming an exponentially increasing difficulty. I've refined the calculation a bit - the original didn't take into account the fact that the time between difficulty increases was not 14 days, but shorter, depending on how fast the 2016 blocks between increases are generated.
I won't go into the details, but the equations are:
E = Ch/((a-1)D)
P
0 = exp(-E)
h
0.5 = -(a-1)D ln(0.5)/C
Where:
C = 0.0002818 is a constant
h is your hashes-per-sec: 1Ghps = 1x10
9a is the difficulty increase factor, i.e. if difficulty goes from 20 to 30, then a=1.5
D is the current difficulty
P
0 is the probability that you will never (never ever ever) generate another block. See note 4 for the meaning of "never".
h
0.5 is the hashes-per-sec that you would need to have a 50/50 probability of generating just one block.
E is the total number of blocks you can expect to ever generate, ever. See noe 4 for the meaning of "ever".
Current values are:
D = 244139
a = 1.3435 (see note 1)
Therefore, with 1Ghps:
E = 3.36 blocks
P
0 = 0.0347
h
0.5 = 206 Mhps
So, if you do buy the rig, you have a 3.5% chance of never ever generating another block. You can expect to create 3.36 blocks = 168 BTC = $1092 at current exchange rates. To have a 50/50 chance of creating a block, you'd need to have 206Mhps (this has nothing to do with you and your rig, it just gives an idea of what the entry-level Mhps is - a top CPU now would generate at most, I expect, 10-12 Mhps).
On the other hand, if you buy $700 of bitcoins now, then you'll have 100 bitcoins right now. That's about 2/3 of what you can expect to get spending on a rig and generating. All depends on whether you think the price is gonna go up or down. Good luck.
Notes:
1. Difficulty is assumed to rise exponentially forever. This is incorrect, but it's holding up much better than I would have expected - see attached graph. The inset to the graph shows the difficulty increase factor. If we average this value over all blocks since the first actual increase in difficulty, we obtain the value a=1.3435
2. Eventually the reward for a block will halve, then halve again and so on. You can expect 3.36 blocks, but if they happen to be generated after the reward halves, then you'll get less than 168BTC.
3. If you mine solo, then you won't get 3.36 blocks, it'll obviously be either 2,3,4,5 or whatever. If you mine in a pool, then you can expect a reward equivalent to 3.36 blocks, less the pool's fee.
4. You will receive these bitcoins slowly. When I say "all you'll ever expect to generate", I really mean "ever" - from now until the sun goes nova and swallows the earth. However, I expect that the exponential increase will stop before then, for one reason or another. Likewise "never".
5. You'll have to add in electricity costs.
6. These values for E, P0, h0.5, assume you start mining *now*, if it takes you a month to get started, then adjust for the difficulty at the moment you start.
If this post saves you money: 15BHRM52yuzjNyvkrdu8dcWFnfpK6eWsXm
I tried to upload a graph, but a message says the upload folder is full, please contact an admin. Any admins listening? In the meantime, I've put it on ubitious:
http://ubitio.us/file/download/328 I can't help that you have to pay for the file (BTC 0.02), but as soon as I can, I'll attach it here.
EDIT: the graph is simple really, it's just a graph of difficulty Vs time, with an exponential fit, and also another curve showing the difficulty increase factor. All info for it was taken from blockexplorer.com.