I had an old Raspberry pi with a Bitmain Antminer 2GH USB plugged into it.

I have joined the bitminter pool and so far have 0.00000094 bitcoins. In other words, I don't expect to get rich.

Researching this question most answers take into account power consumption.

My question is, for this sort of setup that I have with 1 - 4 2GH USB sticks, if I do solo mining, do I have much chance of getting a bitcoin now and then?

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    This is a very frequently asked question. The computation is easy and is explained here. Usually the answer is "no". In your case, at current difficulty levels and solo mining total of 8 GH/s, you can expect to mine one block every 286 years. – Nate Eldredge Jul 4 '14 at 19:38

Let's do the math. The average time to find a block, which is worth a reward of at least 25 BTCs (+fees) is the following:

avgtime = difficulty * 2^32 / hashrate

The current difficulty is 16,818,461,371. Assuming a hash rate of 2GH/s we get in hours:

avgtime = 16818461371 * 2^32 / (2*10^9) / 60 / 60

That's about 10032602 hours or 418025 days. To mine solo successfully, you need much, much more hashing power.

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