Can casual people still mine for bitcoins? As of October 2012, the difficulty seems very high, being over 3,000,000.
I've seen a ad for bitcoins, and watched the video. It said I could mine for them with my computer, so can I?
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Well, you can TRY mining. To see how much coins you can expect, check your computer's GPU on the Wiki page, get its hash rate, and plug that into a profitability calculator, such as mine. This can give you an idea of how many coins can you expect to mine and whether you would get any profit from that.
Unfortunately, most likely you won't be able to mine at a profit using a PC. Bitcoin's difficulty is quite high, the reward will be dropping by half soon, and with the introduction of ASIC miners, GPU mining will be outclassed. However, if you are willing to invest some money into custom hardware, you can still start your career as a full-time Bitcoin miner. But again, you ought to check if it calculates for you.
However, if you want to try your luck at a newly emerging trend of using your GPUs to "mine" for split-key vanity addresses, you can check out my Vanity Pool, or its topic on BitcoinTalk. The process is quite similar, but the profit margin can be better.
Normal people can mine but normal computers can't mine profitably. At least not any longer.
Right now, in mid-October 2012, some people are doing OK mining on GPUs, particularly those who don't pay directly for electricity. However, roughly sometime around the end of November the mining proceeds get cut by half instantly -- something that happens every four years.
After that point, there will not be many GPU miners who can continue to mine -- unless, again, they aren't paying for electricity.
Others have bought specialized hardware known as FPGAs (a BFL single is an FPGA). Those use less electricity than GPUs so they will still mine at a profit.
But a gamechanger is likely coming from ASIC manufacturers. Several are accepting pre-payment on orders now, though not a single ASIC design has shipped yet.
There's no harm that occurs from using your computer (with GPU) to try to learn mining -- if you are looking for a hobby. But to mine for profit will generally only make sense from the purchase of mining hardware.
If you know your estimated hashrate and power consumption, or can estimate it using the wiki, you can work it out for yourself:
Estimated earnings / sec = Ghps * 1e09 / 2^32 * B / D * exch.rate - elec.cost / 1e03 / 3600 * watts
Ghps = estimated device hashrate in Ghps
B = bitcoin block reward, currently 50 btc, soon to be halved to 25 btc
D = mining difficulty, currently 3072321
exchange rate = btc to your currency exchange rate
elec.cost = cost of your electricity in your currency
watts = the estimated power consumption of your computer + GPU
As long as the estimated earnings are > 0 and you don't have to outlay anything, mining won't cost you.
If you mean getting actual profit without cheap/stolen electricity you should at the minimum have a high-end AMD GPU.