It's interesting because I know a good deal about both subjects. I'm near a place that has good gold mining opportunity, and I researched and actually did some (got my panning technique down and everything) with the gold price rise.
Both are about luck and statistical odds. There are pro gold miners today that go weeks without finding more than a couple cents worth, working full-time with great equipment (sluices etc.). But if they keep at it they can hit a good patch and make 10K in one day. You just have to stick with it, and it's random. You'll eventually get something if you do it long enough, but the resources put into it may not make it worth it.
Bitcoin mining works the same. Everyone works on the same mathematical problem, not different ones. The problem is structured such that there is no way to make a program that solves it straight away. All the computer can do is guess then see if the guess fits as the answer. Since computers have different processing ability some can take more guesses per hour or second, whatever, to try solutions. So statistically computers with most processing power have better chance to guess the answer first and win before less powerful computers. However, that doesn't mean even a rinky dink dinosaur computer can't guess right on a few tries and win, it's just unlikely (but it does happen). Just like with gold mining if a computer competes long enough it will eventually get lucky and win. However, it may have taken so much electricity while trying it's not worth it.
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