I don't understand the mining process. How is this distributed? When I run solo mining (I know, it is not recommended, but only for appreciation), is it guaranteed that my solo mining will find a valid block in time x (x=very long)? Or is this just like a lottery, say the mining can run 15 years without any success?
Thanks for your answer.
It is random. As your miner runs, it is like buying loads of lottery tickets. If you hit the "jackpot", you win 50 bit coins.
Mining in a pool means that there is a greater chance of winning, but if you win, the winnings are shared with other miners in the pool (and the pool operator takes a cut).
For example, on your own, you might have a 1% chance of winning per day. However, a pool might have a 50% chance of winning per day. If you win, you would only get 1 of the bitcoins.
The large ones tend to win once an hour or more. In those pools, you have a good chance of winning something but it is shared between lots.
The main point is that in all cases you win the same amount on average, but pools gives more consistency (pools take a fee, so are actually slightly lower).