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My question term race is not about race attack term.

I've read https://en.wikipedia.org/wiki/Bitcoin and want to get practice using Bitcoin, no need to recover electricity bills and get profit now.

One of things not clear to me - is creating new block a race? That is, whichever mining pool first solves puzzle will get the reward, others just wasted processing efforts for that block? If yes, how do small pools compete with the largest one?

If I install say p2p mining software on ordinary PC, can I expect to gain some micro-microbitcoins in several hours (as block is added each 10 minites)? If I join largest pool?

Does mining always means gaining both new bitcoins issued and transaction fees?

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Yes and no:
Yes, the first one to find a block gets the whole reward and the others have wasted their effort. But there is no progress in mining, so every attempt to build a block has the same chance at success. Therefore, your chance at finding the next block is equal to the percentage of mining power you contribute to the network.

Also see:

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