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If the miner with the strongest ability to solve the block wins, why doesn't the same miner win every time? Wouldn't that miner still have the strongest ability to perform the proof of work on the next block and thus win every block?

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Mining is not won by the miner with the "strongest ability to solve the block". Mining is a random progress-free process. Each block candidate independently has a tiny chance to be a valid block.

Each miner is working on a separate, non-overlapping block candidate set. Block candidates assign the block reward to its author with an output in the Coinbase transactions and therefore each miner has their own transaction set differing to that of other miners. As everyone is working on a separate set of work, and every piece of work has an tiny chance of winning (independently of what else was tried!), mining is a Poisson process, rather than a linear stack of work that needs to be powered through. Therefore, the miner with the most hashing power has the greatest chance to win the block, but only probabilistically so.

Think of mining as buying a lottery ticket for each block candidate hashed. Only a fraction of the tickets in the pot are winning tickets, but somebody might draw a winner on their second try, while another has bought fifty losing tickets already. However, when you buy more tickets more quickly, your chance of winning is higher.

For a better overview what mining is, you can have a look at "What exactly is mining?".

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  • Thanks Murch. So the stronger hash power allows you to enter into the pot more often? – Jonathan Chad Faling Feb 24 '15 at 1:38
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    Each hash is a lottery ticket. Hashes per second (hashrate) are lottery tickets per second. If you do more hashes per second then you will find blocks more often. – Dr.Haribo Feb 24 '15 at 7:23

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