Quote from: minedaft on December 09, 2013, 03:49:03 PM

Responding in more depth to Gwallet's fear of wasting effort: You're thinking of "mining" too literally. There is no concept of getting closer to a block the longer you mine. You are no more likely to find a coin in your 3600th second of mining than you were in your first second. It's like rolling dice: say we need to roll a 6 to find a block. The fact that we've rolled five or less for many minutes does not mean we are any closer to rolling a 6. We probably both agree that this statement is silly: "I haven't rolled a 6 at this table yet, so I refuse to switch tables. All of my previous rolls would be wasted!"

More technically, we are generating hashes of (a constant + a variable) over and over again until one of us finds a variable that results in "Hash( const + variable ) < Difficulty". The "const" is a roll up of all previous solutions (the blockchain). There are near infinite values we could put in "variable", a tiny fraction of which would satisfy the formula. So even though we each test thousands of hashes per second, we're not making progress really. There's so many possible inputs that the ones we've eliminated haven't gotten us measurably closer to an answer. So there's nothing preventing us from jumping coins at any time.

It's slightly more complicated in pools, where you are rewarded for every die roll, even if you fail. Surprisingly that incentives you to switch MORE frequently. (Research "pool hopping").

Source: Not a Master in mathematics, did get a useless ivy league degree in astrophysics once though.

+1 and nicely explained.
TheQuinn also did a good explanation on the subject. GayWallets reasoning is plain wrong and having a masters degree in statistics doesn't make it right.