This question might sound dumb
A question can't be dumb; only the answer may be.
If someone were to join the mempool completely solo, and attempt to mine a block (let's say they have insane, basically impossible luck in bruteforcing the hashes) is it technically possible for them from a theoretical standpoint to fully mine a block and get the 6 bitcoin reward all for himself?
It is completely possible for someone to do that in theory. I don't like the way people put that through though; I'm talking about “luck”. On these scientific (one might say) fields of cryptography, there's no luck. There's actually no luck generally, that's an illusion, but let's leave that for a moment. The hashes you computer calculates may be pseudorandom, because you're unacknowledged of the final result until you calculate it, but there's no way to approach this with luck. You have to deal with possibilities.
Let's take the current target:
0000000000000000001398ce0000000000000000000000000000000000000000
If you start generating hashes you'll realize that 1 out of 16 times on average, the message you hash returns a hash that starts with “0”. If you go further for “00” it'll be 1 out of 16
2. Currently, to solve a block you need to find a hash starting with at least 18 zeroes. That's 1 out of 16
18 times on average which is:
1 in 4,722,366,482,869,645,213,696.
Even if we assume that you generate 1 billion hashes per second, it'll take you around 4,722,366,482,869 seconds to finally solve a block,
given that the difficulty remains the same. That's 54,657,019 days.

Thank you for the super comprehensive, and simple response. I didn't really expect to get this many responses.. haha