Is it possible to mitigate this effects by establishing the rule that, when the block chain forks and there are 2 blocks at the same block height, miners always choose the block with the lowest hash (both blocks would obviously have hash below the target).
This is an oft repeated suggestion going back to at least 2011. It opens a trivial attack where when you do get a very low hash you refrain from announcing it, comfortable in the fact that you're guaranteed to win a race should one arise. In doing so, your competition is all wasting their time mining along a path that is likely to lose. The effect is stronger the larger you are, creating an increase in expectation for larger miners that doesn't otherwise exist.
Forgive me if this has already been discussed, but I believe [humbly] that you are appealing to the Monte Carlo fallacy (i.e. that probabilities are cumulative).
a very low hash as in "a solution with a hash value below traget"
You are correct that a miner could withhold a block solution, but it would be of no advantage.
Ofc, it would an advantage. The following block must reference the block the attacking miner is withholding. Thus the attacking miner has more time to find the next block, while everyone else is still working on an block that has allready been found, but not yet broadcasted.
I make this claim based on the assertion that mining is not deterministic, even if a miner set out with a given nonce increment pattern. I'm asserting that mining is only probabilistic, because until a solution is found, there is no guarantee that the solution exists, only a probability of it existing.
That is true, but if I allready tried 10% of all possible solution my chance to find the solution is higher than yours (who just started).
Also there is allways a solution just not allways for any given set of transactions. But since miners can choose the transactions as well as the nounce, there is allways a possible solution.
I think I could make a convincing argument for why the above scenario would be of no advantage, but this hinges on my understanding that mining is not deterministic. The basic argument goes that even if a selfish miner hashes x number of hashes secretly, he is still no closer to a solution than any other miner, therefore there is no advantage to the selfish miner if he excludes other miners for a period of time.
Here is the missunderstanding I pointed out earlier. "Low hash" means "found a solution" in this case. Just a random hash that is no solution is not helping.
By the way, this is the mind bending implications of statistics... I had to work through this myself to convince myself of the security implications of block frequencies (i.e. Litecoin vs. Bitcoin)...
I convinced myself quite strongly that mining is never deterministic, which has this tensions between 'gut feeling' and reality. At first, it made sense to me that once a miner begins mining with a set nonce pattern, the number of hashes to a solution becomes deterministic... however, after further reflection this is not the case.
A miner can hash x hashes, but is absolutely no hashes closer to a solution....
This is correct.
This is why a miner withholding a block gains no advantage.
This, however, is not. Withholding a block that you know will be accepted by the network because it has a very high priority (lower hash value) gives you the advantage to work on the next block before everyone else.