This might be a bit off topic but I'm actually quite curious about this analysis.
If you want to "remine" a block, orphaning somebody else's, it means you must make sure your new block is part of the longest current chain, so you really need to mine two blocks.
Lets say you have 1/n of the hash rate, with expected reward for a block is R+F. The probability to solve two blocks is n^-2. Lets assume negligible fees on the current block but a large melting set of fees on a just announced block. Our expected mining return will be equal for remining when:
(2R+F)n^-2 = R/n or F=R(n-2)
It seems that this is another region where the equations break down as you approach the 50% of hash rate figure. At that rate, the problem becomes similar to the St. Petersburg bet and it appears that such a miner will have incentive to put hashpower toward remining every block.
If you have 1/4 of the hashpower today, you will try to remine (fork the chain) when there is a fee of 2R or 50BTC. At 5% of hashrate, this gives a cutoff of 18x the reward for when it becomes possible to backtrack. Traditionally we have always had a pool or two floating at around the 1/4 level. Therefore when the fees approach ~ twice the reward (and they will eventually if the network stays alive) this will become a problem!
You're analysis is correct, although we have two solutions in the works:
1.
Discourage fee sniping with nLockTime: If clients always create transactions such that only the
next block can include them, it becomes less attractive to re-org blocks because you won't be able to cherry pick high-fee transactions that have been created since the last block. We can implement this right now, although it's relatively weak protection; I mostly wrote the patch because I don't want systems to start making assumptions about nLockTime now that prevent us from implementing that fix in the future.
2.
Transaction checkpoints: Every transaction has a individual "checkpoint" block, and if included in a block in a chain that doesn't include that blockhash the block mining the transaction isn't allowed to collect its fee. You can still re-org a block to grab an individual transaction, but all the other transactions will then (probably) not be available to you. This change requires a soft-fork to implement, but is better protection than #1.
Finally a limited blocksize helps too: if transaction fees are roughly equal you eventually run out of space in the block anyway.
IMO the biggest problem with this re-org business isn't the re-orgs themselves, but rather that it gives incentives for mining pools to get bigger because only a large pool can profitably attempt re-orgs. This could be a serious problem if a significant portion of mining income in the future was in the form of fidelity bond fee sacrifices.
Confirm please: the network currently does not care the value of the hash of a block, apart from it being lower than the value prescribed by the difficulty.
Correct.