The disconnect is that there are alot of competing threads within this thread and the comments are all fragmented within these discussions, and you're taking that as an opportunity to assume that nobody understands bitcoin. It is rude to tell everyone that they don't understand bitcoin because there are differences of opinion.
"Everyone is entitled to his own opinion. But, Senator, you are not entitled to your own facts"
-- Daniel Patrick Moynihan, 2003 or James R. Schlesinger, 1973
Yes. There are those discussing probabilities to override a single block and there are those discussing double spending attacks in general. No one argues that a node with 1% hashing power has a 1% chance of taking a block if he begins at the same time as all other honest nodes. No one argues that a node with 40% hashing power has some slight chance of taking two blocks. But if we discuss a real attack, involving multiple blocks, the difference between 40% and 51% is enormous. While a 40% attacker might be immediately lucky, if he's not he should give up. On the other hand a 51% attacker is GUARANTEED to override the block chain eventually.
While you can complain about a PROOF involving unlimited time and resources, you can not dispute the fact that the 40% attacker has an unlikely chance which becomes exceedingly more unlikely with time, while a 50+% attacker has a likely chance which becomes more likely with time.
I agree with you that the chances of success are very low; but they're also very low at 51%, and only slightly lower at 40%. At 51% hashing power you have to 'get lucky' to generate blocks so rapidly that you have a chance to muck with the block chain, and at 40% you also have to get lucky, just a bit luckier.
NO. This is only true on the first block attempt. These chances rapidly diverge with each subsequent honest block generation.
It is true that the majority hashing power, as long as it is all applied to the same purpose, will always win out in the end, but there will always be 'skirmishes' possible where anyone at all...
YES, but NO. Not unless you are discussing competing malice or network isolation. Honest nodes will acknowledge defeat, malicious nodes will not, much like this thread.
Certainly, clients that wait for 6 confirmations as recommended are safe from any attempt to subvert the block chain that cannot muster 7
I didn't follow your train of thought completely, but... just because we feel certain that 6 confirmations is written in stone, that stone can always
theoretically be broken, with transactions reversed Dwolla style.
blocks before the chain is extended by one block; and I agree that the chances of anyone, even a majority hashing power holder in the range of 51% - 75% or so, being able to generate 7 blocks before anyone else generates 1...
Let me interrupt again. The attacker only needs to generate 7+ before the honest nodes generate 6, perhaps a few more for good measure.