if a pool only gets a block every 6th block its average solution must take 60 minutes to find.. is REDICULOUS
You're digging yourself deeper in the hole. Of course, that is EXACTLY the reason why he only has a block every hour, and hence, about 1/6 of the total amount of blocks.
he only gets a block every one sixth, because there is other competitors that beat him by seconds. and only the fastest guy wins..
as soon as the winner is found the clock resets.. blocks are found in 10 minute average. they do not continue hashing the same data for hours..
they reset and start again on fresh data as soon as a winner is found
As I said, and tried (in vain, apparently) to explain, you're totally wrong about how mining happens. You think it is a cumulative calculation effort (even if you say you know it isn't, you think it takes very close to 10 minutes for every miner each time, whether that miner has 1% of the hash rate, or 40% of the hash rate, it always takes, up to a few seconds, 10 minutes). Can't help you any more. This invalidates much of what you think about many things in bitcoin.
you argue it takes hours, and you knitpick my simplifying of "a few seconds" difference (facepalm)
the few seconds difference is in regards to your scenarios of all pools having equal hash..
you mention 10 pools of 10% hash.. so times would be similar...
10 pools with each 10% of the hash power find, each individually, a single solution on average every 100 minutes (1 hour and 20 minutes). On AVERAGE with an exponential distribution: so sometimes after 1 minute, sometimes after 5 hours. Note that statistically, there is not the slightest influence *on what block* they mine. They could change block at each hash, that wouldn't change their rate of success nor the statistical distribution of their finding solutions. As such, they don't care when they have to switch blocks on which they mine: it doesn't change anything to their success.
Each time they find a solution, they win a block. The chronological order in which the different blocs are found, is the block chain.
Very rarely, it can happen that two pools find a solution within a few seconds interval, while they were mining on the same block - then, one of them will orphan. The only reason why the second pool has an orphaned block, was that he wasn't aware he had to switch the block on which he was mining, and continued to mine on the old block (in vain), and happened to find a solution right at that moment.
If miners would know each-others' solutions instantaneously (no propagation delay, no verification delay) there wouldn't be any orphaning, because at the microsecond when a pool found a block, all others are aware of this, and switch to the next one. So if 3 seconds later, a miner finds another block, it is already the following block, not an orphan on the old block. Orphaning only happens because of delays between miners.
It is simply fascinatingly amazing to be talking about bitcoin technical aspects, and to miss this ultra elementary aspect.