1

I believe there will be a simple flaw in my understanding somewhere.

From what I can tell for any given block you increment a nonce up to 2^32 (4294967296) per second (and the timestamp every second) in order to find a suitable hash.

Thus if you have a mining rig that can do 4.3Ghash/s, you can cover all possible block hashes in any given second.

What am I missing here, and if this is the case, why do mining rigs with this specification or higher not find all the new blocks?

5

You assume that there exists (exactly?) one block for each work unit. This is not true, there are many variables (timestamp, nonce, transactions in a block, extranonce inside the block's coinbase transaction, ...), and all of them influence the block's hash. Each hash has a chance (as of October 2013) of less than 1 in a billion billion (1.15*10^18 to be precise) to be below the difficulty target.

Each miner searches a different part of the search space (which is, for all intents and purposes, infinitely large), hoping to find a valid block before anyone else does, but there is no "progress" to be made: every attempt has exactly the same chance as any other attempt. The nonce in the block header is just a way of making a particular group of attemps faster to search through.

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