This video implies that, while expensive, it's not that expensive to calculate a correct nonce. Why, therefore, is mining now only viable to huge ASIC farms? My presumption is that it must be to do to with either speed (i.e., the farms get there first), or influence (i.e., the farms have more peers, so can sway the vote in their favour).
Every 2016 blocks, the difficulty adjusts. This is supposed to take 20,160 minutes, but if the timestamps indicate that it took less than that, the difficulty will increase, requiring more leading zeroes. If it takes more time than 20,160 minutes, the difficulty will decrease, essentially requiring less leading zeroes.
Also worth pointing out that the hash can be evaluated as an integer. Instead of requiring an exact number of leading zeroes, you require the hash to have an integer representation than is lower than a certain value.
There's actually a lot of work that has gone into Bitcoin to make sure that having higher hashrate and higher influence does not make it more likely so that you can find a block. Ideally, if you have 0.01% of the hashrate, you have a 0.01% chance of finding each block, and if you have 33% hashrate, you have a 33% chance of finding each block. In reality, Bitcoin is not quite this perfect, but it's pretty close. The 33% hashrate miner may have a 34% or 35% of actually finding each block.
It's absolutely brilliant. Blocks come at approximately 10 minute intervals whether it's just two people cpu mining in their basement or a global network of ASIC farms consuming megawatts.
It's certainly been fun to watch. When I started mining on the very first publicly released GPU miner, my ~$500USD ATI PCI GPU yielded a block (each with a 50 bitcoin reward) every hour or two. I was mining somewhere around 10% of all the blocks in the chain.
Now, doing that very nearly requires owning a hydroelectric dam.
https://en.bitcoin.it/wiki/Difficulty
https://en.bitcoin.it/wiki/Target
Basically, every 2016 blocks (around 11-14 days) new difficulty is calculated based on the time it took to find the previous 2016 blocks.
Whenever someone gets new fast hardware, blocks get solved quicker, but then the difficulty gets adjusted after 2016 blocks, and it becomes hard again (but even harder for the people with worse hardware).
Just wanted to add that some people are looking replacing this 'Proof-of-Work/Mining' mechanism with a different method called 'Proof-of-Stake [0]. Other cryptocurrencies have already implemented this.
If you jump into the blockchain/bitcoin rabbit hole you will eventually come across this :)
For the most part, proof-of-stake has been strictly rejected as a viable means of building decentralized consensus by the industry experts.