Is that so? I thought by design, a certain number of bitcoins were able to be mined at a given time, so the difficulty increases as more and faster miners start mining coins.
Yes, I think it's like you say: the "cost" of mining a bitcoin is not necessarily related with the costs of your electricity bill (at least not directly). "By design" it should take the entire system (= all CPUs/GPUs/whatever involved in verifying transactions) 10 minutes average to verify a given number of transactions.
There follows that if more powerful computing units become available - such as the specially designed ASICs - the "harder the task becomes" to verify a "bitcoin block" (a number of transactions).
To verify a transaction is mathematically easy and cheap: you verify the input (e.g. 1 bitcoin) and make sure the sum of all outputs (there can be several outputs for any given transaction) is not larger than the input. Verifying the signatures of the sender and receiver is also cheap (basically calculating some hash value of the transaction with the given public keys of the participants and compare with the given hash values).
Now here comes the clever trick: in order to make it "hard" to verify a block of bitcoin transactions the verifier itself has to sign the transaction, together with a "grain" (a counter of some sort). Signing means "hashing" the transaction again with the verifier's private key (so it can be yet verified by others, given the public key of the original verifier). And "hashing" any given value basically results in some "random" number (at least the has value behaves like a random value - it is off course not random).
And the riddle to solve is now the following: in order to earn ("to mine") a bitcoin the hash value of the verifier needs to be below some "system-wide threshold value". If it is larger, the verifier increments its "grain" (counter) and repeats the hashing algorithm (note: changing just a single bit in the input dramatically changes the resulting hash value, given that a "good hash algorithm" has been chosen!). Until the final hash value of the verification is smaller than the given threshold.
And since the "first come, first served" rule applies (as always in life): the faster you can verify the transaction and get below that threshold, the better, because the first one succeeding in verifying that "block of transactions" earns a bitcoin!
So there follows: the faster your computing unit, the more likely are you going to earn bitcoins. And the faster your computing unit, the more power are you going to burn (so yes, there is probably a co-relation between the bitcoin value and your electricity bill).
If people start turning off their computers the average time it takes to verify a block of transactions increases again, and the threshold will be dynamically increased (making it "easier" again to verify a transaction).
Oh and by the way: that "threshold thing" is not just for fun: it is part of making the whole system work. It
must be hard to verify a block of transaction, otherwise people could start cheating and verify false transactions (e.g. spend the money twice or several times!). As long as at least 51% of all bitcoin users (in terms of CPU power) are honest people (and don't fake transaction verifications), the system works, because it will always have more CPU power to "overrule" the wrong transaction verifications (roughly speaking).
At least that's what I understood so far... roughly
