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As far as I understand, gas is paid out to the miners, but every node in the network runs each and every contract that is submitted to the blockchain. Doesn't this mean that other ethereum nodes are running lots of code for free? Also if every node is running all of the code all of the time, doesn't that mean that the combined computing power of ethereum is equal to that of just one computer?

If this is truly the case, then why is it being talked about as if it could replace things like AWS? If this is not the case, then how is the result of running a smart contract verified?

All of the resources I've been able to find on Ethereum are very hard to follow especially regarding this question.

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Doesn't that mean that the combined computing power of ethereum is equal to that of just one computer?

Yes.

From Reddit, Ethereum: web 3.0 or 1999 smartphone, which is it? Or is it somehow both?

@linagee answered:

The most trustworthy computer in the world does not need to go faster than a 1999 smartphone, because nothing like it exists. Existing blockchains are like a calculator compared to Ethereum.

(You could construct a network where every node is doing different problems, but then they don't have a consensus on the answers they generate. You'd have recreated centralization.)

tl;dr: If you had a knob that at one end said speed and the other end said trust, this would be cranked to 11 at trust.

The Ethereum computer is about trust, not about how fast it can compute or how much data it can store.

Smart contracts are verified by running it through the Ethereum Virtual Machine, which is precisely defined.

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you actually ask multiple questions, so let me start with the gas question:

I have the same understanding, that gas is paid out to whoever mines a transaction/contract. As well, when a contract is successfully mined, it's globally available across all nodes (turing-completeness).

The point I do not get from your question is why nodes should run code for free? Everytime a contract is used, their users have to pay for that usage in the form of gas (to be converted from ether).

The idea of gas was implemented to counter infinite loops and DOS-attacks resulting in having to pay for execution (and there are more reasons to it).

On the question of "combined computing power" you have to help me out with your definition of "computing power". What do you mean exactly? CPU? Memory? Storage? APIs?

What is your thinking behind the verification of running smart contracts with regards to AWS?

Sorry for asking questions on your questions, but to me they are rather open :)

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