This comment demonstrated the fundamental point of your misunderstanding. Your ordering of events is not how it works. Eve doesn't "jump in the middle" What actually happens is this:
12:00:00.000 - Eve - BUY $10.00
12:00:00.000 - Eve - SELL $10.01
12:00:00.200 - Alice - SELL $10.00
12:00:00.300 - Bob - BUY $10.01
Eve was there before Alice & Bob. This is KEY to understanding what is going on here. Even is NOT jumping in the middle. Eve provided a service to both Alice & Bob and got paid for it.
Here's another way to think about it:
Alice wants the ability to sell her stock whenever she wants for a "correct" price. Right? That doesn't come for free. Someone has to figure out what the correct price is. That takes effort and costs money. Humans used to do this (they were called market makers). Now computers do it because they're better/faster/cheaper at it (just like they're better at a lot of things humans used to do).
They're also cheaper at it. The cost to Alice of getting to sell whenever she wants at a good/correct price has actually gone down from what it used to be. You can see this in the shrinking spreads. It used to be we only had price accuracy to a dime or a quarter. Now it's generally down to only a penny! Even though Eve is making money Alice is getting a way better deal than she used to before someone figured out how to program Eve to do it instead of the slow and expensive Harry the Human.
Here's another way to think about it:
Alice wants the ability to sell her stock whenever she wants for a "correct" price. Right? That doesn't come for free. Someone has to figure out what the correct price is. That takes effort and costs money. Humans used to do this (they were called market makers). Now computers do it because they're better/faster/cheaper at it (just like they're better at a lot of things humans used to do).
They're also cheaper at it. The cost to Alice of getting to sell whenever she wants at a good/correct price has actually gone down from what it used to be. You can see this in the shrinking spreads. It used to be we only had price accuracy to a dime or a quarter. Now it's generally down to only a penny! Even though Eve is making money Alice is getting a way better deal than she used to before someone figured out how to program Eve to do it instead of the slow and expensive Harry the Human.