"In your favor" is how it is required to be implemented by law. You get the absolute best price on the books at the time it hits the exchange.

Of course that doesn't stop low-latency firms exploiting information differentials to get their bids in before your order makes it to the exchange, a process called front-running. It would be illegal for your own brokerage to frontrun you, but pretty much all discount brokerages sell information to third parties, which enables those third parties to front-run. Ever wonder why your Robinhood trades are free?