There's been ppl here who have gotten matching or better and others who weren't and left. One guy who went to imgur wasn't able to get matched despite him giving his manager a few weeks notice when he knew an offer was coming.
You have to prepared to take the offer and leave if you use this kind of leverage. It is not risk free. Also you put your manager on notice, so they will be looking to replace you next possible chance.
Only if you have a terrible manager. I believe there is nothing wrong with seeking out a position to understand your value. Managers should respect that as they will likely do the same at some point.
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Mention the salary, but more importantly the growth opportunity. If you are a high performer they'll match.