I've played mid stakes for quite some time but I have not worked off the tables with math and constructing ranges like I should. I am trying to get to the point where I can work on several spots off the tables in able to discuss spots intelligently on these forums.  So, this is probably a pretty basic question that all of you GTO/math wizards can easily answer...

Let's say I bet $100 into a $100 pot on the river as a pure bluff. This means my bluff has to work 50% of the time, but my opponent just needs 33% equity to call. Does this mean that I need my opponent to fold 50% of his range or 66% of his range? Is folding X% of his range synonymous with folding X% of the time?

I would think that the answer is my opponent needs to fold 50% of the time for my bluff to be profitable, meaning at least 50% of his range has less than 33% equity against my range.