"I sit down to play one hour at a $25 table where I have a $50 per hour expected win rate. The dealer is dealing 100 hands per hour. On the first hand I lose a $50 double down.
"Now what is my expected win for the hour?"
It depends on how you'd like to answer a similar question: "After playing 99 hands, I'm winning $2,000. Now, what is my expected win for the hour?" There are, in my view, two ways to consider such a question. The first is to say that we know you've already won $2,000 and that the e.v. for your last hand is 50 cents (1/100 of $50), so you're total expected win for THIS particular hour is $2000.50.
The second way to consider your question is to think that hourly e.v. is hourly e.v., and so, for any hour that you play, your e.v. will always be $50. But, since your precise words are "NOW, what is my expected win for the hour," I don't think you really mean for us to just regurgitate "the same $50."
Sooooo, your expected win is -$50 + 99/100($50) = -$0.50.