EV Question???

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?

If your a priori EV is +$50/hour, but you start off the first hand with a $50 loss, your post-hoc EV is not $0 for the hour.

my response should read:
"""
If your a priori EV is +$50/hour, but you start off the first hand with a $50 loss, your post-hoc EV is $0 for the hour.
"""

Because if I win that first double down, which wins 50 bucks, my EV is now $100 for the hour rather than $50? Is that $50 I just won my EV for the hour? Extra EV for the hour?

I don't think so. The outcome of one hand doesn't influence your overall EV. Your EV factors in those wins and losses over time...

"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.

Don