Perfect! I thought it should work out, but it's nice to have real world confirmation to go along with theorycrafting. The luck element is exactly why I keep gems stockpiled, the most I've had to do to complete any event was spend gems once.
I guesstimated my daily income per slot at 2K, but haven't gotten around to tracking data to figure out a reliable income per hour played. I suspect that your 1200 per day is probably more accurate for a "normal" player than my number, so I'll keep that in mind the next time somebody inquires about this topic.