Doing some numbers on the fancy poop bot. I've now had my Litter Robot 4 for 4 months. I have 3 cats, I use World's Best Cat Litter and was using 32 lbs/mo. for approximately $35 in two litterboxes I emptied 1-2X/day.
I've used a bag of litter in four months, for a savings of about $100. I empty one bin once per week when I get a notification. My back hall does not smell like a litterbox. At all.
Complete convenience item. Best QOL purchase in a while.
Litter alone recovers the cost in just over 2 years, but the real glory is in the time. Using a conservative estimate of 2 hrs/wk cleaning and maintenance, I get back more than 100 hrs/yr. and the cats always have clean litter.
I recognize there are far cheaper litters than WBCL, so YMMV.