Reminds me of the time a dealer tried to convince me with "math" that I was guaranteed to save money by buying the extended warranty. I asked if that meant they were guaranteed to lose money, and if so, why they were trying so hard to sell it to me. They moved on pretty quick from that.
It’s really a kind of insurance, and like insurance it’s a gamble. On average dealerships must win, or they would’t offer it, but that’s not to say that some customers don’t “win” if they got unlucky with their car.
That being said, I opted out of it with my last car.
I did buy an extended warranty for one car, never had a warranty claim until it broke down with only about three or four months left on the warranty. That one paid off.
In another car (same mfr) I looked into getting one when the regular warranty was about to run out. Sales guy looked and said: main thing that happens to these older cars is X and Y and you already replaced X so it's not worth it. I always wondered if what he really meant was "main thing that happens is something expensive and I'd rather get paid retail to fix that". Either way I skipped it and never had a problem.
To be fair to the dealer, it might still make sense for him to sell you the warranty even if they would be likely to lose money on average. For starters the salesman himself gets commission on selling the warranty, but he might not get anything on service and repair. Also warranties are cash in hand that you can amortise over the warranty period, so it's effectively a steady revenue stream rather than bursty fits and starts. That enables more efficient financial planning.
