Everyone's math is going to come out differently

. I can only relate what WE do. AP and DVC, so our cost per card is $150.
TIW, every year, 12 years. We also visit 2x per year on a regular schedule, and have figured out how to get 3 trips per card, by carefully timed purchases.
DW and I go to a SIG every evening, 8 days per trip, twice per year.
Our documented savings are in excess of $500 per year, 12 years running.
Now, we are a COUPLE - children are grown. We almost ALWAYS tip 20% (generally add on to the 18% built in TIW Tip). So really? we pretty much get the system to pay most of the Tip that we would have paid anyway

.
Really, the
DDP is better for "Chicken Finger, Mac & cheese" children. You must run your math, for YOUR Family.
All personal opinion - I'm not necessarily right, no one else is necessarily wrong.