Yellowstone in late July with no reservation--Am I crazy?

"Our 40' motorhome and Jeep easily fit in Mammoth and Madison - without reservations."
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A question not necessarily only about the "rig size", but the timing; was your visit within the previous couple of years? In my experience, finding a site in Yellowstone without reservations in the past 2-3 years, particularly with a large rig, is a real crapshoot. Sometimes one can luck out, but the combo of a large rig and 4 kids would send me to the reservation system faster than a bunny! :R