In the past I've done this when I've been open for a Federal Holiday but then wind up with no kids, or just one. I would do a sign up sheet with a three child minimum (or a two family minimum if one family had 3 kids) If not enough kids signed up I was closed.
For weather related issues I just close due to that. But I had an issue where a sick child could NOT be picked up due to bad roads/weather years ago. It really opened my eyes to a liability that most providers don't usually see.

All that said, if it's just a random day where I am open and wind up with one kid, I make it work. The others are paying also, so it's not as if I'm only getting paid for that one child.

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