How many people should I overbook for an event?

Perhaps you could over-invite as usual, but place a disclaimer on the invitation. Something like “Space (supplies?) is limited. First come-first served”.

Do you have a history of more than last year? If you have a regular record of no shows, over book at that rate. Sounds like you should be overbooking by 30 -40%. You don’t want to cut it too close.

For weddings they say 10% of guests who RSVP will not show up. That is not true in all cultures. At my daughters wedding we had 10% MORE show up than RSVP’d. I would guess, unless you are inviting people from a culture that has different practices, 15–20% of those who confirm will not show.
You can boost that with reminder invites or notes that arrive 2 weeks out, 1 week out and 1 day out. People have every intention of attending these things then forget. If someone called all the families the DAY OF the even and reminded them you would REALLY boost your attendance

@Judi do you think the homeless families will all have cell phones so you can call them all? I think transient homeless families have a slightly different reliability rate than most upscale wedding guests.

I like @augustlan ‘s suggestion about “first come first served” in an event like that.

That is a variable that might change things. I still believe that the more reminders closer to the event that people get (by phone, mail or personal contact) the better your “closing” rate will be. Especially with this demographic.