How likely is it to find an open first-come-first-served campsite in Joshua Tree on a busy weekend?

The odds of walking into an open first-come, first-served site on a busy Joshua Tree weekend are low. The National Park Service states plainly that these sites are "highly competitive on holidays, most weekends, and the springtime" and that they are "full nearly every weekend from Sept-May and most weeknights during our busy spring season from mid-February to April." On weekends specifically, the park says the first-come sites are "typically full by Friday afternoon." Source: https://www.nps.gov/jotr/planyourvisit/campgrounds.htm

The three first-come, first-served campgrounds are small. Belle has 18 sites, Hidden Valley has 44, and White Tank has 15, each costing $25 per night. All three sit at an elevation between about 3,800 and 4,200 feet and offer pit toilets, tables, and fire grates but no water. White Tank and Belle close for the summer, while Hidden Valley stays open year-round. Source: https://www.nps.gov/jotr/planyourvisit/campgrounds.htm

Because these 77 combined sites serve a park that draws heavy weekend traffic nearly nine months a year, the park's own guidance is to arrive early in the week rather than count on a Friday or Saturday arrival. The NPS advises that "the earlier you arrive in a week, the better chance you will have to secure a site" and recommends booking ahead instead at Recreation.gov for Black Rock, Cottonwood, Indian Cove, Jumbo Rocks, Ryan, or Sheep Pass, which are reservation-only and bookable up to six months in advance. Source: https://www.nps.gov/jotr/planyourvisit/campgrounds.htm

If every campground inside the park is full, the park notes that overnight parking along roadsides is not an option, since "sleeping in your vehicle overnight along the roadside or at a roadside pull off is not allowed." Visitors without a site are directed to camp on nearby Bureau of Land Management land or seek lodging in gateway communities. Source: https://www.nps.gov/jotr/planyourvisit/campgrounds.htm

For anyone who does not want to gamble on a first-come site, reserving one of the six reservation-only campgrounds ahead of time is the more reliable path for a weekend visit, since the park's own data shows the unreserved sites are the exception that fills first.