You can use Arcade to create an expression.

I dont really know what im doing (first time using Arcade). Just pasted the code from: [VxCount = !shape!.pointcount fuction in AGOL][1] and modified last line to output 0 for even number of vertices and 1 for odd. You can of course change this to output whatever value you want with some if/else:

    Function CountVertices(geom) {
        var cnt_vertices = Null;
        var geom_type = TypeOf(geom);
        Console(geom_type);
        if (geom_type == "Point") {
            cnt_vertices = 1;
        } else if (geom_type == "Multipoint") {
            cnt_vertices = Count(geom.points);
        } else if (geom_type == "Polyline") {
            var cnt_line = 0;
            for (var i = 0; i < Count(geom.paths); i++) { 
                cnt_line += Count(geom.paths[i]);
            }
            cnt_vertices = cnt_line;
        } else if (geom_type == "Polygon") {
            var cnt_pol = 0;
            for (var i = 0; i < Count(geom.rings); i++) { 
                cnt_pol += Count(geom.rings[i]);
            }
            cnt_vertices = cnt_pol;
        } else {
            // this should not happen...    
        }
        return cnt_vertices;
    }
    
    
    return (CountVertices(Geometry($feature))-1)%2

[![enter image description here][2]][2]

  [1]: https://community.esri.com/thread/235025-vxcount-shapepointcount-fuction-in-agol
  [2]: https://i.sstatic.net/gVD0V.jpg