Various comments from the Cornhole Game Players forum about center braces on cornhole boards.
Whether to add a center brace
from CGP member hondo - A brace underneath is a must. Without it, your bags will bounce like crazy when they hit near the center of the deck, especially if you're going with 1/2" plywood.
from CGP member Naperville Bags - You will be much happier with a center brace. Even if it is just a 1x4 or 1x3. Just something to get rid of that bounce that happens with 1/2 plywood tops.
from CGP member Ospriteo - I use a 1x3 near the center of the plywood. I glue the board to the plywood and use screws for the sides
from CGP member Louis Clarke II - I just screw mine in. I use a Kreg Jig to attach mine (no glue). I make a small relief cut in the corners (where the top of the brace meets the inside frame and the bottom of the board) for ease of installation.