The three-dimensional chess game played in The Big Bang Theory has seven shelves, or levels. It is the Tri-Dimensional Chess variant originally created for Star Trek, which the series uses as a recurring prop and plot device for Sheldon, Leonard, and the other characters.
The seven-level layout consists of three fixed 4-by-4 boards and four smaller movable attack boards, each measuring 2 by 2 squares. The extra boards can be repositioned during play, giving the game its distinctive vertical strategy. Pieces move across and between levels rather than staying on a single flat board.
A common mix-up is to count only the three main boards, which can lead to the answer 3, or to confuse the game with other commercial 3D chess sets that use different numbers of tiers. The Big Bang Theory’s version is based on Star Trek’s familiar seven-level design, so 11, 9, and 5 do not fit this specific game. The show often uses the set for jokes about intelligence and complexity, but the underlying board design is a genuine fictional chess variant with published rules.