The board game Sheldon invented in The Big Bang Theory is called Research Lab.
The game appears in “The Guitarist Amplification,” the seventh episode of season 3. Sheldon creates and tests it with Leonard and Penny, treating the project with the seriousness of a scientific experiment. The episode aired on November 9, 2009.
Research Lab is fictional and was created for the sitcom. It is not the same as Rock Paper Scissors Lizard Spock, the expanded hand game Sheldon popularizes in season 2. “The Big Bang Board Game” and “Sheldor” are also incorrect options; neither is the title of Sheldon’s invented board game.
A nearby detail fans sometimes mix up is that Sheldon invents or redesigns several other games and game-like activities throughout the series, including a three-player version of chess and the fictional game Counterfactuals, which he develops with Amy. However, the board game explicitly identified as Research Lab is the one introduced in season 3’s “The Guitarist Amplification.”