The Bonus Game is a mini-game featured only in HTFA GB. It's played after every level except the last.
In this game, the player has to guess where the 1UP is located between three identical cups. If the player guesses correctly, the 1UP is obtained, otherwise the player will proceed to the next level without the prize.
The location of the 1UP isn't assigned at random, so an experienced player can simply pick the same sequence of cups in one run of HTFA GB.