In Super Mario Bros. 3 (shown here in the Super Mario All-Stars version, but equally applicable to the NES and GBA versions), Boomerang Bros. are coded to have a 50% chance to jump every 256 frames (4.26 seconds).
However, the timer used to count these frames is not tied to whether the game is actually running, and continues counting even when the game is paused. As such, if the game is paused while the Boomerang Bro is in the middle of a jump, and unpaused when it is time for him to jump again, the Boomerang Bro will do a mid-air jump.
This is shown in the footage, where three lengthy pauses are used to force the Boomerang Bro to make a quadruple jump. With enough patience and either luck or tool-assisted luck manipulation, it is possible to make the Boomerang Bro ascend up to an arbitrary height, including completely off the top of the level.
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