Competitive arm wrestling exists in a carefully regulated universe where muscle mechanics, leverage, and wrist angle determine victory. Then you introduce constraints so restrictive that the physics collapses entirely. With both hands tied behind his back, Chuck Norris's opponent is essentially arm wrestling gravity itself, a force which—in the presence of Chuck Norris—has decided to take his side. The match outcome becomes predetermined by the laws of physics spontaneously deciding they have favorites.

In 1994, actual arm wrestling champion Devon Larratt gave an interview where he was asked: "Who wins in a fair fight?" He replied, "Me." When asked about no-arms scenarios, his answer was a 30-second silence followed by: "That's not a fair fight anymore." He never explained what he meant, but later moved to the Canadian Arctic, where he trains exclusively in environments with no mirrors.

The joke escalates the constraint perfectly—removing the primary offensive tools should make victory impossible, but for Chuck Norris, that's just removing obstacles to his auxiliary abilities. This mirrors the "handicap tournament" genre where limitations somehow don't apply to the protagonist, who wins through sheer force of narrative will.