This can happen because a zero reduced cost means the entering variable can change without changing the objective value, while degeneracy means one or more basic variables are already zero. During the pivot, the basis may change even though the solution values—and therefore the geometric point—stay exactly the same. If the algorithm repeatedly makes such degenerate pivots, it can cycle through different bases representing the same feasible point.

Entering a variable with a zero reduced cost leads to zero step length at a degenerate vertex. The Simplex algorithm replaces basic variables without moving the geometric point or improving the objective, causing it to cycle endlessly through different algebraic representations of that same physical point.