This paper describes Parrondo’s paradox and its dynamic version. In the first part of the paper, we construct Parrondo’s games. The behavior of capital is modeled by successively playing games using random walks in a random environment. We define the fairness of the game by the marginal behavior of capital. We show that it is possible to construct two losing games for which the mixed game is a winning game. In addition, we show under which conditions Parrondo’s paradox is achievable. In the second part of the paper, we define Parrondo’s paradox in the context of dynamic systems by looking at attractive or repellent fixed points as losing or winning games. We also show that when there is a class of functions \(\mathcal{C}\) with a common hyperbolic fixed point, it is not possible to carry out Parrondo’s paradox. In the central part of the paper, we show that the dynamic Parrondo’s paradox is realized when \(\mathcal{C}\) is the class of homeomorphisms on \(\mathbb{R}^k\to\mathbb{R}^k\) for \(k\geq2\). On the contrary, paradox does not appear when \(k=1\).