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We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in , and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step. An explicit implementable scheme requires to approximate thefatcat:oxkb7lha2bg4zjx6fmpj43va3q