Let \(S\) be a finite set. In the paper [Transform. Groups 17, No. 1, 157-194 (2012; Zbl 1255.16034)], by \textit{I. Heckenberger, A. Lochmann}, and \textit{L. Vendramin}, the authors named \textit{game} on \(S\) any finite subset of triples of elements of \(S\); a \textit{plague} of such a game is thus a subset \(S'\) of \(S\) such that \(S\) is the smallest subset \(T\) containing \(S'\) with the property that whenever two of the three elements of a triple in the game are in \(T\), then all the three elements are in \(T\). The Nichols algebra of a finite dimensional braided vector space \((V,c)\) is said to have \textit{many cubic relations} if the dimension of the kernel of the operator \(1+c_{12}+c_{12}c_{23}\) is at least equal to \(\tfrac{1}{3}(\dim V)\). Small plagues on quandles have applications in the determination of quandles which do not admit Nichols algebras with many cubic relations; indeed, as shown [loc. cit.], if the Nichols algebra of a nonzero Yetter-Drinfeld module \(V\) over a finite quandle \(X\) is finite dimensional and has many cubic relations, then any plague of \(X^3\) has at least \(\tfrac{1}{3}(d^3-d)\) elements. Here, a plague of \(X^3\) means a plague of a certain game on \(X^3\) defined by means of the Hurwitz actions. In the paper under review, the author introduces a method for constructing small plagues on a quandle. The sizes of such plagues are computed for all indecomposable quandles of size at most 47 and for all simple affine quandles of size at most 128, and an upper bound for dihedral quandles of arbitrary size at least 7 is presented. As a consequence, it is shown that there are no Nichols algebras with many cubic relations for non-braided indecomposable quandles of size at most 47, except sizes 5 and 12, and also for non-braided simple affine quandles of size between 7 and 128, and for all dihedral quandles of size at least 7.