The best type of paint to use on cardboard is acrylic. Acrylic paint is very similar to oil-based paint in that it does not penetrate the paper and leave it soaked, but it is less expensive.
Cardboard has the same consistency as regular paper. When paint is applied to cardboard, water is absorbed in the layers, which may compromise the cardboard's durability. Once the paint dries, the cardboard stiffens back up and becomes slightly brittle. Before applying the last bit of paint to a cardboard picture, a gesso primer should be applied to set the painting and to create a higher-quality image that lasts.