We shall consider further variations in the games, obtaining more general Betti maps. We shall also illustrate some links of the Betti map with several other contexts (Manin's theorem of the kernel, linear differential equations, Pell's equation in polynomials, Belyi maps,  extremal polynomials,  Integration in finite terms, Functional transcendence, Kodaira-Spencer map, ...) and state some theorems, both of existence type and finiteness type (obtained mainly in joint work with David Masser).