Evading predictors with creatures

We continue the theory of evasion and prediction which was introduced by Blass and developed by Brendle, Shelah, and Laflamme. We prove that for arbitrary sufficiently different $f,g\in ^{\omega }\omega$, it is consistent to have ${\mathfrak{e}}_{g}<{\mathfrak{e}}_{f}$, where ${\mathfrak{e}}_{f}$ is the evasion number of the space $\prod _{n<\o }f(n)$. For this we apply a variant of Shelah's ``creature forcing''.