We consider finite combinatorial two-player games. We show a way how to combine several games into one for which we know that B has a winning strategy. Then we consider the search problem: given a strategy for A find moves for B that beat the strategy. If A's strategy is given by a circuit, this is a total NP search problem (TFNP). We consider a version of the game in which the game and A's strategy is given by an oracle and ask how many queries are needed to beat the alleged strategy. Our result shows that for such games there is a hierarchy with respect to the length of the games used in the construction. If the length is k then the number of queries needed is roughly k-times iterated exponential.