This paper deals with two classes of two-person zero-sum games, in which the strategies of both players are of a special type. Each strategy can be split into two parts: a taking and a guessing part. In these games two types of asymmetry between the players can occur. In the first place, the number of objects available for taking does not need to be the same for players. In the second place, the players can be guessing sequentially instead of simultaneously; the result is asymmetric information. The authors study the values and equilibria of these games, for all possible numbers of objects available to the players, for the case with simultaneous guessing, as well as for the variant with sequential guessing.