The Obsessive strategy seeks to collect just one type – or two if one of them are the Lions – and thereby receive maximum value on every turn in, even though the rate of turn-in may be low. If playing Obsessive, it is vital to avoid polluting the safe with undesireable types. Thus, it is usually wise to populate your show window with types which you won't mind purchasing yourself, or with types which are so desireable to someone else that they are certain to be purchased, and purchased before the player himself will have to purchase, unless of course someone happens to fortuitously populate their window with exactly what the player wants, which is rare.
If none of these seem possible, the player may want to try an Omnivorous approach. In this mode the player seeks to clear the hand on every turn, putting as many cards as possible into the safe. Per turn in value received is low, but turnover is rapid. In addition, the player uses the entire hand each turn and it is difficult to trap an Omnivorous player into a difficult buying decision. But on the other hand, the player may be able to lower the profit values of anyone pursuing an Obsessive strategy. Omnivorous players should stock their show window so as to make them as undesireable as possible and generally end up purchasing their own stock. On the other hand, someone else may be pursuing the same strategy, in which case one should take care not to create a show window which is more desireable than others and thus lose those cards to someone else. A third tactic is to place only one card in the show window, one which is very desireable to others. In this way, one earns a point for very low outlay and yet still has 5 cards to put into the safe. One might want to first consider whether a leader is being unduly helped by such a move, however.
Which strategy to follow chiefly depends on just two factors: the player's draw and the what else is happening around the table. If the player has received a lot of matching cards, it generally indicates an Obsessive approach while a very mixed hand usually indicates Omnivorous, although if it appears everyone at the table is pursuing the same, Obsessive might deserve more consideration.
Changing strategy in midstream does appear to be possible. Although it is easier to go from Obsessive to Omnivorous, the reverse is possible with luck, and especially in games with only three players where there is more time to change. Of course, variations to either strategy are possible, usually arising from a willingness to accept lower profits in exchange for having a negative effect on the profits of the another player, especially the leader.