Combine the information about your opponent's sum and all the exposed cards (in the Row, your hand, and the 2 out-of-play cards) to figure out what cards your opponent could possibly have. Keep in mind that some card combinations may be more likely than others.
Use the Play! command to force your opponent to play when you can take advantage of the card played.
Use the Play! command to shrink your opponent's hand so that she will have fewer choices on her next turn.
If your opponent has zero cards, you will get a chance to play twice in a row--try to take advantage of this!
Don't leave your x2 marker until the end. Some chance at 2 points is better than none!
Don't forget to use your captured tokens to Ask your opponent's total. Again, they are wasted if not used before the end of the hand.
Use the Guard! command to protect yourself when you are vulnerable.
Don't use the Pass! and Guard! commands indiscriminately, or you may lose by running out of tokens. Conversely, try to run your opponent out of tokens.
Try not to let your hand get too small, since that gives you fewer options.
Squares 1, 2, 8, 9, can only be marked by one card combination. 3, 4, 6, and 7 have two card combinations. 5 has three card combinations. Knowing these combinations will help you attack and defend the squares you care about. For instance, once all the 5's are out of play, squares 8 and 9 will not be marked again (before reshuffling).
It can also be useful to keep track of which cards remain in the deck, especially when it gets small.