When you are down to approximately the last 12 cards, it is considered to be late play in the hand of the game. You should at this point make it a practice to count the number of cards remaining, every single time it is your turn. If it is an odd number it means that you have the extra pick coming. This represents a tremendous advantage to you and should not be relinquished under normal circumstances.
However, when playing a hand to win, you should pick up any discards by your opponent that will get you a meld instead of picking from the stock. In playing to the wall though, it is not wise to pick up an opponent’s discard instead of picking from the deck because that will extend the life of the game, when your most important concern would be getting to the last two cards.
Under certain circumstances, you might pick up a discard that gives you a blocking combination. That means that if you have a safe card to throw and are reasonably sure that the card or cards need to complete the meld are still in play, taking an opponent’s discard can be an important defensive maneuver in the late play of the hand.
For example, if you know that your opponent is holding three Kings and you have the fourth one in your hand and he suddenly discards a king, you need to be aware of the fact that he is attempting to change his hand to another combination in hopes of winning. To do this, he needs two picks and discards to get rid of his other two kings. In this situation if you pick up the first king discard, you will automatically achieve a wall hand or even a possible win. If your opponent is foolish enough to throw a second king, you could win the hand. Even if he doesn’t throw the second King, your opponent could no longer win his hand.
Only in the rarest of occasions do you want to pick up a card that is not needed in the middle or late stages of the hand. It should only be done to confuse an opponent, but even then you are taking a major chance of screwing up your own hand and possibly causing him to win anyhow, leaving you with more points. Here is an instance in which you would take an unneeded card. If you are holding nine melded cards with a completely dead card and you are playing a hand for gin. Your opponent knows two of the melds, but he does not know the third one. If he is a good player, he is holding any cards that he feels you need to call gin. He will then discard a card that is completely useless, but that doesn’t mean it is a dead card. By picking it up, and discarding your other dead card, you have now given him an indication of what our other meld or combination is, but of course only you know that it is not the truthful meld. He will then discard one of the cards he has been holding thinking you had a different meld, and you can then pick it up and call gin.
Picking an opponent’s discard in the late stages of the game and relinquishing an extra pick should always be done when the discard puts you under a count. It should never been done for the purpose of reducing your hand to come close to getting under the count. If you can remember this then you are well on your way to winning a game, even in the late stages.