The calculations mentioned in the mathematic and odds article are gin mathematical problems and solutions, but they are not of great strategic value to the player in the game. In gin rummy every play requires a decision that could, if carried to the extreme, be based on a pure mathematical formula. Every card has certain offensive benefits if retained as well as having certain defensive detriments if throw. These benefits and detriments can be reevaluated by considerations given to score and count.
The point count system that we will explain below was developed with an eye towards helping the gin player make the correct decisions during play. It is based primarily on establishing a defensive value for every card based on the number of ways that this card can be used by an opponent. Without any knowledge of either discards or your own, every Ace or King can be used in any one of four ways. Every Queen and Deuce can be used in five ways. Every other card in the deck from the 3 to the Jack can be used in six ways.
In calculating the relative safety factor of a discard, we will start with the fact that a card which can be used in any of six ways by an opponent is the wildest or most unsafe card that can be thrown. Such a card is given a numerical value or rank of six. When a card is 100% dead and cannot be used by an opponent in any way, it is given a numerical rank of zero. Therefore, a card that can be used by an opponent in any one of four ways, will receive a rank of four. A card that can be used in any one or two ways will be ranked two. A one way card receives a rank of one, and so on.
The basic value in using this system is that in practically every gin hand many occasions come up when we have a choice of cards to throw and the determining factor is its overall safety. The point count system method represents a simplified way to truly determine the relative safety value of any one card as compared to another.
The major factor in this system is the fact that after the first discard is made and after each subsequent discard and pick, the numerical safety value of the cards change. For instance, if you had to decide between throwing the 7♥, and the Q♦, your obvious choice would be the Q♦ since in itself it has a safety factor of five as against six for the 7♥. But, assume that the 8♥, has already been discarded and you are holding the 7♣ in a meld in your hand, the safety value of the 7♥ has been reduced to a numerical rank of two. That is, the original possible combination in which the 7♥ could have been used as a meld consists of either a 7♣ and 7♦, a 7♣ and 7♠, a 7♦ and 7♠, a 8♥ and 9♥, 5♥ and 6♥, 6♥ and 8♥.
By elimination of the 7♣ and 8♥ by meld and discard, the 7♥ now has a safety factor of two, and thus would be a much safer throw than the Q♦ and its five value. It is very important to remember that as the unused deck diminishes, the relative safety factor of each card becomes more important since the possibility an opponent’s using a wild discard increases substantially.