Mathematics of Gin Rummy

It is, I take it, the author's privilege to point out-and the player's privilege to ignore-the fact that there are 15,820,024,220 possible ten card hands in Gin Rummy. In every game there occurs a certain incidence of useless statistics. I don't expect you to remember how often in how many billion hands your present holding will occur. I shouldn't be surprised if you fail to remember that the chances of the dealer’s is being dealt a meld in his first ten cards are about 2 out of although, if you do, it will improve your game. I won't insist that you remember that the chances of the non-dealer's being dealt a meld in the first 11 cards he sees are about 1 out of 2, although noting the subtle difference in those odds will make you a better player. I'm not schoolmarm enough to insist that you learn by rote everything I know about every game I know. When you need the mathematics, they'll be here for you.

Play Gin Rummy with Cards in Hand

You should pay close attention to what happens when you play certain cards from your hand at Gin with Gin Rummy Rules. When you are the non-dealer and have been dealt 11 cards, the chances that your opponent can use the first card you discard from your hand in a meld are: It is important in your play of the cards that you know and make your play conform to the above odds. It is also important to remember that when you hold a split sequence, such as the three and five of spades,you have only one chance of forming a three-card meld-by drawing the four of spades. Remember also that if the king of hearts is dead and you hold the king of spades, you now have only one way of forming a three-king meld and only one way of making the king queen-jack of spades. And don't forget that if the ten of spades too is dead, there's no way on earth of your making a four-card meld with the spade king.

Knowledge of Cards

Knowledge of the number of ways a card can be used to form a three-, four- or five-card meld must be a part of every competent Gin player's equipment. In Gin, the seven is the most valuable card in the deck as far as forming melds is concerned, just as the seven is the crucial number at Dice because it occurs oftenest. The seven can be used to extend melds more than any other card. The seven can be used in seven different seven-card-sequence melds, whereas the most valuable of the 12 other ranks can be used only to form six-card sequences. I don't want to overload you with mathematics observation. It would confuse rather than enlighten you if I were to detail the number of ways any card can be used to form sequence melds of six or more cards. I have chosen to restrict the following table-which should be memorized by every Gin player-to three-, four- and five-card melds.
The above table is useful mainly when the player using strategy for deciding which card to discard. Note that the five, six, seven, eight and nine are likely to be most useful to your adversary; the king and ace the least useful. (And observe, too, that the number of ways in which a card can be useful is directly affected by the number of pertinent dead cards known.) The disadvantages of the ace, deuce and 3 are somewhat balanced by the fact that they are low-count cards, useful in knocking.