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Mathematics and Skillful Play

As we’ve stated before, the mathematics of gin are based primarily on the law of probability. Considering that you will play thousands and thousands of hands you are going to notice it more and more. For example, in one particular hand if you are dealt a preponderance of black cards, it is only going to stand to reason that your opponent will be dealt a preponderance of red cards. The same thing can be said if you have a high percentage of even cards, then chances are your opponent has a high percentage of odd cards. You can also assume that when you have a large amount of high cards, your opponent will probably have a large amount of low cards. If you can understand this simple fact then you are already well on your way to grasping the laws of probability in gin rummy.

Most experts that have played this game for a long period of time have a guideline for this called “Rule of Fourteen”. It means that they consider all cards to have a face value. Ace through 10 are represented by their particular number. Jack is valued at an 11, Queen is a 12, and the King is valued at 13. The average in the middle is of course a seven so the law of probabilities states that all things will average to their mean value. For example, if the mean value of all the cards in your hand should be 7, the “Rule of Fourteen” says that if you have 2 kings you will probably pick up 2 aces, and if you have 2 eights, then you will probably wind up with 2 sixes. Both of these cards add up to 14 so you can see how they are figuring it will work. Most experts assume the same about their opponent’s hand. If your opponent throws a nine, then he will eventually throw a 5, or if your opponent discards a queen then he will eventually throw a deuce. If you notice from his play that he is accumulating 10’s then it is safe to assume by the law of probability that he will also be accumulating fours. The “Rule of Fourteen” is used as a guide when you have to make a choice of discarding between two cards that you have in your hand that may benefit the other player.

When the cards are first dealt out, and you have 10 cards that means that there are 42 cards left that are closed to you. These consist of the cards held by your opponent as well as the cards remaining in the deck. Obviously the odds at this point on any one of these cards being the top card and the card that you are looking for are now considered to be 41 to 1. If your hand is the type that requires either of two cards, those odds are cut in half. If your hand is such that any one of four cards could give you what you want, the odds of picking any one of these four cards are only 10 to 1 and so on. The odds that you will pick the card you want will automatically change after each play since there are fewer cards that are still unknown to you.

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Are The Odds In Your Favor?

Since the laws of probability have already been discussed it is only fair to discuss the odds that have so much to do with the probability. Reviewing the basics of the odds, you need to remember that once you have picked up 10 cards you then have 42 cards that are unknown to you. That makes your odds 42 to 1 that you will pick up the card that you want. Each time a card is picked up and discarded, it lowers your odds significantly that you will get the card that you want. Now that you are familiar with the basics, let us move on to more advanced odds and how it works to have the odds in your favor.

Since the odds increase in your favor every time you pick a card from the unused stock, as well as when your opponent discards, it only goes to show that the odds for your opponent also increase. After you pick 5 cards for example, the odds then decrease from 42 to 1 down to 37 to 1. That means that there are 37 cards left unknown to you. AS more and more cards are exposed the odds again change, but they change more than just mathematically.

For example, if you have K ♦, Q ♦ then the only card in the deck that can fill that run is the J ♦. Until such time as you have seen any jacks played or you have seen the 9 ♦ and 10 ♦ played, the chances of your picking the jack are 1 against the balance of those cards remaining in the deck. However, if you have already learned through play that your opponent is saving jacks, could be saving jacks, or could be holding the 9 ♦ or 10 ♦, then obviously the odds are changing very dramatically that you will not be getting a J ♦. That is not exactly because of the mathematical percentages.

While the basic odds of any given play remain constant, the mathematical percentages that work for or against you are based not only on the odds of any given play, but on the advantages or disadvantages that increase to you. For example, if your opponent is on a triple schneid, and you are playing for a card that might let you go gin and will enable you to win a triple schneid, then taking a 10 to 1 shot, or even a 15 to 1 shot might seem worthwhile to you. On the other hand, if the situation were reversed, you would not conceive of taking such a long shot because the advantages of playing the hand in that manner are not worth what you might lose by taking this wild chance.

The expert play differs greatly from the average player because the expert is much more advanced in going beyond the ordinary percentages involved in any given play. That is, the expert measures these percentages or odds against the advantages and disadvantages to him on every play.

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Card Memory

Having what is known as “card memory” is extremely important in the game of gin rummy because as the play progresses you are going to be in dire straights if you don’t remember a certain card has already been played if you are waiting on that card. A few fortunate card players are lucky enough to have a photographic mind as well as a retentive memory, but most players have to really work at developing card memory. There is not exactly a system for remembering the cards, but it is simply a matter of training by constant practice.

At the start of a hand, you should try to visualize the 52 cards in the deck, and then deduct the 10 cards that you are holding. As you or your opponent discard cards in turn, you should eliminate these cards from the pictured deck in your mind. After the initial deal, and by the time 1/3 of the stock has been used in play, you should have a fairly accurate picture of the type of cards remaining in the deck. You should also know the type of cards which your opponent can and cannot use.

It is important to remember specifically the cards that you discarded. He will normally pick 1 to 3 of these cards, and they should not be difficult to remember as you had them first. You should keep reviewing the cards he picked up while noting at the same time which cards he is discarding. This will allow you to calculate correctly which cards your opponent is holding. In time this will come easier to you, but for now you need to practice at not only remembering this, but you need to develop a system for general recollection of early discards even if they hold no meaning to you at the time. Near the end of the game, you may need to reorganize your hand based on the earlier discards and if you don’t remember them then you won’t be in a good position to win the game.

Many players have a habit of helping their memory during the play of a hand by repeating the cards to themselves that their opponent is holding. This doesn’t necessarily always work though, because if a player is tired or has seen many hands up to this point, it may confuse them on the next hand. For example if you are repeating a certain run that you are sure your opponent is holding, the following game your mind may keep repeating the certain run, giving you a disadvantage because you think he has different cards then he really does. Then when you pick up the cards or if you see the cards, it may confuse you even more. In other words, one of the most important parts of a card memory is the ability to forget a hand once it is completed.