Mathematics and Skillful Play

Posted in Score & Counts

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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