Taking Full Advantage of the Odds

Posted in Mathematics of Gin Rummy

Since gin rummy is a game of percentages and odds, an expert player takes advantage of any odds that favor him. However, there is no rule of thumb in the game that is so rigid that you must adhere to it regardless of any other circumstances. If so, there would be no real skill in playing the game. You would only need to learn the rules and then follow them 100%. The only rule that should be given any degree of rigidity is to always take full advantage of the odds that favor you. Despite all the knowledge of the score and the count, these things are relative and are based on and dependent on the various situations as they exist at any given time. A situation may occur, for instance, where the hand at a given moment is most favorable to you, but this favoritism may be completely destroyed by attempting to play for a count.

For example, you are dealt the following card with the knock being a 7Гўв„ўВЈ:
AГўв„ўВ , AГўв„ўВҐ, AГўв„ўВЈ, QГўв„ўВ¦, JГўв„ўВ¦, 10Гўв„ўВ¦, 10Гўв„ўВ , JГўв„ўВ , 8Гўв„ўВ¦, 3Гўв„ўВ¦

You are not on score in any game, the hand is single, and you have a count of 28 in the first game column. Your opponent, whom you have dealt to, discards as his first card the JГўв„ўВЈ. Do you know what you would do?

At this point, a pick of either of two cards, the QГўв„ўВ  or the 9Гўв„ўВ , would allow you to knock. Your chances of being able to knock without such a run are not too good, but if you pick the 9Гўв„ўВ¦, KГўв„ўВ¦, or the AГўв„ўВ¦ you would be under the count. Under such conditions, you must consider the odds of getting under count compared to that of getting a meld. The number of cards unknown to you at this point is 41 since you have seen the 10 you hold, plus the one that your opponent has discarded. The practical odds are about 14 to 1 against your getting a meld card that you need on this pick from the stock. However, if you pick the JГўв„ўВЈ, and discard the 8Гўв„ўВ¦, you would need only one of the following cards to knock: JГўв„ўВҐ, QГўв„ўВ , 9Гўв„ўВ , 10Гўв„ўВЈ, and the 10Гўв„ўВҐ. The percentages in your favor will have almost doubled.

There are still disadvantages to picking the JГўв„ўВЈ. First, you would have to throw the 8Гўв„ўВ¦, which even though it is the second play of the hand, is a fairly wild cad. Second, you will be giving up a pick from the deck, which might be one of the three possible cards that will allow you to knock. Third, you are giving your opponent some indication of what you are holding and you cannot expect back from him any other cards in that particular area. The latter could be somewhat of an advantage because your opponent might feel forced to hold clubs above and below the Jack. The expert player would weigh all of these advantages and disadvantages against the particular odds, as well as against the rigid principle of getting under the count.

Nine out of ten times, this hand will be won, the count gotten under, or the hand won on a knock, before your opponent actually gins the hand and go outs in the game. With odds such as these, the expert player would certainly be very foolish not to take advantage of the opportunities offered by this type of hand.

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