Math in Card Games
Date: 10/06/2000 at 10:11:25 From: Jack Joshi-Powell Subject: Card games How exactly is math involved in the playing, creating, and setting up of card games? I've checked many books and Web sites, but they talk about strategy, not math.
Date: 10/06/2000 at 12:49:13 From: Doctor TWE Subject: Re: Card games Hi Jack - thanks for writing to Dr. Math. Exactly what kind of card games are you talking about? I can think of at least three categories: games using standard playing cards (4 suits of 13 cards each) or similar decks (like Bridge, Cribbage, Poker, etc.); games that use card decks specific to that game (like Old Maid, Quartet, Set, etc.); and the new "customizable" or "collectible" card games (like Pokemon, Magic: the Gathering, etc.) Whichever type of card game you are referring to, they use math in many of the same ways. First, the designs of the cards are themselves an exercise in geometry (along with a little bit of psychology and physiology). Designers must consider the size of the cards. Too large or too small, and the cards are impractical to hold in one hand. The shape of the card is also a geometric consideration. Most cards are rectangular with rounded corners, but what is a good height-to- width ratio? Some games use other-shape cards, like square or round cards, instead. Are these better or worse in terms of handling during a game? Then there's the symmetry of the cards. The faces of the cards in some games (particularly the "customizable" card games) have no symmetry, while others (particularly standard playing cards) have two-way or near two-way symmetry, and yet others have four-fold symmetry. My wife doesn't like playing with standard playing cards because she's left-handed and the corner symbols on most playing card decks are designed for right-handers. She spreads her card hand "backward" and thus sees the blank corner instead of the card symbol. The card backs are frequently symmetric geometric patterns as well. Math is also involved in the design of the game in terms of winning and losing. In many games, the designer wants the probability of each player winning (assuming equally good strategies) to be equal, or as nearly equal as possible. But determining whether the first player has an advantage or disadvantage is an exercise in probability. It would not be a very interesting game if the first player could always win. For casino games like Blackjack, the house has an advantage. But if the advantage is too large, players won't play the game; they'd lose their money too quickly. Of course, if the house doesn't have the advantage, the casino loses money and will go out of business. So determining the probability of winning is an important step in the design of a game. Determining the best playing strategy also involves math. Knowing how to determine the probability of the occurrence of random events can help a player determine the best strategy for winning. The play of many card games also requires basic arithmetic skills. In many games, you have to add or subtract points. (For example, in Blackjack you need to add the values of your cards and subtract it from 21.) Some card games, like Twenty-Four, require the players to do mathematical computations as part of winning the hand. (In the game Twenty-Four, each card has 4 numbers on it. The first player to be able to make an expression that equals 24 using the 4 numbers and basic arithmetic operations wins the card.) Some "customizable" card games also have a "casting cost" or equivalent requirement before a card can be put into play. The player must determine what combination of cards (s)he can afford to play on each turn. Most card games also require some form of scorekeeping from round to round or hand to hand. This often just involves simple arithmetic, but that is math as well. I hope this gives you some ideas as to where to start. Perhaps you can then explore these areas in more depth for the particular game or type of card game you're interested in. I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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