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Math and Card Games By: Candace DiBiano Symmetry in Cards Notice that playing cards are symmetric . The top of the card is the same as the bottom, just reflected backwards like looking in a mirror. Shape of Cards The shape of the card is also a geometric consideration.

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Math and Card Games

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Math and card games l.jpg

Math and Card Games

By: Candace DiBiano


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Symmetry in Cards

  • Notice that playing cards are symmetric.

  • The top of the card is the same as the bottom, just reflected backwards like looking in a mirror.


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Shape of Cards

  • The shape of the card is also a geometric consideration.

  • Too large or too small, and the cards become impractical to hold in one hand.

  • What is a good height-to- width ratio? Some games use other-shape cards, like square or round cards, instead.


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Math in Game Design

  • 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.


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Math and Strategy

  • 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.


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Blackjack

  • In blackjack the player and the dealer are both dealt two cards. All face cards are valued at 10, aces at 11.

  • The player wants to get as close as possible to 21. The player can be “hit” with more cards to try to get closer to 21.

  • If you go over 21 you automatically lose, this is called “busting.”


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Strategy in Blackjack

  • Using the “optimal strategy” in blackjack, which was calculated using mathematics, you can actually come out 1/100th of a cent ahead of the casino each game!

  • Learning how to count cards (remembering what cards have come up already) can increase your edge further.


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Card Counting in Blackjack

  • By keeping track of how many high cards and how many low cards you’ve seen, you can tell what must be left in the deck.

  • This tells you how to bet, since high cards are good for you, and bad for the dealer.

  • This is because a dealer is forced to “hit” on less than 17, and if there’s more high cards the dealer will “bust” a lot.


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Mathematicians take over Vegas

  • In the 1990s math students at M.I.T. calculated exactly how to use this method to count cards.

  • They formed teams and headed to Las Vegas. They were able to make $400,000 in one weekend, using this strategy.


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Mathematicians take over Vegas

  • Card counting is not illegal, nor is it considered cheating by casinos.

  • However if you start winning big, a casino is a private business, and can kick you out whenever they want.

  • This is what eventually happened to the mathematicians wherever they went.


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Math in Poker

  • Mathematicians also calculate the probability of getting different hands in poker.

  • It can get pretty complicated: http://mathworld.wolfram.com/Poker.html


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Today’s Activity

  • Today we will be discovering in groups the probabilities of picking sets of cards.

  • We will also be figuring out how to assign “points” to the different cards in the set.


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