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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. Image:

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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. What are some games designed so each player has an equal chance of winning? (war) What are some games designed where one side has a slight edge? (roulette, most casino games, also games like “go fish” where one player goes first) Image:

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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. Do you think knowing math could really help you win? (Yes, in the case of blackjack knowing the optimal strategy can give you a tiny edge of the casino). Image:

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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.” Before bringing up the bullets on this slide, ask the class if they know how to play blackjack, and have one students explain the game to you. Image:

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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. Before bringing up the second bullet, ask the students if they know what it means to “count cards.” Image:

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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. You can ask the students: Do you think card counting is unfair? Should it be illegal?

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Math in Poker Mathematicians also calculate the probability of getting different hands in poker. It can get pretty complicated:

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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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