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Math and Card Games

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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  1. Math and Card Games By: Candace DiBiano

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.”

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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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