Math and Card Games

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Math and Card Games - PowerPoint PPT Presentation

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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Presentation Transcript

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.
• 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.
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.
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.
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.”
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.
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.
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.
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.
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
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.