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Measurement of Probability

Express ratio of favorable and possible outcomes as fractions, decimals, and percents.

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Does the House Always Win?

“Blackjack!” It’s a word that excites and seduces card players and casino-goers worldwide. The practice of card counting in the game of blackjack is something that’s often talked about in pop culture: the ability to use the probabilities that certain cards will appear to create an advantage for players over the dealer, who represents the casino, or the “House.” Developing counting techniques can be tricky, but with a grasp of probabilities, the basics of card counting are easy enough to understand—it’s also prohibited in many casinos, so you should only practice your techniques at home!

It’s All in the Cards

Card counting techniques are most often used in blackjack, a game in which the objective is to beat the House. To begin the game, the dealer deals two cards to every player, including the House. Players then decide to “hit” or “stand” in order to try to get as close to 21 points as possible, without exceeding 21 (called “busting,” which results in a loss). Aces count as either one point or eleven points depending on the player’s choosing, cards 2-10 count as their numeric value in points, and face cards (kings, queens, and jacks) count as 10 points. One card of the House’s hand is dealt face down and the other is dealt face up, meaning everyone can see one of the House’s cards. All the other players’ cards are dealt face down. Depending on the cards in a player’s hand, he or she can ask for another card (“hit”) or keep his or her cards without taking more (“stand”). Automatically, players are seen to have an advantage over the House since they know one of the dealer’s cards. However, the odds of blackjack are slightly more sophisticated.

One basic technique for card counting relies on statistical evidence that aces, 10s, and face cards are more advantageous to players than to the dealer, while lower cards, such as 4s, 5s, and 6s, end up hurting the players more than the dealer. The rules of blackjack state that the dealer should always “hit” (take another card) if the House’s hand totals 12-16 points. Thus, if a dealer “hits” with a hand between 12-16 points and draws a 10 or face card, he or she will “bust” (exceed 21 points) and the player will win. So, if you can figure out and keep track of the concentration of high cards (10 points or more) to low cards (less than 10 points) in the deck, this information will help you decide whether it’s more favorable to “hit” or “stand” and thereby increase your odds of beating the House—which is why casinos frown upon card counting!

See for yourself: http://wizardofodds.com/games/blackjack/card-counting/introduction/

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If you are playing blackjack alone against a dealer and you are dealt a 6 and a 4 and the House card that you can see is a 9, what is the probability that you’ll be dealt a card worth 10 points if you “hit”?

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