How to Teach Probability With Blackjack
Probability can be a difficult math concept to grasp. Make teaching it easier by making it more exciting. Playing blackjack is fun and can help students learn the basics of probability, while still allowing advanced math concepts and strategies to be explored.
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Things You'll Need
- Math textbook with unit on probability and unit on relationship between fractions, decimals, percents and ratios appropriate to grade of student
- Information on basics of blackjack
- Decks of cards
- Paper
- Pencils
Instructions
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Tell students that they will be studying probability by playing blackjack. This will motivate them to pay attention.
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Study the basic concepts and formulas for understanding and calculating probability, using a textbook to establish probability definitions, examples and worksheets.
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Study the relationship between ratio, decimals, fractions and percents as laid out in your math textbook.
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Explore the chance of flipping over a certain card. Hold a deck of cards and ask your students what the chances are that you will flip over a 5. Then flip over one card. Put the card back, shuffle the deck and then flip over another card. Repeat this 25 times and record each time that a 5 is drawn from the deck. Give the students decks of cards and have them repeat the process you demonstrated 25 times. Have them record their findings and share them with the class. Compare these trial and error results against this formula:
Total number of chances divided by the total number of possible outcomes.
There are four of each card in the deck and 52 cards in total. Four divided by fifty-two is 0.077 (rounding up) and multiplying by 100 gives the percentage, which is 7.7 percent chance of drawing a 5 from the deck.
4/52 x 100 = 7.7 percent
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Teach the basics of blackjack. Basic rules can be found online (see Resources). There are some variations to the game, but choose a very basic version to start. Make sure you define the main terms of blackjack, such as a natural blackjack, betting, "hit me" and staying.
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Play blackjack with your students and then discuss the dealer's advantages.
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Have students calculate their odds of getting a card they want on each play, not shuffling the deck in between. This is the formula:
Total number of chances of getting the card you want divided by the total number of cards still left in the deck.
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Teach some of the variations on the game of blackjack, such as splitting, surrendering and doubling down, and discuss how these variations change the odds for the dealer and the other players. Have the students explore new strategies by implementing these variations.
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Calculate the probability of getting a natural blackjack (a total of 21 with your first two cards) by trial and error---shuffling, then dealing out two cards and recording the results 25 times. Then calculate using this formula:
Total number of chances from the first pick (16 cards that are worth 10 points) and the total number of chances from the second pick (four aces), multiplied by each other (64) and divided by the total number of outcomes of the first pick (52 cards in a deck) and the total number of outcomes of the second pick (51 cards left in the deck), multiplied by each other (2,652) and divided by the number of cards being drawn, in this case two (1326). The answer is 64 divided by 1326, multiplied by 100 and rounded up = 4.8 percent.
(16 x 4) / [ (52 x 51) / 2 ] = 64/(2,652/2) = 64/1,326 = 0.04826 x 100 = 4.8 percent
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References
Resources
- Photo Credit Blackjack image by MAXFX from Fotolia.com
