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As a parent, you want the best for your child. This means finding the finest education for your beloved in all areas.
But maybe the finest education has failed to get your child to like math. The teacher doesn’t inspire your child, and they would rather play games that deal with the drudgery of homework. Math doesn’t have to be boring. Over the past 2 years, I’ve found an amazing tool to engage children in math as a volunteer at Summers-Knoll, a progressive, project based school in Ann Arbor, Michigan.
Summers-Knoll stresses education based on experience. Hands on math is better than an abstract set of concepts. I’ve found blackjack to be the single most amazing math education tool. Children from ages 4-14 become fascinated with the game, not even realizing they’re learning math and probability.
This article explores my experiences in getting children from pre-school through middle school to love math through blackjack. It’s a how to guide for parents looking for fun way to engage their children in math. This article isn’t for everyone. If it makes you squeamish to pass out casino chips to eighth graders, you should stop reading now.
However, for those with an open mind, you’ll find a new world in which to engage your child’s natural curiosity for math. In addition, blackjack provides some real world lessons as it models the randomness of real life. Let’s take a look.
Blackjack as a math tool started with a conversation.
Valerie Tibbs-Wynne teaches kindergarten at Summers-Knoll. As I was dropping off my son to her class, she told me about how she used the game of 21 in her kindergarten math curriculum.
Hands-on math is better than an abstract set of concepts.
Blackjack, or 21, is a card game in which players compete against the house to have the highest hand value without going over 21. In the beginning, each player gets 2 cards. Cards 2 through 10 have the value according to their number, while the Jack, Queen and King have a value of 10. An Ace can have a value of 1 or 11, whichever gives a better situation for your hand. For example, if you get dealt a 10 and an Ace, a value of 11 for the Ace gives a total of 21, the ideal hand.
With only 2 initial cards, it’s not possible to go over 21. Then you can either hit (take another card) or stand (refuse any further cards). You want a hand with a higher value than the dealer’s hand. However, you bust (or lose) if your hand value goes over 21.
The changing value of an Ace becomes important as you draw more cards. Suppose after getting a third card you have a Jack, 8 and an Ace. If the Ace has a value of 11, you bust with a hand of 29. Instead, a value of 1 keeps your hand at 19. Blackjack is an amazing educational tool because it requires math to play the game. Your child must use addition to find the value of a hand before making a decision about hitting or standing.
Children as young as 4 can do this by counting the markings on the card. The math is hands on, as the child touches each symbol to count the total. Once they master these basics, blackjack requires more advanced ideas to play the game well. Let me show you.
When Val told me about her use of blackjack, I was volunteering as a math teacher for some first graders “hungry for math.” And hungry they were. One of them asked for an algebra problem. First grader.
Blackjack was the best math experience I gave those kids the entire year. And not by a little. The children learned the game quickly, and they became good at figuring out the value of each hand. With the basics established, I had the chance to introduce simple probability. For example, suppose you have a 10 and 6. Should you hit?
Blackjack provides some real world lessons as it models the randomness of real life.
To make this decision, you must first determine what cards prevent you from going over 21. This suggests that subtraction is a useful real world tool. 21 minus 16 is 5, so getting an Ace, 2, 3, 4, or 5 makes a good hand.
What are the chances of getting one of these cards? I would show the first graders the 13 possible cards from the deck (Ace through King). They could count that 5 of them made for a good hand. 5 in 13 gives a 38 percent chance that the player doesn’t go over 21, assuming a complete deck to simplify the math.
I also taught the the first graders the rudiments of basic strategy, which acknowledges that the game gets played against a dealer. At the beginning of each hand, the dealer gets one card hidden face down but another exposed face up.
In blackjack, the players take their turn before the dealer, a disadvantage for the player. If you go over 21, you lose even if the dealer later also goes over 21. The value of the dealer’s up card gives the player valuable information. Remember, a Jack, Queen and King all have a value of 10, which means 4 in every 13 cards (or 31 percent) have a value of 10. The dealer’s down card has a large chance of having a value of 10.
If the dealer has a visible card of 6, then his most likely hand is 16. The dealer hits on 16 and below but stands on 17 and above. If the dealer has 16, there’s a reasonable chance of going over 21.
Now suppose the player has a hand with a value of 12. Usually, you hit on this hand. However, against a dealer showing a 6, millions of computer calculations show that a player should stand. Don’t risk going bust. Instead, let the dealer go bust. The first graders could grasp how these basic probability ideas applied to blackjack. After a few sessions of playing blackjack, they were making sound but counterintuitive decisions when the dealer showed a weak hand. After we finished with blackjack, I spent the rest of the year trying to find a math tool as good.
I experimented with Backgammon, thinking the probability inherent in a dice game would make it interesting. However, the game lacks the basic math of determining the value of a hand in blackjack. In addition, Backgammon has a much steeper learning curve. I also tried to invent a blackjack type dice game called 24. You rolled 4 dice, knowing you couldn’t go over 24. You can roll another or stand, and compete against other players. However, the mental math gets really hard on the initial roll, even for adults.
Don’t risk going bust. Instead, let the dealer go bust.
Blackjack was the best math tool.
After working with first graders for a year, I transitioned to math with the seventh and eighth graders at Summers-Knoll. I had no intention of using blackjack to teach math. These students were learning either algebra or geometry, and in the spirit of the school, I wanted to do math in line with their interests.
The geometry kids were studying formal logic as an introduction to proofs. That’s fun, I thought, as formal logic lets you ask a basic question about whether you can prove every mathematical truth. As Godel showed us with his Incompleteness Theorems, the answer is no. I did a math lesson on incompleteness, one of my favorite subjects. It went over okay. Huh, you can’t prove everything. Okay, old man.
However, during the course of our conversation, the subject of blackjack came up. I don’t remember the context, but my reaction was, “You’ve never heard of counting cards or the book Bringing Down the House? The movie 21 based on Jeff Ma’s adventures in Vegas?” No, they hadn’t.
On my next visit, we started playing blackjack. The older children were engaged immediately while providing some hilarity that never happened with first graders.
First, the notion of “hit” to draw another card now had a physical element. Instead of just saying “hit”, the boys smacked the head of their nearest male friend to indicate the desire for another card. And it wasn’t a love tap. The arm swung like a bat in a home run derby contest. The upper cut swing landed at the base of the cranium.
Second, the middle school students quickly picked up basic strategy, so we moved on to counting cards to beat the house. This requires wagering chips with each hand. (No, there was never any money exchanged for chips.) One of the boys started betting half of his stack on each hand. This is not a good idea, and I took this opportunity to introduce some computer programming. I brought in my laptop and coded up simulation of his play in front of the students. It takes less than 20 lines in Python, and I hoped to impress on them the possibilities, yet ease, of stochastic computer simulation.
The geometry kids were studying formal logic as an introduction to proofs.
In the simulation, I assumed that the player wins 60 percent of hands (an absurd, way too high assumption). Then I made the player bet half of his bankroll with every play. The simulation showed how you almost certainly lost all of your money after a small number of plays.
Did it work? Not at first, but the student eventually reduced the size of his bets. He needed to change his strategy to pass the student-initiated blackjack final which I’ll tell you about in the next section.
Since the middle school students picked up basic strategy so quickly, we moved on to counting cards. This strategy of beating the house takes advantage of how the odds of the game as cards get dealt. To understand this, consider the impact of different types of cards.
High cards, such as 10, J, Q, K and A, are good for the player. With more of these cards in the deck, the more likely the player will get strong hands like 21 or 20. Moreover, a higher than usual density of these cards leads to more busting for the dealer, as he must hit on 16 and lower. Low cards, like 2 through 6, are bad for the player. Those strong hands of 21 and 20 are less likely, and the dealer has better odds to not bust when hitting on 16.
To beat the dealer, you bet the minimum when the deck is against you and bet more when the deck favors you. To determine the status of the deck, consider this simple Hi-Lo strategy from the appendix of Bringing Down the House:
- Subtract one from your count for every 10, J, Q, K, A dealt
- Add one to your count for every 2, 3, 4, 5, 6 dealt
The higher the count, the better your odds.
Remember, high cards in the deck are good for the player but bad for the house. You don’t want to see these cards come out of the deck, which accounts for the -1 when a high card gets dealt. The students were able to count cards with some practice. As we played more hands, they saw how the math based strategy gave them an edge over basic strategy.
I also developed a problem set to reinforce the ideas for the students. The students didn’t love it. I tried to offer extra chips to those who emailed me the answers, but only one of 5 students took my offer.
Blackjack is an amazing educational tool because it requires math to play the game.
However, the kids did make up their own final: beating the house in the long run. They each started with a 100 units of chips, and they began each new session with the same chips they had at the end of the previous session. As each session added more hands, luck played a smaller role in their performance as measured by chip count.
Over the course of 4 weeks, each of the 5 students ended up with more than 100 chips. Good fortune certainly played a role in this result, as we only played 21 hands. However, as a teacher, it’s good to take advantage of this luck to reinforce that probability does work in the real world.
Blackjack is a fantastic tool to engage children in math and probability. In my experience, I’ve found nothing better for a wide range of ages. My youngest son started playing blackjack at the age of 4. He put his finger on the symbols on each card to count the total value of his hand.
Blackjack also engages teenagers on the verge of high school. They can handle the probabilistic concepts behind the counting strategies necessary to beat the dealer. Students could also use blackjack to learn computer programming. In playing with the middle school students, many situations came up for which we didn’t know the optimal decision.
Monte Carlo simulations that use random numbers can determine these optimal decisions. Students could learn the basics of Python, create a data structure for the cards, use a random number generator, etc.
Blackjack is an incredible math tool. No matter the age of your child, grab a deck and start playing today.
Ed Feng has a Ph.D in Chemical Engineering from Stanford and runs the sports analytics site The Power Rank.