I spent many years teaching math part time at a small college. The college offered associate degrees so it only offered two different math classes.
The first one was basic math covering addition, subtraction, division, multiplication, and basic fractions. The second course taught basic algebra and percentages.
Without venturing down the long road of bashing the public school systems that most of my students came out of too much, the fact is most of them were terrible at math.
Most of my students were terrified of math and acted as if they never had a single math teacher who tried to connect with them, even at the lowest level. The entire situation was quite sad, but I was able to develop easy to learn and use systems to help them gain knowledge and confidence in their abilities at the same time.
The truth is most people only need a simple understanding of math to be able to do what they need to do on a daily basis. Simple addition, subtraction, multiplication, division, fractions, and percentages are all they need.
The ability to figure out what 20% off means can go a long way when you’re shopping. This is especially true when you’re shopping on a budget for food or other necessities.
Even though most of us carry around a cell phone with a calculator on it, many of my students didn’t even know how to use it to figure out percentages.
Because of my background in gambling I was able to use many simple examples and tactics to help my students learn. Not all of my systems were designed with gambling examples, but many of them were.
This is where the information in this post was developed. You can use many or all of these examples and techniques to help anyone learn more about math.
I learned many of my math skills at an early age by playing card games, including poker and blackjack, with my family. As I learned more about math and gambling I started learning about other gambling activities which made me learn more about math.
I’m not for or against teaching math using gambling concepts to children. I’ve read arguments that teaching children about gambling leads to a higher rate of gambling problems later in life, but I think it’s a load of crap.
The opposite happened with me. I can’t usually let myself play a game without an edge, so I avoid most forms of gambling for more than small stakes.
I also used gambling games to help both of my children learn more about math and neither of them shows any signs of gambling problems.
So it’s up to you to decide at what age to introduce ambling as a form of learning math, but these tips can and will work for people of all ages.
Another nice thing about the gambling concepts used to teach math in this post is you don’t have to play for real money. You can play blackjack or poker with any deck of cards and you can play games like roulette for free online. So you don’t need to risk any real money to learn more about math.
I’ve included 7 ways to teach math using gambling concepts below.
1 – Cards and Simple Odds and Percentages
Thousands of games of all types use cards. The standard dec of 52 playing cards is a small packet of endless possibilities.
You can buy books listing rules for hundreds of games based on a simple deck of cards. And new games are being invented all of the time.
A deck of cards is available almost anywhere you turn. Gas stations and convenience stores keep them as well as grocery stores, department stores, and thousands of online stores also offer them for sale. It’s easy to find decks of cards for a dollar or two within a short distance of most of the population in many countries.
Though I’m sure I’m outside of the norm because of my gambling background, but I have over 50 decks of cards in my house. Even my parents, who’ve never gambled in their life, have half a dozen decks of cards or more in their home.
The magic of a standard deck of playing cards is they all have the same 52 cards. The cards are divided into four suits of 13 cards each, with an ace, king, queen, jack, and 10 down to two in each suit.
This means that each deck has four of each ranked card.
This is an easy way to start teaching anyone about simple odds.
If you shuffle a deck of cards and turn over the top card what are the odds that it’s a heart? One out of every four cards is a heart, so it’s easy to show why the odds are one out of four. It’s also easy to convert this to a chance in terms of percentages. The percentage chance of it being a heart is 25%.
You get the percentage by dividing the 13 hearts by the 52 total cards, or by dividing the one by four from the one in four chances. When you divide the numbers you get a decimal of .25.
This is where you teach someone that to convert a decimal to a percentage you move the decimal point two places to the right and stick the percentage sign, %, on the end, so .25 becomes 25%.
What are the chances of the first card being an ace?
The deck has four aces so four out of 52 are aces. But you also know that each suit of 13 cards has an ace, so the chances are also one out of 13. This can be changed to a percentage the same way as in the previous question. In this case you have a 7.69% chance of the first card being an ace.
This is also an opportunity to teach someone how to reduce fractions or ratios. Four out of 52 reduces to one out of 13. Four goes into four one time and four goes into 52 13 times.
Once you learn all of the simple odds and percentages you can continue using a deck of cards to learn more advanced mathematical concepts. Many of these are used in games like poker.
Here’s a common example:
If you have four cards of the same suit what are the odds that you get a fifth one from the deck on the next card?
You know the deck has 48 cards left and that nine of them are the same suit as the four you already have. This means that nine out of 48 of them complete your flush. Nine divided by 48 tells us that you have an 18.75% chance of the next card completing your flush.
It’s easy to come up with dozens of possible applications and examples to teach math using a standard deck of 52 cards.
And the best thing is you can usually make the learning experience a type of game, so it doesn’t scare your pupil as much as straightforward math. This is especially true when you’re teaching children, but it can be useful in any learning environment.
By making it a game people pay more attention and tend to play longer than they would if you simply beat them over the head with direct math lessons.
2 – Blackjack Addition Skills
If you want to quickly teach someone how to add up to 21 using all of the possible combinations from one to 11, teach them how to play blackjack.
The goal in blackjack is to get as close to 21 without going over or not go over 21 and have the dealer go over 21. Basically you want to have a higher total than the dealer without busting or not bus and have the dealer bust.
Aces can be used as one or eleven, all of the face cards and 10’s count as 10 and all of the other cards are worth their face value.
By playing blackjack you quickly learn how to add numbers of 11 and under. Once you master this skill it’s easy to start using bigger numbers.
Most of us don’t need to work with large numbers inn our day to day life so if you can master the small numbers it takes care of most of the ones you need to know.
Once you learn how to add the cards used in blackjack you can start learning about the strategy used to give you the best chance to win.
Here’s an example:
If you have a total of 11 or less you know that you can take another card without the risk of going over 21. Even if you have 11 and draw an ace, you can use the ace as a one.
Next you start comparing your total to the dealer’s total and how likely the dealer is to bust. The dealer has to follow a strict set of guidelines so many times they’re likely to bust.
Here’s an example:
If the dealer has a total of 16 they have to take another card. You know that any card valued at six or higher makes them bust. So any six through king makes them bust, and only an ace up through five is safe for them. This means eight cards make them bust and only five help them.
Using this information you know it’s probably best to stand if you have 15 or 16, because the dealer has a good chance to bust.
The more you play and learn, the more math skills you develop.
Another addition trick for small numbers is to use a pair of dice. Roll the dice and quickly compute the sum. Then add a third die and practice adding the three numbers after each roll. This can continue as you add more die.
Though the number are small, if you create a game that requires the sum of the die used you’ll be amazed at how quickly anyone learns how to add the numbers.
3 – Fractions and Roulette
Though you can also use a deck of cards to teach fractions, like I covered in the first section, roulette offers a wide range of bets that are all based on fractions.
Roulette wheels come in two different versions, one with 37 numbers and one with 38 numbers. For these examples we’re going to use the one with 38 numbers, called an American roulette wheel. It has the numbers one through 36, a zero, and a double zero.
The chance of the ball landing on any single number is one out of 38, or if you use it as a fraction, 1/38.
If you make a bet on two numbers your chances of the ball landing on one of them is two out of 38 or 2/38. This can be reduced by dividing each number by two. The reduced fraction is 1/19.
Continuing with this example, if you bet on four numbers the chance of one of them coming up is 4/38, or 2/19.
Other popular roulette best are on a column of 12 numbers or on all the even or odd numbers, or on all of the black or red spaces.
A bet on 12 numbers is a fraction of 12/38 or 6/19 after it’s been reduced.
A bet on even, odd, red, or black is a fraction of 18/38, or 9/19 after reducing.
When you add or subtract fractions the bottom number has to be the same. When the bottom number are the same you leave the bottom number the same and add or subtract the top numbers.
If you bet on one number we determined the chances are 1/38. If you bet on another number you’re essentially adding 1/38 and 1/38. The bottom numbers are the same so you add the top numbers. So the answer is 2/38.
4 – Coin Flipping
When you have a fair coin, meaning one that is balanced so it lands on heads and tails an equal number of times, what are the chances or odds it lands on heads when you flip it?
If you said 50% or 50 / 50 or one out of two you’re correct.
What about if the last four flips all came up heads? What are the odds or chances of heads coming up on the next flip?
This surprises some people, but the odds are the same 50 / 50 as before. A fair coin doesn’t have a memory so what happened in the past has nothing to do with the possibility concerning the next flip.
This is an important concept for gamblers to understand so they don’t make bad bets based on patterns that don’t exist, but it’s also an important mathematical concept that everyone should understand.
Humans tend to try to find patterns in things. Many believe that we do this because we want to have control and by finding order in things we exert a type of control.
So if we track a series of coin flips and see that heads has come up more often than tails over the last 10 flips we have the choice of making one of the following determinations.
- Tails is more likely to come up next because it has to even out.
- Heads is more likely to come up next because it’s hot right now.
- Heads is more likely to come up next because the coin is biased.
- Heads and tails have the same chance of coming up next because every single time the coin is flipped each side has an equal chance of coming up.
Of course the final determination is correct if the coin is fair. If you’re playing with a loaded coin then the third determination is correct, but regular coins are unbiased.
When you consider this problem with a coin it’s fairly easy to see that the past doesn’t have anything to do with the future.
If you still think the past coin flips can predict the future ones please start over at the beginning of this section and study it again. Keep working through it until you understand why a coin has the same chances of landing on heads and tail on every flip.
Now that you can see why a coin flip is truly random and has the same chances of landing on either side no matter what the previous results were, what do you think the odds are for a roulette wheel to land on black on a spin following a series of seven straight reds?
If you said anything except the exact same odds as any other spin you need to go over the coin example again. Though it’s not important for this discussion the ball has a chance to land on black 18 out of 37 times or 18 out of 38 times, depending on if the wheel has a double zero or not.
But many people track the roulette results and make bets based on what just happened. Many roulette systems that don’t work are sold to people using this same type of incorrect logic.
Anything you do that has truly random results, like flipping a coin and spinning a roulette wheel, is independent of past results every time you do it. You know that over thousands of hands or spins or flips the results will even out and equal the correct percentages and odds, but over the short term anything can happen.
The more times you flip a coin the closer the percentages will come to 50% on each side, but not many of us are going to be able to flip it millions of times.
You need to make sure you understand the difference between what happens in the long run and the randomness of the short run.
Here’s an example:
If you flip a coin five times and it comes up heads all five times it may seem like the result is not normal. But would you think the result not normal if you flip a coin 100,000 times?
Don’t you think that over 100,000 flips that it will come up heads at least five times in a row once? It probably will do so many times.
So the difference is that one time you’re looking at a small sample size of five and the other you’re considering a much larger sample size.
To the coin the sample size is infinite. It’s one long never ending game of coin flipping.
Another important thing to understand is the difference between a random event like flipping a coin and what you learned in the first section about a deck of cards. The first card to be dealt from a shuffled deck of cards is random with each card having a one out of 52 chance.
But as soon as you remove a card from the deck it changes the odds of what can happen. So the next card is still random, but the past changes the future in this example.
If the first card is an ace, then the chances of the next card being an ace are lower because the deck only has three aces remaining.
Do you see the difference?
To some people this seems like common sense but many have a difficult time distinguishing between games with no memory and ones where the most recent results change the expected results moving forward.
Don’t feel bad if you’re still struggling with this concept. You’re not alone and it’s a difficult thing to grasp at first.
This is one of those things that you may struggle with and then something happens and it’s like the light has been turned on. At this point you may wonder why you didn’t see it all along.
If you’re still struggling to see the difference take some time to go over the section about playing cards and this section again.
These concepts probably won’t change your life, but they’re important enough that you should understand them. If you’re a gambler it’s important to your bottom line to understand them. This is mostly so you don’t get fooled into making poor betting decisions based on seeing patterns that don’t mean anything. This is a costly mistake.
5 – Percentage Edge and Payback
If you know where to look you can find information about casino games that include details about how much they make for the casinos. This information is usually expressed as either the house edge or as a payback percentage.
The house edge is used for games likes blackjack, craps, and roulette. Payback percentage is usually used for video poker machines and slot machines.
The house edge is the percentage that the house keeps on average from each dollar wagered on the game. The payback percentage is the amount of each dollar wagered returned to the player on average.
Before we continue, recognize that in order to get the house edge for a machine that has a payback percentage, all you have to do is deduct the payback percentage from 100 and you now have the house edge.
Here’s an example of house edge:
If you play blackjack with perfect strategy in a game that offers good rules you can often play with a low house edge of .5%, or a half percent. This means that for every dollar you bet you can expect to lose a half a cent in the long run. If you play less than perfect strategy and in a game with worse rules the house edge might be 2%. In this game you lose 2 cents per dollar wagered in the long run.
Here’s an example of payback percentage:
If you’re playing a video poker machine with a payback percentage of 98.5% that means that for every dollar you bet the machine returns 98.5 cents on average in the long run. Recognize that this is the same as a house edge of 1.5%.
Also notice that I included the phrase in the long run in each of the examples. Remember that you just learned in the coin flipping section that things don’t always even out in the short run. Sometimes you need to do something hundreds of thousands of times or more for the expected percentages and odds to play out.
Payback percentage and the house edge are the same. In the short term almost anything can happen, but over time the percentages will end up being where they’re supposed to be.
Understanding percentages is helpful in the world outside of gambling. If you’re shopping and see an item advertised as a percentage off you should be able to get a close idea of how much it costs.
If an item sells for $18 normally and is listed at 20% off do you know how much it costs?
You can figure it out one of two ways. You just learned both ways to do it when you read about the payback percentage and the house edge.
You can convert the percentage off to a decimal and multiply it times the original price to figure out how much the discount is, or you can deduct the percentage off from 100, change it to a decimal, and multiply it by the original price to figure out the sales price.
Here’s an example:
With an original price of $18 and 20% off you change the 20% to .20 and multiply it times $18. This gives you $3.60, which is the deduction from $18 to give you a sales price of $14.40.
If you subtract the percent off from 100 you get 80%. Change that to a decimal and you get .80, which you multiply by $18. This gives you the same sale price of $14.40.
You can use these same two simple equations to determine the sale price or amount off for any goods or services. Just plug on the numbers and you quickly have the results.
Eventually you’ll get good enough to determine roughly what things are without using a calculator.
This is a valuable skill so you know when something is not rung up at the correct price when you’re buying it.
6 – Budgeting and Bankroll
Most of us have to live on a somewhat fixed income. So we need to keep our spending within a certain budget to avoid having financial problems.
When you gamble you need to use a budget of some sort as well. Most players call this a bankroll.
If you run out of money in your bankroll you can’t play anymore. This is much the same as if you run out of money you can’t buy groceries.
Even though a budget is important, the majority of people, at least the ones in my math classes, don’t use a budget. For some reason they don’t want to use a budget and are resistant to starting one, even if they know that they should.
This resistance may come from a form of denial or it may be laziness. If you know that you don’t have enough money to do everything you need to do it can be painful to put it down on paper. It may seem more real when you see it in black and white.
But it doesn’t change the acts.
I tried to teach my students that it’s better to be informed and know what’s really going on because it’s the only way they can take control and start changing their situation.
I used a gambler and their bankroll to show a form of budgeting to my students.
This took the spotlight off of them and used an example that wasn’t the same as their day to day life, but was easily translated when we finished.
We also used some of the things included in the other sections above when looking at a bankroll so I got to reinforce many of their other lessons at the same time.
Here’s an example:
Bob wants to go to the casino on his next trip and play for six hours each day for four days. He likes to play baccarat and always bets on the banker. The house edge for the banker bet is 1.06%. Bob bets $20 per hand and plays 100 hands per hour.
In order for Bob to be able to play the entire time he needs to take four times his expected loss to make sure he doesn’t run out of money.
Figure out how much Bob will lose on average while playing and then determine how much his bankroll needs to be.
Remember the formula to determine his loss per hour on average is house edge as a decimal times amount wagered per hand times hands per hour.
.0106 X $20 X 100 = $21.20
This means that on average Bob is going to lose $21.20 per hour playing.
He plans to play six hours a day for four days so he’s going to play for 24 hours.
24 hours times $21.20 per hour is an average loss of $508.80.
Because he needs to take four times as much to make sure he doesn’t run out of money the final number is $2,035.20.
This is also an excellent example of how much gambling costs. I always point out to my students that baccarat has one of lowest house edges in the casino, but even with relatively small bets of $20 per hand it quickly adds up.
Showing them how they can lose over $500 by just playing for 24 hours, which happens to be the same number of hours in a day, usually has a profound effect on them.
Most of them swear off gambling on the spot because many of them live on less than that a week. The $2,035.20 number is even more eye opening to them.
This gives me the opportunity to explain why he needs so much. I cover how the long run is one thing but the short term has wild swings. This is another way of explaining that anything can happen in a small sample size, no matter what the long term percentages end up being.
7 – Predict the Future with Expected Value
Expected value is one of the more difficult mathematical concepts in this post, but if you learn and use the other lessons included above you can quickly learn how to predict the future.
Expected value predicts the future by using the math behind games and wagers to show you the amount you can expect to win or lose on average every time you’re in a particular situation.
Here’s an example:
If you remember the section about flipping a coin you know that every time you flip a fair coin you have a 50 / 50 chance that it lands on heads. If you bet $1 on heads and win $1 when it lands on heads and lose $1 when it lands on tails you know that in the long run you’re going to break even.
This means your expected value is zero.
The way to determine this using math is by taking your 50% chance of winning and multiplying it times the two outcomes.
50% of the time you get your $1 back and win $1 and 50% of the time you lose your dollar. So if you flipped the coin 100 times 50 times you get $2 and 50 times you get nothing. It costs you $100 to flip the coin 100 times. The 50 times you get back $2 is equal to $100. The $100 you invest is equal to the $100 you get back, creating an expected value of zero.
But what happens if you find someone who pays $1.25 when you win and you still only lose $1 when you lose?
You’re total cost to play 100 times is still $100, but when you win you get back $2.25. Multiply $2.25 times the 50 times you win and you get $112.50. This is a profit of $12.50.
To get your expected value for every time you flip the coin you divide the $12.50 profit by the 100 times you play. This means you win on average 12.5 cents, or twelve and a half cents, every time you flip the coin.
Of course over any 100 flips the results might not be exactly 50 / 50, but by being able to determine the expected value you know how much you can expect to win per flip over time. In this example you’d want to flip as many times as possible because you now it’s profitable for you to play.
Coin flips are easy to figure out, but you can use expected value in most gambling games to help you understand the long term profit or loss from playing.
You can also use what you learned in the section about the house edge and payback percentages to determine expected value.
Here’s an example:
If you’re playing a slot machine with a payback percentage of 97% and you play 100 spins per hour at $1 per spin you use the following calculation.
The first thing you do is subtract the 97% payback percentage from 100 to determine the house edge. This leaves you with 3%. Then convert this t a decimal by moving the point two places to the left. In this case it leaves you with .03.
Now multiply the .03 times 100 hands per hour times $1 per spin and the answer give you your expected loss per hour.
.03 X 100 X 1 = $3
This means that on average your expected value per every hour played on this machine is a negative $3. In other words you lose $3 per hour.
Your expected loss per spin is 3 cents. You get this by dividing the $3 loss per hour by the 100 spins to get the loss per spin.
Any game where you know the house edge uses the same formula to determine your expectation. Simply plug in the edge as a decimal and multiply it by the decisions per hour and cost per decision.
This gives you the expected loss per hour. If you simply want to know the expected value per decision you multiply the house edge as a decimal times the cost per decision.
Here’s an example:
You’re playing a video poker game with a house edge of 1.5% and you play $5 per spin. To determine the expected value of each spin convert the 1.5% to a decimal, .015, and multiply it times your bet per spin of $5.
.015 X $5 = .075
This means you lose seven and a half cents per spin.
As you can see your expected value can be positive or negative. Most situations in gambling are played with a negative expectation because of the house edge.
Use these 7 ways to teach math using gambling concepts to turn learning into fun. Any time you can make learning or teaching activities into a game it has a better chance of working.
If you can learn and use everything on this page you’ll find that the simple math you need to use in your everyday life is easier. You don’t need to get everything down perfectly the first time. If you don’t completely understand a section go back and study it again.
Then get out a deck of cards or find some free games to play online to practice what you learn.