## Black Jack and Math

The game of blackjack is all about numbers and math. Looking back, I have always thought it was about luck but the more I read about it and the more I play the game I have come to realize the game is all about probability and math and this is even more obvious the more I play blackjack. In order to win at blackjack regularly, it’s not enough to know the rules but we also need to have some idea of strategy. And almost all strategies employed in the game have a strong connection with math.

**The Basics**

*Strategy*

For us to understand clearly how math and blackjack go together, we must look at the strategies involved in the game. Many individual especially the professional players, mathematicians, and some researchers have put it numerous time and effort in trying to decipher blackjack strategies that could tip the game’s favor towards themselves. One basic strategy and a very common one is card counting. This has emerged back in the 1950s which caused a lot of problems to cousins. They went so far as to employ spotters for card counters and those caught are kicked out and banned from the casinos. Card counting is based on three key factors that influence the game: the dealer’s card that is showing, and the two initial cards we are dealt with.

*Math and Card Counting*

Both the math involved in blackjack and card counting has a very clear connection if we want to win the game. Card counting is not some mere strategy that curious players can learn overnight, it takes skill. Since the game is to be as inconspicuous as possible, all counting and solutions have to be in our head so having a good head for numbers comes very handy. Back in the day, many players figured out a way how card counting can increase their odds of beating the dealer. But card counting is not the sole reason why people win at the game. The numerous subtleties of the game help too and paying close attention to their relationship with the card we are dealt with, the dealer’s card, and the ratio of our bets. They are all interrelated in a complex way to win us the hand.

*Variance*

Among the entire math concept related to the game blackjack, this is weighted more heavily. As I mentioned before, blackjack or any card game for that matter is all about probability and variance explains it well. The term is used to describe the difference between the actual results we get and the expected advantage. To put it in another view, if we have been playing a game for which our expected advantage is to accumulate $20 dollars an hour and we plan to play for 100 hours, we expect to get $2000. But if when we looked at our records, we have actually just accumulated $1500 which means we are $500 below our expectation. This is the variance and it could also flip the other way and go over our EV.

## What To Look For In A Calculator

In many lines of work, calculators are a necessary tool that is used every day. Many fields like engineering and accounting need calculators and they are usually the best people to ask advice on how to get a decent one. I, on the other hand, don’t need one all the time. I barely do any computing in my everyday life and when I would need one, there’s always the calculator on my phone it is quite useful. But I have had the chance to choose a calculator when I was still in school. Our teacher back in high school required that we have a scientific one and she outlined a guide on how to choose the best one. I have dug deep in my brain to remember the guidelines on what to look for in a calculator.

**Choosing the Best Calculator**

*Functionality*

When deciding to buy one, make sure it is able to do the necessary function that you’ll be doing most. A scientific calculator has many different features included but it would prove too complicated for tasks that only require simple math like adding number and such. Your phone calculator can be sufficient in doing most mathematical tasks but would be inept for complicated ones. So make sure you decide on a calculator that will fit your needs.

*Durability** *

The calculator I had back in high school is still with me to this day. This is because our teacher foresaw the clumsiness that most high school students are prone to and instructed us to get one that is fall-proof. She was right, I can’t remember the number of times my calculator fell to the floor from my desk. Invest in one from a good brand because those are the ones that will last long no matter how much you use it and you won’t have to keep buying one over and over again.

*Battery Life*

Choose one that won’t need battery changing often. Most calculators won’t require a change in battery for a few years but if yours runs out of power, changing the battery can be a hassle, so make sure you get one that is power efficient. Or better yet, get one of those models that you can charge through an outlet or your computer. It saves you time when you’re in the middle of working something and you have to make a quick run to get a new battery.

*Test out a Few before Purchasing One*

The best way to know what kind of calculator you want is to try using it first before deciding on getting one. Try borrowing a few of your colleagues and classmates and see which one is the right fit for you. Back in high school, almost everyone got the same kind of calculator because one, it was what our teacher used and two, it was very user-friendly. If I forget mine at home, borrowing one from a friend is easy enough without me struggling to know how to use it.

## Graham’s Number

Let’s make a thought experiment. Imagine the biggest number we can possibly think. 100 septillion?100,000 septillion? Now raise it to the power of septillion. Would that be the biggest number we could every possibly arrive at? Not even close. How about infinity? Surely there’s no bigger number than infinity. The very definition of it tells us that it is unending, that it goes on and on forever. But there is an amount so very huge our human brains can barely comprehend its vastness. I can’t even wrap my mind around the concept of a number this large. But this article will try to shed some light about Graham’s number and how truly enormous it is.

**Graham’s Number**

*History*

Graham’s number is a solution that arises out of a problem presented by the mathematical field of Ramsey Theory. It was named after Ronald Graham who provided the number as a simple way of explaining the upper bounds of the problem he worked on with Martin Gardner, a Popular Science writer. It was later published by Gardner in the publication Scientific America in 1977 which made it known to the general public. At the time of its publication, it was the largest positive integer ever to have been presented in a mathematical proof.

*Context** *

Graham’s number came about as a solution to a mathematical problem. In math, there is such a thing as combinatorics which concerns itself with counting. Its application is vast but primarily combinatorics looks at a network of numbers and their relationship to one another. Mathematicians who deal with this branch for mathematics look at ways to “color in” graphs and links to higher dimensional cubes. They try to count the number of possible relationships each number to each other and basically Graham’s number is the solution for that. The possible relationship is almost unending and hugely, hugely vast.

*Analogy*

To be honest with you, there is no single mathematician out there wise enough to explain Graham’s number in such a way that normal people would be able to digest it. The best analogy Graham used was in the context of hypercube but I won’t even begin to pretend I know what that is all about. The best analogy that I can come up with is by using groups of people. Take note, this is a very watered down version of the real answer, only used to explain the concept to those, not in the field of mathematics. There are four groups of people and we connect them through lines that we color either blue or red. We try to satisfy the question of what is the smallest value of members for each group to satisfy a given parameter. The lowest possible is 6 and the highest possible answer is Graham’s number.

*Mind-Bogglingly Big*

Graham’s number is huge, so very huge the entire universe does not have enough information to represent its entirety. People use it interchangeably with infinity but they’re wrong because Graham’s number is finite. It has an ending although it will take close to forever to reach.

## Why Math is not that Hard

Growing up, I was the kid in school that loved math. Most of my classmates complained about end about how hard they find the subject and how confusing the topics were but not me. I understood math pretty well. I picked up the topics fast and often I had to help my other classmates when my teacher was busy helping other students understand the number. As I grew up and learned more things about people, I started to understand why most people hate math. It’s all about perspective. People are used to looking at a problem a certain way and therefore address it as such. But math is different. A conventional way of trying to understand it won’t work if people lump it up with other challenges in life. This article is aimed to help people change their perspective and appreciate math for what it is, an art form.

**Changing Perspectives**

*Break it all Down*

Math is a complicated relationship between formulas and numbers. Not understanding one will lead to a domino of effect for students not to grasp the entire concept. The key is to break it down into smaller chunks that are easy for students to digest. I find it easier to determine each step of solving a problem, introducing it to students slowly and letting them practice with different variations of the problem before proceeding to the next step. As they grow familiar, it boosts their confidence and will encourage them to take on the next step.

*Encourage and Inspire** *

I had a great math teacher growing up. This is partly the reason why I loved the subject so much. She could command the room without saying a word and she had a knack for making a subject about numbers interesting. The way she taught and respected her students was a big factor, why I gave more effort in doing well in class. She never undermined the struggles that some of my classmates had in her subject. She was constantly encouraging and usually spent a couple of hours outside of her work to help students who were struggling with a concept.

*Explore other Resources** *

If you find the subject hard, don’t hesitate to explore other options. I grew up in a different time where the only other resources we had outside of class was the library. Times are different now. The internet is a treasure trove of information in every shape and form. Many YouTube tutorial videos are available online explaining in great details and quite creative ways difficult concepts in math.

*Practice makes Perfect*

At the end of the day, it all boils down to practice. Math can be considered a new language and in order for us to become fluent in it is to practice practice and practice. This step cannot be overstated enough. It is one thing to understand the concept but quite different to apply it time and time again. There are numerous ways of applying a math concept and only knowing one way will lead to failure. Look up other examples online and practice solving them.