BLACKJACK, POKER AND PROBABILITY
I have taught statistics at the college level for almost fifteen years and have worked as a mathematician for twenty years. The way that I got started is simple; my dad was a card player. He was a little more than that; he was a very good card player. He did this using mathematics. Although he had no formal education beyond high school, he was very good at calculating probabilities in his head quickly.
Growing up he often played cards with my brothers and me. We did not play Crazy Eights or Go Fish, we played Poker or Blackjack. He often dealt "ghost hands" to explain how the probabilities changed based on the cards showing and the cards in your hand. I developed an interest in probability and statistics and ultimately decided to pursue a career as a mathematician. My brothers followed similar career paths with degrees and careers in mathematics and engineering.
In the classroom and in textbooks, the explanations of probability concepts are often accompanied with problems involving playing cards, Poker, and Blackjack. Examples are usually based on a standard 52 card deck, which is known as a "Poker Deck" in some countries.
To understand some of the basics, you need to understand the cards in a standard 52 card deck. I often have students in the classroom or online who have never been exposed to playing cards. There are two colors (red and black), four suits (Clubs, Diamonds, Hearts, and Spades), and 13 different denominations (Ace, two through ten, Jack, Queen, and King). Each of these denominations is represented in each of the suits. I know it sounds elementary to note this, but many students really have not been exposed to playing cards, Poker, or Blackjack.
Along with these denominations you can also get other "counts" such as 12 total "Face Cards" (four each of the Jack, Queen, and King). In calculating other probabilities, you will need to know other things such as whether the Ace is considered "high" (greater than the King) or "low" (less than the two). In Poker and Blackjack it can usually be considered either based on the best hand you can make.
Let's look at some basic probabilities. The probability of drawing a "red card" is simply 26/52 or 1/2 simplified since 26 of the 52 cards are red. The probability of drawing a "Heart" is 13/52 or 1/4 simplified since 13 of the 52 cards are Hearts. It follows that the probability of drawing a Jack or any other single denomination is 4/52 or 1/13 since there are four each in the deck.
Other more interesting probabilities come about when you specify more about the probability you are calculating. The probability of drawing a "red eight" would be 2/52 or 1/26 simplified since there are only two eights that are red (eight of Hearts and eight of Diamonds). The probability of drawing any face card would be 12/52 or 3/13 since there are three different face cards (Jack, Queen, and King) in each of the four suits.
It gets really interesting and more applicable to games such as Poker and Blackjack when you consider "Conditional Probability". In other words we are interested in calculated a probability based on certain conditions. One simple example of this is shown in the probability of drawing an "Ace on your second card" given that "you drew an Ace on your first card". An important note here will be whether you are considering "with replacement" or "without replacement". For our example we will look at "without replacement". Therefore you have drawn one Ace and set it aside; leaving three Aces in a deck of 51 cards (remember you took one out). This gives a probability of 3/51 or 1 out of 17 simplified.
These conditional probabilities are very important when playing games like Blackjack or Poker and change based on the cards that you can see on the table. This is the reason that most casinos use multiple decks and shuffle often on their Poker and Blackjack tables. It makes it much more difficult to calculate and make decisions based on probability.
Let's look at one final simple Blackjack example. Let's say you are playing Blackjack with a standard 52 card deck with seven of your friends and you are dealt a "six and a seven" which total to 13. The object of the game is to be the closest to 21 without going over. There are many rules concerning which hands to "hit" (take a card) or to "stand" (not take a card). I am not concerned with these rules in this simple example. In Blackjack you can see one of the first two cards that each player and the dealer has been dealt and any future cards they have been dealt. You are the fourth person to get the option to "hit or stand". You have seen nine cards on the table, plus the two in your hand and none of them are eights. Therefore your probability of drawing an eight would be 4/41 since there are four eights in the deck not showing and 41 cards that you "have not seen". It gets a little more complicated based on the hands on the table, but this serves as a good example.
My dad chose to "teach us" with Poker and Blackjack, but there are numerous games that offer the opportunity to teach your children about math and probability. You may also find that you learn more about it also, and maybe you can gain an edge at the next "Poker Night" in your neighborhood.