It’s been known that Mathematics and Casino Games go hand in hand. These games we all enjoy are mostly all about numbers. Whether the games are based on Luck or Skill, about 98% of all the games are all numbers.
The mathematics of gambling is inexhaustibly interesting. In fact, without the field of mathematics known as “probability,” we wouldn’t have gambling—or, at the very least, we wouldn’t be able to discuss it rationally.
A probability is just a number that reflects the likelihood of an event. And it’s always a number between 0 and 1. Something with a probability of 0 will never occur. Something having a probability of one (which is also 100%) will always occur.
Probabilities can be expressed as percentages, but it is not the only way to do so. It can also be expressed as a fraction. 50% is the same as ½. A probability can also be expressed as a decimal. 50% is the same as 0.5.
Only a few wagers are safe bets. Almost often, one side has an advantage over the other. Being able to discern that edge is an important component of being a savvy gambler. This post begins with an explanation of what probability is and how it is calculated, followed by prime examples of how it is applied in practical applications.
Mathematics on Roulette.
Roulette is a simple game that demonstrates probability in action. An American roulette wheel contains 38 potential outcomes, which are denoted by the numbers 0, 00, and 1-36. The 0 and 00 are both green. Half of the other numerals are black, while the other half are red.
You may use this information to determine the likelihood of almost any result or combination of outcomes. You may compare those probabilities to the payoffs for the bet to discover if one side has an advantage and, if so, how significant that advantage is.
Let’s start with some of the most prevalent bets in roulette: the outer bets. These are wagers on odd/even, high/low, or red/black. They all payout at the same odds. You place a ₹100 wager on one of these possibilities and win ₹100 if you win.
At first glance, that appears to be a reasonable bet, but when you examine these wagers more thoroughly, the house has a distinct edge.
Let’s assume you bet on black. There are 18 black numbers on the wheel, however, there are also 20 non-black numerals. (18 of the numerals are red, and the remaining two are green.) So, only 18 of the 38 potential events win your bet.
As a result, the chance is 18/38. This bet is perhaps best understood by translating it to a percentage, of 47.37%.
So, the casino will win this wager 52.63% of the time, and you will win the rest of the time. It’s easy to understand how, if you play this game long enough, the casino will eventually win all of your money.
You may even compute the percentage of each wager that the casino will win in the long run—this is known as the house edge.
This is how you do it:
Assume you place 100 bets and get the mathematically predicted results. (This never happens in real life, but if you play for a long enough time, the actual outcomes will begin to approximate the predicted ones.)
You will win ₹47.37 but lose ₹52.63 in this situation. That works out to a net loss of ₹52.63 – ₹47.37, or ₹5.26. You lost an average of 5.26% of each bet since you bet ₹100 on those 100 wagers.
That is the house edge. As it turns out, that is the house edge for all roulette bets (except for one). In certain ways, the green 0 and green 00 are where the house gains an advantage. If those numbers weren’t on the wheel, the rewards for all of the bets on the table would provide neither side an advantage.
They are, however, behind the wheel. And it’s the difference between life and death.
Mathematics on Blackjack
Blackjack is a casino game played against the dealer. While most games are played against each other or within a system but in blackjack, you are playing in order to win against the dealer. The math on Blackjack is so easy when you get the hang of it that you will realize that it’s an elegant game.
A “natural,” also known as a “blackjack,” pays 3 to 2. That’s a two-card hand with a total of 21. There are only two card values that can result in such a hand: the aces, which count as 11, and the 10, J, Q, and K, which each count as 10.
It is impossible to acquire a blackjack if all of the aces in a deck are gone. You simply cannot do it. When a 10 is dealt, your odds of getting a blackjack fall.
At the same time, every time a lower-ranked card is dealt, such as a 2, 3, 4, 5, or 6, the chances shift slightly in the player’s favor.
As a result, a card counter will employ a technique to keep a rough record of the ratio of high cards to low cards. The low cards are counted as +1, while the high cards are counted as -1. If and when the positive count rises, the counter knows he has a greater than average chance of receiving the 3 to 2 payoff. As a result, he increases his stakes appropriately. He wagers more as the count rises.
When the count is 0 or negative, he reduces his bet. There’s a lot more to card counting than that, but those are the fundamentals. They’re also mathematically based.
Mathematics on Poker
Poker math must be the greatest on this list. It’s astonishing to know how much math is embedded with Poker. So let’s get right on it.
Let’s consider you’re playing 5 card draw and you’re handed a hand with four cards to a flush. You’re going to discard a card in the hopes of drawing a flush.
What is the likelihood that you will succeed?
The deck is down to 47 cards. Nine of these are the outfit you require. (Each suit has 13 cards, four of which are currently in your hand.) So your chances of getting the card you require are 9/47, or 19.1 percent. That equates to nearly one in every five people or 20%.
If you think you must win the pot with this hand, you may calculate how much money needs to be in the pot for you to profitably call bet.
Let’s say there’s $10 in the pot and you have to pay $1 to stay in and draw that extra card. If you win, you will be rewarded 10 to 1 on a 4 to 1 draw. You’ll lose over 80% of the time, but you’ll win so much of the time that it will make up for it and give you a nice profit.
In reality, let’s repeat the math from above, but this time we’ll assume you perform it 100 times in a row. You will lose $80.90 but win $190.10, making a profit of $109.20. These are fantastic pot odds.
On the other hand, if the pot was just $3 and you had to pay $1 to enter, you wouldn’t earn a large enough payoff to make this a viable gamble. You’d still lose $80.10, but you’d win $57.30, resulting in a net loss of $22.50.
But, in a real poker game, there are additional possibilities to consider. In this case, you can raise in the hopes of scaring your opponents out of the pot. When you do this, you must assess the likelihood that this technique will succeed. You can include it in your expected value.
This is when reading the other players comes into play. Some individuals believe that reading people is all about predicting what they will do 100 percent of the time.
However, in reality, you make educated judgments about their chances of doing anything. If you believe your opponent will fold to your bluff 50% of the time, your approach will change dramatically.
To sum up, it’s quite fascinating to see how much mathematics plays a vital role in these casino games we play. It is really important to know these aspects in order to clear the doubts and play safe during the uncomfortable situations while playing the games and understanding whether you are winning or losing but the most important fact is playing well knowing these circumstances and having fun.