11 Gambling Probability Examples

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We are producing an article with 11 examples of gambling probability since we believe that using examples is one of the simplest ways to convey a message. Many people struggle with math, and probability is a subfield of mathematics. But it’s much simpler than you might think to figure out the likelihood that something will or won’t happen.

The 11 instances and their relevance to probability are given below.

1. How to calculate the probability of an event

The first idea to grasp is that probability is a term that relates to unpredictably occurring events. It’s a means to quantify numerically the likelihood that a specific event will occur or not.

Furthermore, a probability is always a number between 0 and 1, which is the first thing to understand. You should know that an event that will never happen has a probability of 0, and I’ll explain it a little more in the bullet point below this one. The likelihood of an event occurring always is 1.

You can quantify anything that might or might not occur with a number between 0 and 1. And it’s simple to calculate that amount.

You divide the total number of events that can occur by the number of ways that an event could occur.

Here’s a simple illustration:

You do a coin toss. There are two scenarios that are equally likely to occur. You are interested in the likelihood that the coin will land on heads. The likelihood of it landing on heads is 12, as there is only one possible outcome. Additionally, you may write that as 0.5, 50%, or 1 to 1.

Down below we will go into further detail.

2. Probabilities presented in the form of fractions, decimals, percentages, and odds

y definition, all probabilities are fractions. However, there are numerous methods to express a fraction. In #1, I provided instances involving the toss of a coin.

Let’s examine a another illustration. Consider that you own a coin with two heads.

How likely is it that the coin will come up heads?

How likely is it that it will land on its back?

Given that there are two heads, there is a 100% likelihood that the result will be heads and a 0% chance that it will be tails.

That can also be written as 1/1. (which is just 1). You might also write it as 1.0. However, the majority of people feel at ease presenting it as a percentage.

In Dungeons & Dragons, you can use dice that are different shapes and have fewer or more sides than six. Let’s illustrate this with a 4-sided die.

What are the probabilities of rolling a 4 on a 4-sided, numbered 1-4 die?
There is only one way to get that outcome, yet there are four alternatives.

3. The likelihood of tossing a coin

Let’s revisit the coin toss illustration. I’ll use it as an illustration of how to determine the likelihood of several events.

Consider the situation where you wish to determine the likelihood of receiving heads twice. You add the two probabilities together to determine the likelihood that one event will occur AND another event won’t.

We have a 0.5 chance of obtaining heads in this scenario. The likelihood of obtaining heads twice in a row is 0.5 X 0.5 = 0.25.

It is clear why this is the case when considering all of the potential outcomes:

Two tails are possible.
You might receive heads twice.
On the first toss, you might get tails, and on the second, heads.
On the first toss, you might receive heads, and on the second, you might get tails.
There are four possibilities, but only one of them leads to the desired outcome.

4. Probability and six-sided dice rolling

Let’s examine a different probability example utilizing a standard six-sided die. There are 6 outcomes on the die: 1, 2, 3, 4, 5, or 6.

Any particular one of those numbers appearing is 1/6 likely.

But what if you wanted to determine the likelihood of receiving either a 1 or a 2?

You multiply when figuring out probabilities in a problem that uses “AND.”

But if you use “OR,” you have to add.

The likelihood of receiving a 1 is 1/6. Additionally, 1/6 of the time, you will receive a 2.

1/6 plus 1/6 equals 2/6, which is halved to 1/3.

You can alternatively write that as 2 to 1 odds, 33.33%, or 0.33.

5. Chance in card games

In card games, there are many different probabilities at play, but they are all based on a small number of characteristics shared by a deck of cards.

There are 52 cards in a typical deck of cards. There is a 1/52 chance of receiving any certain card.

Clubs, diamonds, hearts, and spades are the four distinct suits that make up the deck of cards. The likelihood of drawing a card from a certain suit is one-fourth.

Additionally, there are 13 possible rankings for the cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace.

There is a 1/13 chance of drawing a card of a particular rank.

However, one of the fascinating aspects of card games is how the distribution of cards alters the likelihood of receiving further cards.

Here’s an illustration:
You’ve been dealt an ace as your opening card in a game of blackjack using just one deck. How likely is it that the upcoming card will likewise be an ace?

In the deck, there are now only 3 aces left. There are also only 51 cards left in the deck.

Therefore, the likelihood is 3/51, or 1 in 17, or 16 to 1.

Here’s another illustration:

You’re engaged in five-card stud. You are dealt three aces and a deuce. The only opponent you have is holding four cards, none of which are aces.

In the deck, there is only one remaining ace. The deck still has 44 cards in it.

The likelihood of landing the final ace on your following card is therefore 1 in 44.

6. Roulette wheel probabilities

There are 38 places on an American roulette wheel where the ball can land. There is a 1/38 chance that the ball will land in a particular pocket. Additionally, this can be stated as 37 to 1.

This is a wonderful illustration of how the casino gains an advantage over the player. 35 to 1 is the payout for this wager.

Over a sufficient amount of time, the casino will almost certainly profit handsomely from this wager because the chances of winning are 37 to 1 and the payoff is only 35 to 1.

Additionally, the payout for every wager made on the roulette wheel is not in line with the likelihood of success.

Let’s look at some of the other roulette wheel probabilities before I get into more detail on the house edge.

There is more to the pockets’ numbering. They have color as well. There are 2 green ones, 18 black ones, and 18 red ones.

The likelihood that the ball will land in a green pocket is 2/38, or 1/19, or 18 to 1.

The likelihood that the ball will land in a black pocket is 18/38, or 9/19, or 37 to 18.

The chances of the ball ending up in the red pocket are equal.

Additionally, you can wager on whether the ball will land on an odd or an even number. The green pockets in the 0 and 00 are considered neither. The odds of winning odd or even are therefore the same as those of winning a wager on black or red.

These are but a few instances. You have a bewildering array of wagering options while playing roulette.

There are also different Roulette strategies which we cover on our guides section.

7. How a casino game’s house edge operates

The proportion of each wager that the casino anticipates winning over the long run is called the house edge. The simplest approach to figure this out is to assume that a player is betting $100 every wager, calculate his average long-term loss, then divide it by the number of wagers.

I’ll use roulette as an illustration once more because it’s helpful.

On one number, you wager 38 times at the roulette wheel. You would only win once and lose 37 times if you had a mathematically ideal set of spins, which is what you want to assume when figuring out the house edge.

You will receive $3500 as the payout on the winning wager, which is 35 to 1. But the 37 lost spins will cost you $3700. $3500 less $3700 equals $200 in net loss.

The average loss you incur per spin is $5.26 when you split $200 by 38.

The house advantage for the game is 5.26%.

Keeping in mind that the house edge is a long-term mathematical expectation is key. In the short term, anything is possible (and frequently does happen).

However, as you approach tens of thousands of results, you’ll see a tendency in the actual results in the direction of the predicted outcomes.

The casino’s business strategy is based on the law of huge numbers. Players want to have the rare brief streak of luck. The casino is aware that the actual predicted outcomes on all the other wagers being continuously placed around the casino more than make up for these brief streaks of good fortune.

8. The chances in blackjack 

One of my favorite examples of probability in action is blackjack. Because the deck of cards has a memory, unlike roulette, this is the case. In a game of blackjack, the make-up of the deck changes each time a card is dealt. The chances are altered as a result.

Card counters are able to get an advantage because of this. They have a method for monitoring these changes to the deck’s composition.

Here’s a prime illustration:
You’ve discovered that all four aces have previously been dealt while playing single-deck blackjack. What is your chance of getting a blackjack?

There is no chance of landing a blackjack because a blackjack requires an ace plus a card worth 10, and there are no more aces in the deck.

However, you may also determine the likelihood of landing a blackjack when dealing with a new deck of cards.

You’re estimating your chances of drawing an ace on either the first or second card. Your likelihood is 4/52 since there are 4 aces in the deck. When you lower it, it becomes 1/13. This is a “or” question, thus we include those together

1/13 + 1/13 = 2/13

But now the “and” component of the issue comes into play. An ace AND a 10 are required. The king, queen, jack, and number 10 are among the 16 cards in the deck, each of which is worth ten.

Your chances of drawing another card with a 10 are 16/51.

16/51 X 2/13 = 32/663. That is equal to 4.83% of the time, or almost 5%, of the time.

You can roughly estimate how frequently you’ll receive a blackjack because 5% is the same as once every 20 hands.

Using basic blackjack strategy you can gain the best advantage against house without counting cards.

9. Video poker and slot machine probabilities

One of the best things about video poker is that despite the fact that it resembles a slot machine, it is not one.

Here’s why that’s fantastic:

The only game in the casino with murky math is the slot machines. In other words, there is no way for you to know what the payouts and/or odds are on a slot machine.

Yes, pay tables exist for slots. Consequently, you are aware of the payouts for different symbol combinations on the reels.

However, there is no method for you to determine the likelihood of a specific symbol appearing on a reel.

You could compute the chance, the house edge, and the payback % if you actually KNEW this.

Here’s an illustration:

Lemons are one of the main symbols in the game you’re playing. There is a 1/10 chance of receiving a lemon on each reel. You win 900 coins if you get three lemons.

The likelihood of receiving 3 lemons is 1/1000, or 1/10, 1/10, and 1/10. That works out to 999 to 1 in odds.

(Remember that you multiply when the question contains the word “and” to determine probability. You are interested in the likelihood of receiving a lemon on lines 1 and 2 and 3 in this case.

Assume that you are wagering $100 per spin in this high stakes game.

You spin 1,000 times. You lose $100 on each of those 999 spins, for a grand total loss of $99,900. You win 900 coins, or $90,000, on one of those spins. $9900 ($99,900 – $90,000) is your net loss.

If you multiply that by 1000 spins, you will lose $9.90 on average.

Therefore, this game has a 9.9% house advantage. When it comes to gaming machines, casino employees focus on the payback percentage. Simply put, that is 100% less the house advantage, in this example 90.1%. It indicates the portion of each wager that the casino returns to the player as opposed to the portion that it keeps. It’s also known as return to player at times.

These odds are known to casinos and slot machine makers. The game was made by them. They are the only ones who are aware of these chances, though, as a random number generator powers the games. If the game were mechanical, you could figure out the odds only by knowing how many symbols are on each reel because each symbol would have an equal chance of appearing.

However, a lemon might be set to appear once every 12 spins, once every 15 spins, or once every 20 spins, depending on the programming. There simply isn’t a way to know.

On the other hand, video poker replicates the odds you’d find in a deck of cards. You also understand how much each card combination will pay off. Additionally, you are aware of the likelihood of each combination.

This data can be used to determine the game’s house edge and payback percentage.

Here’s an illustration:
We are aware that a pair of jacks or higher pays off at even money in a normal Jacks or Better game with a 9/6 pay table. That hand will appear roughly 21.5% of the time. Therefore, for that specific hand, the expected value (payback percentage) is 1 X 21.5%.

For each potential hand, you can perform the same computation. You multiply your potential payout by the likelihood of being dealt the hand. The overall payback % for the game is then calculated by adding up all the choices.

The payback percentages for video poker are also fantastic because they are nearly usually higher than those for slot machines.

The second fantastic thing about video poker is that it provides you with some mental stimulation that a slot machine doesn’t. Each hand’s strategy must be chosen. You have a better chance of winning if you play them appropriately.

10. How to estimate return on investment

The amount you anticipate a wager to be worth is known as the expected return. A positive expectation bet is one where the payout exceeds the risk. Otherwise, it’s a wager with a low expectation. Gamblers will occasionally abbreviate this as +EV or -EV.

Here’s how to figure out how much a wager is worth:

You multiply the likelihood that you will lose money by the likelihood that you will lose money. The likelihood of winning is then multiplied by the amount you stand to win. You can calculate your anticipated return by dividing one by the other.

It’s that easy.

Roulette will serve as an example (again).

You wager $100 on one certain number. If you triumph, $3500 is yours. $100 is lost if you lose.

At first glance, it seems like a fairly decent offer, doesn’t it?
However, let’s calculate.

There are 38 numbers on the roulette wheel, thus your odds of winning are one in thirty-eight. Your chances of losing your wager are 37/38.

1/38 X $3500 = $92.11

37/38 X -$100 = -$97.37

There is a $5.26 discrepancy. That is the amount you anticipate losing, and the negative number is larger. That wager has an estimated value of -$5.26.

This type of math is also applicable to daily life. I’ll elaborate on that later.

11. Making use of probability in daily life

Actually, this is the most significant part of the article. You can utilize your understanding of probability to make decisions in the real world that are superior than those made by the majority of people.

That decision’s expected value is an easy one to understand.

Let’s examine a more real-world, everyday example, though. Let’s say you’re thinking about parking in a space designated for people with disabilities.

There is a 20% chance of receiving a ticket for this, and the parking fine may be $200. There will be a $40 loss in such case.

However, parking there will save you from having to walk for a half-hour, and you are a highly compensated consultant making $250 per hour. That implies that each half-hour of your time is worth $125.

Take the risk since your time is worth significantly more than $40.

That illustration, of course, disregards any moral consequences. You could feel morally conflicted about occupying a parking space meant for a person with a disability.

Here is another relevant illustration:

You are 45 years old and heavy. If you don’t reduce weight, the doctor says you’ll only live to be 60 years old. However, if you undergo weight loss surgery, you will live to be 68 years old.

However, there is a 1 in 800 possibility that you’ll pass away throughout the weight loss procedure.

What is the right choice, mathematically speaking?
Since it will be simpler to perform the math if the life expectancy figures are taken as absolute certainties, let’s suppose that they are.

If you choose not to use the operation, you have a 100% probability of passing away 15 years sooner. That is fifteen years.

If you have the procedure, your chance of gaining 18 years is 799/800. There would have been a gain of +17.98 years.

Also, your likelihood of passing away 30 years early is one in 800. (at age 45). Another -0.04 years of projected loss result from that.

17.98 – 15 – 0.04 = 2.94 more years of anticipated life.

And it’s likely that you’ll appreciate life more throughout that period. You’ll have more time for hobbies, be able to date more people, and need less medical care.

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