How Is Probability Used In Gambling

1. How Is Probability Used In Gambling Rules
2. Probability In Games
3. Probability And Gambling
4. Casino Game Probability
5. How Is Probability Used In Gambling Terms

Most of what I learned about odds and probability is what I picked up through independent study. Did you know that odds and probability affect gambling more than most? And there’s a bit of luck involved, of course.

How Probability is used in Games of Chance. Human beings seem to have a natural instinct for gaming and gambling. The Egyptians were playing a board game called Senet over 5000 years ago, and it’s likely that simpler games preceded this. Our minds seem to be programmed to want to play, and to want to win. This hub is all about calculating lottery probability or odds. In order to make it relevant, I decided to base it on the Grandlotto 6/55, the lottery game with the biggest prize money here in the Philippines. There will be two different cases in the hub: the probability of winning the game with all six numbers matching, and the probability of having n numbers matching. Roulette is a simple game, and it’s a great example of probability in action.

Today, I’ll be going over some little-known facts that might just give you a better understanding of odds. Here are seven things I know about odds and probability that you probably don’t.

1 – Probability Deals With Random Chance

Math is a broad subject, and like most broad subjects, it’s subdivided into smaller subjects. “Geometry,” for example, is the branch of math that deals with distances, sizes, and shapes. “Trigonometry” is even more specific. It’s the branch of math that deals with angles and triangles.

Probability, along with statistics, is the branch of mathematics that deals with random events and measuring how likely they are to occur.

Understanding probability is especially important in gambling and investing, but it can change your life in all kinds of ways. To get a better idea of how you can apply probability-based thinking to your life, check out a book by David Sklansky called DUCY? Exploits, Advice, and Ideas of the Renowned Strategist.

How Is Probability Used In Gambling Rules

2 – Probability Measures How Likely Something Is to Happen

If you want to know how far one point is from another, you use “distance” to measure that. In the United States, distances can be measured in inches, feet, yards, and miles.

Another example of a word used to describe a measurement is “volume.” You can buy milk by the quart or by the gallon, for example.

“Probability” isn’t just the mathematical study of likelihoods. It’s also the word we use to describe and measure how likely something is to happen.

Probability, by its nature, is measured differently from other kinds of measurements.

3 – It’s Always a Number Between 0 and 1

Most things we measure using arbitrary units. In the previous example, we use inches to measure distance and ounces to measure volume.

But in probability, we use a measurement that’s based on fractions. And the probability of an event happening is always just a fraction that’s less than or equal to 1.

If something has a probability of 1, it’s a sure thing. It will happen every time.

Here’s an example: If you have a jar with 20 marbles in it, and all those marbles are white, and you pick a marble from the jar without looking, the probability of picking a white marble is 1.

The probability of picking a black marble is 0. There aren’t any black marbles in the jar.

Probability In Games

It gets more interesting when you put different colored marbles in the jar. If you put 10 white marbles and 10 blackjack marbles, you have a probability of 1/2 for getting a white marble at random. You also have a 1/2 probability of getting a black marble at random.

The formula for probability is simple, too. The probability of an event is the number of ways that event can happen compared to the total number of possible events.

In the marble example, you have 20 possible events (20 possible marbles you could pick at random). 10 of those are white. The probability of getting a white marble at random, then, is 10/20, which reduces to 1/2.

You can express that probability in multiple ways, too, not just as fractions.

• You can express that probability as a decimal, 0.5.
• You can express that probability as a percentage, 50%.
• Or you can express that probability as odds, 1 to 1 or “even odds.”

That last way of expressing a probability, as odds, is especially useful in gambling.

4 – Odds Are A Way of Describing Probability That Are Especially Useful

The odds of something happening are just a comparison of the number of ways it can happen versus the number of ways it can’t happen. In the marble example, you have 10 white marbles versus 10 black marbles, so the odds are 10 to 10 of getting a white marble.

You can reduce that just like you would a fraction to get even odds – 1 to 1.

Let’s change the example, though. Now, let’s suppose you have a jar with 5 white marbles and 15 black marbles in it. Your odds of drawing a white marble are 15 to 5, which reduces to 3 to 1.

For every possible white result, you have three possible black results. Obviously, you’re likelier to get a black marble in this situation than you are to get a white marble.

One of the reasons that this is so useful is because odds are also used to describe how much a bet pays off. A lot of bets are even money bets. You bet $100, and if you win, you get $100. If you lose, you’re out $100.

But in some bets, you might win more money than you’re risking. For example, you might place a bet where you could win $200 and only risk $100.

You can compare the odds of winning with the payout odds to see whether you or the other party to the bet has the advantage.

This is what makes it possible for poker players to play professionally and win in the long run. They put their money in the pot when they have better payout odds than odds of winning. This is also what makes casinos profitable. They pay out bets at odds less than your odds of winning.

5 – The Casino Has a Mathematical Advantage for Every Game

When you play casino games, the casino always has a mathematical advantage. It’s easier or harder to measure depending on the game you’re playing and the rules.

The easiest example might be roulette. The math behind the house edge is relatively easy to calculate.

Let’s look at an even money bet, a bet that the ball will land on a red number.

You have 18 red numbers on a roulette wheel, 18 black numbers, and 2 green numbers. You have a total of 20 ways to lose and 18 ways to win.

The odds, therefore, of winning are 10 to 9. But the payout is 1 to 1.

Let’s say you place this bet 19 times in a row. You’ll win 9 times, and you’ll lose once on average, in the long run.

If you bet $100 every time, after completing those 19 bets, you’ll have won $900 and lost $1000. This results in a net loss of $100 over 19 bets. Your average loss per bet is $100/19, or $5.26.

Since $5.26 is 5.26% of $100, we say that the house edge for that roulette bet is 5.26%.

The calculations for the house on other bets in other games might be different and even more complicated, but you can count on this – the casino always has the mathematical edge over the player.

6 – The House Edge for Each Casino Game Is a Known Quantity

For every casino game, the house knows what its mathematical edge is. The player can do a little research and find the house edge for every table game, too. You can use this information to inform your gambling decisions.

An easy way to do this would be to only play the games with the lowest house edge.

A simple comparison of the house edge in blackjack, 0.5% in some games, with the house edge in roulette—5.26%—tells you that blackjack is the better game.

But for the gambler, one game in the casino has an unknown house edge. That’s the slot machine.

To calculate the house’s advantage, you must know the probability of each event as well as the payouts for those events.

Modern slot machines use a random number generator (RNG) to determine outcomes. Not every symbol has the same probability of showing up. Some symbols might show up two or three times more often than some other symbols, for example.

The casino, though, has the details for the slot machine games’ probabilities. They know which slots have a house edge of 5% and which slots have a house edge of 15%.

You can’t know, though, unless you clock a large number of spins and extrapolate the data. Even then, you could be way off.

7 – The Theory Behind Probability Has Real-World Implications

You can use the ideas behind probability to inform your decisions in life. Using probability, you can measure the expected value of the various decisions in your life. You just compare the potential loss with the potential win and make your decisions accordingly.

Probability And Gambling

Here’s a silly example: You’re at a bar with a friend, and he decides he’s going to make a pass at every woman in the bar.

What does he risk? He risks potential rejection, but his self-esteem is strong, and rejection is meaningless to him. He’s basically placing a free bet because if he loses, he isn’t out anything.

If your friend is reasonably charming and good-looking, he might have a close to 100% probability of going home with one of these women. On the other hand, if he’s a poor communicator and only average-looking, he might only have a 1 in 20 probability of getting a date.

It’s still a positive expectation bet because he’s risking nothing with a potential gain. You, on the other hand, might suffer terrible anxiety and hate rejection. If that’s the case, you might only make passes at women in the bar who pay attention to you first. The cost of making a pass at every woman might just be too high for you.

In the book by Sklansky I mentioned earlier, he suggests attaching dollar amounts to such decisions. How much money would you pay to avoid rejection? How much money would you pay to get a date? What is the probability of rejection versus the probability of getting a date?

Casino Game Probability

That’s a silly example, but you can use the same probability-based thought process to make career decisions and other life decisions.

Conclusion

Probability might be the most important branch of mathematics. It’s certainly the most practical, especially if you gamble as a hobby or for a living.

I recommend taking a class in probability or at least studying a probability textbook. Definitely explore the ideas in the Sklansky book I recommended in the introduction.

Probability is the measure of likelihood that an event will occur. It quantifies as a number between 0 and 1, where loosely speaking 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (head & tail) are both equally probable. In this case the probability of head and tail are equal. Since no other outcomes are possible, the probability of either head or tail is 1/2 ( which could also written as 0.5 or 50 %)These concepts have been given an axiomatic mathematical formalization in probability theory which is used widely in such areas of study as arithmetic, statistics, finance, gambling science (in particular physics), artificial intelligence/machine language learning, computer science, game theory and philosophy to draw inference about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems. When dealing with experiments that are random and well defined in a purely theoretical setting (like tossing a coin) probabilities can be numerically described by the number of desired outcomes divided by the total number of all outcomes. For example, in tossing a fair coin two times the possible outcomes in first and second toss may be Head & Head, Head & Tail, Tail & Head or Tail & Tail, i.e, there are four possible outcomes. Out of these four possible outcomes the chance of getting Head & Head is 1 out of 4 which is expressed as ¼ =0.25=25%.

The word probability is derived from the Latin Probabilities, which can also mean probity; a measure of the authority of a witness in a legal case in Europe and often correlated with the witness’s nobility. In a sense, this differs much from the modern meaning of probability, which in contrast is a measure of weight of empirical evidence and is arrived at from inductive reasoning and statistical inference. The scientific study of probability is a modern development of mathematics. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia but exact mathematical descriptions arose much later. According to Richard Jeffrey, before the middle of 17^th century, the term probable means approvable and was applied in that sense, unequivocally to opinion and to action. A probable action or opinion was one such as sensible people would undertake or hold in the circumstances. The 16^th century Italian Polmath Gerolmo Cardanodemonstrated the efficacy of defining odds as ratio of favorable to unfavorable outcomes which implies that the probability of an event is given by the ratio of favorable outcomes to the total number of possible outcomes. Aside from the elementary work by CARDANO, the doctrine of probabilities dates to correspondence of Pierre de Fermat and Blaise Pascal (1654), Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli’sArs conjectandi (Posthumous 1713) and Abraha de Moivre’s'Doctrine of chance(1718)' treated the subject as a branch of mathematics. “The emergence of probability” of Ian Hacking’s and “The Science of Conjecture” by James Franklin clearly shows the histories of the early development of the very concept of mathematical probability.

The theory of errors may be traced back to Roger Cotes’s Opera miscellanea (posthumous 1722) but a memoir prepared by Thomas Simpson (1755) first applied the theory to the discussion of errors of observation. The reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable and that certain assignable limits define the range of all errors. Simpson also discusses continuous errors and describes a probability curve. The first two laws of error that were both originated with Pierre-Simon Laplace. The first law was published in 1774 and stated that the frequency of an error could be expressed as an exponential function of the square of the error. The second law of error is called the normal distribution or the Gauss law. Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors.

How Is Probability Used In Gambling Terms

Like other theories, the theory of probability is a representation of its concepts in formal terms- that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic and any results are interpreted or translated back into the problem domain. There have been at least two successive attempts to formalize probability, namely the Kolmogovformulation and the Cox formulation. Probability theory is applied in everyday life in risk assessment and modeling. The insurance industries and markets use actuarial science to determine pricing and make trading decisions. Government applies a probabilistic method in environmental regulation, entitlement analysis and financial regulation. In addition to these, probability can be used to analyze trends in Biology (e.g. Disease spread) as well as ecology (eg. biological Punnett squares). It is also used to design games of chance so that Casinos can make a guaranteed profit, yet provides payouts to players that are frequent enough to encourage continued play. Another significant application of probability theory in everyday life is reliability. Many consumers’ products such as automobiles and consumer’s electronics, use reliability theory in product design to reduce the probability of failure. Failure probability may influence a manufacturer’s decision on a product warranty. The cache language model and other statistical language models that are used in Natural Language Processing are also examples of application of probability theory. So theory of probability is an inseparable component in our real life.