Welcome everybody today to a talk on Probability and Gambling.

A subject I have more than a passion for as an occasional mathematician, a card player and gamer, an occasional not very successful gambler and as a long-term small stock market investor.

Everyone here has used the concept of Probability Theory countless times in their lives, usually successfully*, with an innate understanding of the ground rules despite no formal teaching in the matter. The discussion today may or may not improve your use of it but could add some interest to your lives in future.

We live in what some have described as a Goldilocks world +, Yet one that is also full of pitfalls and danger

What is Probability? A simple maze of contradictions and complexities.

Horatio

The time keeper

There are more things in heaven and earth, Horatio,Than are dreamt of In your philosophy.

Possibility is pure imagination, the stuff of dreams with no real-life outcome or occurrence.

Practicality is an event or outcome or real life happening.Probability however is the science of imagination turning into reality Probability is a unique science, the only science that cannot be proved or falsified. “In theory, there is no difference between practice and theory. In practice, there is.“ Yogi Berra

Probability is the likelihood that something is to happen expressed in percentage terms. It is the difference between practice and theory. It is a consideration of the chance of any event we care to consider happening in the future.People have played games of chance for virtually all of written history. The Egyptians played with dice around 3000 B.C.

As a science probability theory has always been intricately associated with gaming and gambling.

Yet “God may not play dice with the universe”- Albert Einstein,

Any event, happening, an object and a time all have this uniqueness in common in our world.

The probability of their existence or non-existence always sums up to one.

In Probability the occurrence of an event is called P and the non-occurrence 1-P.

Take an apple on a table . It is either there or not there.

Determining the chance of it being there is complicated by many factors beyond our control.

If we can stipulate the factors, we can estimate that probability for the factors that we know.

The golden rule is that a probability must always lie somewhere between 0 ,non existing, and 1, completely existing.

To this end we often describe it in terms of percentage as a percentage is usually expressed in terms of a hundredth of one.

Originally Probability found application as strategy in games of chance then in all forms of gaming and warfare. Virtually every aspect of business life and activity from the stock market to pensions , annuities and life insurance use it. It has found niches in every field of scientific testing.Weather prediction, shipping and air traffic control and even in store inventories.In the personal field it can even help you find the perfect match in life.It is paramount in the medical field in both evaluating the success of drugs in drug trials but also in diagnosis of cancers. Offshoots include medical equipment like CT scanners and MRI’s.Now we have the advent of AI.Sadly, back to warfare, the Terminator is approaching reality.

The use of the numbers 1-9 came from India to the Arab world, modified by adding in the number zero. It reached Spain and Italy by 1000 A.D Probability has only developed as a science in the last 400 years when European mathematicians were able to consider it and subjects such as Gravity, calculus, the movement of the planets with mathematics

In 1654 Antoine Gombaud, Chevalier deMere, a French nobleman was puzzled by an apparent contradiction concerning a popular dice game.The game consisted in throwing a pair of dice 24 times; Would betting on a double six in 24 throws be profitable?He was trying to establish if such an event has probability greater than 0.5.

Puzzled by this and other similar gambling problems he called the attentionof the famous mathematician Blaise Pascal. In turn this led to an exchange of letters between Pascal and French mathematician Pierre de Fermat.Probability science was born.The first documented evidence of the fundamental principles of the theory of probability.

“The basic bit is that most events [choices] in life are binary.A Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, “success” and “failure”, in which the probability of success is the same every time the experiment is conducted.Either/ or, The fire or the frying pan, flight or fright. Heads or tails, sink or swim.There is a principle called Occam’s Razor, a razor being a sharp simple choice ”The simplest explanation is usually the best one” Events exist in a sample space. This can be discrete, continuously discrete or continuous.The number of probable events that can occur in a sample space at any one time must always add up to one.When sample spaces overlap as in having different times and different numbers of events the same rule applies.In all simple or basic probabilities decision tree diagrams are used to help work out individual choice ratios and total number of outcomes per run of events.Large data sets take massive amounts of time to work out tree branch solutions .Listing all possible outcomes from tossing a coin 64 times in a row leads to a gigantic number>Immortalised in the story of a grain of wheat on a chessboard doubled every square.*2 to the power of 64 = 18,446,744,073,709,551,616.2 to the power of 63 = 9,223,372,036,854,775,808.

Baye’s theorem “New information should be given proportional rather than equal status initially.” Or don’t throw the baby out with the bath water.One man, Bayes , came up with the idea that led to Probability being able to be used for real life situations involving many different choices occurring randomly. This allows the original data to combine with new data without making large new adjustments.Baye’s Theorem, properly applied, enables Probability predicting easily on complex data bases when new information is provided.This then enables previous predictions to be altered and extended as in weather forecasting.It helps improve the accuracy hence safety of the standard deviation ranges for structures like Bridges, roads and aeroplane wings.It enables greater accuracy in prediction of health outcomes and life expectanciesIt allows continual modification in the direction of the new data without changing the thrust of the original hard-earned data. Bayes’ theorem (alternatively Bayes’ law or Bayes’ rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.[1]

Probability events coexist with a new style of maths called Set Theory. A schematic effective in dealing with multiple events occurring over multiple fields. Some events are dependent on previous events. Others occur in the same time frames with no dependence on each other.

I am not even going to try to explain Set theory rules like -P[A] plus P[A*] =1 the probability of something occurring and not occurring equals one. – P[A] plus P[B]= P[A]XP[B] -P[A] to….. P[X] =1 -P[A] given P[B] [dependent] = P[A] +P[B]Set theory and Venn diagrams differ in the rules of addition and multiplication because they deal with percentages in a fixed range of 1.

Are you lucky? Seriously? Have you won the lottery?Do good things happen to you in life?

When we study Probability, we unconsciously assign merit to one side of a choice and detriment to the other. Having a windfall, attaining a good job, having a happy childhood and happy family when we grow up. Avoiding illness and debt.Luck appears to be a random quality and Lady Luck chooses whomsoever she wants.

Phil Bradbury winning his gold medal in skating for Australia.Finding a Picasso in a second-hand shop.Having a medical event just after retiring.

Luck, good luck, is beating the odds the odds in a desirable way.In other words moving to the right side of the average outcome.But is it truly random?

Events are random, people are random, and outcomes seem random but the degree to which probability rules in our lives can be altered by our own actions. “The more I practice, the luckier I get.” Used by Gary PlayerThe choices we make, whether we have free will or not, influence both the direction we go in and the outcomes we achieve.

We initiate those choices by choosing whether or not to take action, how much and where we apply it. This does not guarantee success, but it increases the chance of success.

The fellow who finished second to Bradbury and Bradbury himself took steps to try to win a medal. They spent years practicing and honing their skills. They had genetic skills that let them skate extremely well. They were born at the right time to compete in an Olympic Games at a good racing age. Probability dictated that Bradbury should lose. Luck decided that he reached a pinnacle first.

Nothing is permanent except the fact of change’

To be, or not to be, that is the question: Whether ’tis nobler in the mind to suffer The slings and arrows of outrageous fortune, Or to take Arms against a Sea of troubles, And by opposing end them:

If luck is a matter of common sense and application why isn’t everyone happy and lucky and successful? The answer is that other people are also trying to improve their lives and their odds in the great Probability race of life. This reduces the chances of others who are competing for the same goals. One of the rules of physics is for each force there is an equal and opposing force.Another is that nature abhors a vacuum.Basically every system achieves a balance where it can, a stable or comfortable position where all those forces of randomness settle down and a status quo is established.This balance is always at risk from external and internal forces.Taking the earth as an example it could be hit by a meteor or have a volcanic eruption.In the societies we live in, we can affect both ourselves and others with our actions.When we take action improving our odds we reduce the odds for someone else.Since they are capable of taking action themselves there will be a push back effect.There is also collateral improvement and damage to others of a lesser nature. the ripples and butterfly wings we might see and cannot see.