# Probability in Gambling and Betting

The articles that are devoted to probability in gambling and betting. The topics include: the difference between probability and luck, winning chances, common myths and mistakes players make when assessing the probability, expected return etc. Clearly illustrated on simple examples.

## Chance

What is chance, the mysterious force that sometimes shapes our destinies and influences the course or outcome of events, not only in betting or gambling? Does anything happen without any cause? How is chance practically utilized? What is a random event and a random experiment?

## Chevalier de Mere's Dice Probability Problem

The old (17^{th} century) and one of the most famous probability puzzles of two dice games of the Renaissance gambler Chevalier de Mere. The solution was discovered by no-one else but Blaise Pascal.

## Evidence of Divine Providence

You don't have to worry that we're changing the focus of our server. Let's look at one of the oldest mathematical or probabilistic proofs, dating back to 1710. Dr. John Arbuthnott systematically studied the numbers of births and their genders for the past 82 years. He came to the conclusion that larger numbers of male births than female births are not the result of chance but of divine providence. How did he reason?

## Expected Return and Risk in Business

Let us follow another example of how the expected value can be used – this time in business. We will be able to make a qualified choice between two products (that we can manufacture) based on the expected return and associated risk.

## Expected Value in Gambling

The expected value (EV) is a powerful tool to determine a house advantage (in other words a player's disadvantage) of any wager in any casino game, but it is also essential for mathematically perfect play of Poker.

## Fair Bet

The fair bet is such a bet whereas the expected return (or value) of the bet is null (or neutral) for all parties involved. There are usually two parties: a player and a casino, a player and a betting company, alternatively two friends who make a bet between each other. The meaning of the fair bet is clearly illustrated by examples.

## Investment Expected Return and Risk

The use of expected value in investments. We will pick up a few stocks and demonstrate the calculation of the expected return and risk for both individual stocks and portfolio.

## Monty Hall Three Door Puzzle

The use of expected value in investments. We will pick up a few stocks and demonstrate the calculation of the expected return and risk for both individual stocks and portfolio.

## Probability Assessment

Let us have a look at common myths and mistakes that players of casino games make when assessing probability and let us also find out why it is necessary to beware of rash or seemingly clear conclusions.

## Probability, Odds & Luck

The theory of probability is essential for a proper evaluation of individual wagers of various casino or gambling games. We will get familiarized with the definitions of gambling games, luck, investment and calculation of probability.

## Random Number Generation

Generating random numbers without following a pattern, and thus making them predictable, and ensuring they have a corresponding distribution (i.e., so that some numbers do not occur more frequently than others in a long sequence) is a more complex task than it might initially seem. What is a random number generator, and what methods are used?

## True Odds & House Advantage

To find out the House Edge, we need to compare the two things – true odds and a payout ratio. While the payout is quite clear, because it is simply quoted by a casino, true odds need to be calculated on the basis of the probability theory.

## Two Beagles Probability Puzzle

Two beagles is a remarkable probability puzzle by Marilyn von Savant, a woman with the highest IQ in the world (218 points) who is written down in the Guinness Book of Records. She often contributes with similar probability riddles to a magazine.