Given that you are a fan of the pokies – or else would not likely be reading this right now – you probably have some idea and understand of odds and probability. It is pretty easy to understand for example, that if you flip a coin that is not weighted one way or the other, the odds of getting either heads or tails are the same, that is 1 in 2. This can also be written as a percentage chance of winning, that is 50%, or as a ratio like1:2. Understanding it in this common sense way is different from gaining a true understanding of the maths at work with probabilities. We get asked often about what probability theory is and how it really works. So now we will try our best to explain.
In essence, probability relates to ascertaining what the odds are, or what the chances are, of an event happening, such as a coin landing with heads facing up when flipped as in the above example, or of winning the lottery, or of drawing a card, or of any other thing you can imagine. While probabilities and odds are commonly used when gambling to ascertain chances of winning, you can pretty much assess the probability of an event at all, if you have enough information, whether it is related to gambling or not.
Probability is the number you get when you divide the number of ways an event can occur by the total possible number of outcomes in any particular scenario. For example. For example, if the event the want to establish the probability of is drawing a black card from a full deck of card, we would need to divide the total number of ways to draw a black card (26 as there are 26 black cards in a full deck) by the total number of possible outcomes, that is, 52 because there is a total number of 52 cards in a full deck (not including jokers). 26 divided by 52 is 0.5, giving us a probability of ½, or 0.5, or 1:2 – the same probability as when we flipped the coin.
Now, the logic behind “probability theory” has been around for ever, and with simple examples such as these it is very obvious how probability theory works, you might even be wondering what the point of having a mathematical theory for something so simple is, of why you would need a formula to work out basic things such as this. However, if you have been gambling for a while, and particularly if you have been playing casino games, you will know that most probabilities are not this easy to determine. The mathematical study of probabilities is relatively recent – compared anyway to the very long history of logical assessment of probabilities. In fact, gambling, which has been around since ancient times, was a major factor in the development of probability theory. Basically, people wanted to know with greater accuracy and in more precise detail, what their chances of winning at any given game were.
The mathematics of probability
So when people wanted to know what their chances of winning at any particular game were with greater accuracy than they could get just by following the logic, they turned to mathematicians who developed The mathematics of probability, or what is known as Probability Theory. As with most mathematical approaches to the problems of normal daily life, there are some terms you need to be aware of that are used with different meanings than you might be used to. When mathematicians assess probabilities, they use formulas in which they refer to “events”. An “event” is a thing that s likely to happen or not happen – an occurrence that are being assessed for their probability. Events in probability theory are represented by algebraic variables, usually “A”, and probability is represented by decimal numbers on a continuum from 0 to 1. Thus, the probability (P) of event A (for example, drawing an Ace from a deck of cards) happening is represented in the formula as “P(A)” “p(A)” or “Pr(A)”. An event that is impossible, for example, drawing five kings from a deck of cards, has a probability of zero. An event that is absolutely certain to happen, for example, drawing a card between 2 and ace from a deck without jokers, has a probability of one.
Sometimes we need to calculate the probability of two or more events happening at the same time. This is slightly more complex but is still a relatively simple task. It is simply a matter of multiplying together the probabilities of each of the individual events. For example, if we rolled two dice at the same time, the probability of rolling a two on one die is one in six (P=0.1667). This probability of getting a two on the other die is also 0.1667. The probability of rolling the two dice at the same time and getting two on BOTH of them however, is ).1667 x 0.1667. Therefore P=0.027. Note that although it seems less likely to get four on both dice than to get, say, a one and a five for example – this is merely a product of our mind. The odds are identical. An important factor to consider is whether the events are dependent or independent. For more information on this check our Frequently Asked Question What is the difference between dependent and independent events?.
For more information on odds and probabilities you can check our other Frequently Asked Questions concerning the mathematics of gambling.