Just a bit of clarity.
From here:
http://www.problemgambling.ca/en/resourcesforprofessionals/pages/probabilityoddsandrandomchance.aspxProbability: A Definition
Probability is the likelihood or chance that something will happen. Probability is an estimate of the relative average frequency with which an event occurs in repeated independent trials. The relative frequency is always between 0% (the event never occurs) and 100% (the event always occurs). Probability gives us a tool to predict how often an event will occur, but does not allow us to predict when exactly an event will occur. Probability can also be used to determine the conditions for obtaining certain results or the long-term financial prospects of a particular game; it may also help determine if a particular game is worth playing. It is often expressed as odds, a fraction or a decimal fraction (also known as a proportion). Probability and odds are slightly different ways of describing a player’s chances of winning a bet.
Probability
Probability is an estimate of the chance of winning divided by the total number of chances available. Probability is an ordinary fraction (e.g., 1/4) that can also be expressed as a percentage (e.g., 25%) or as a proportion between 0 and 1 (e.g., p = 0.25). If there are four tickets in a draw and a player owns one of them, his or her probability of winning is 1 in 4 or 1/4 or 25% or p = 0.25.
Odds
Odds are ratios of a player’s chances of losing to his or her chances of winning, or the average frequency of a loss to the average frequency of a win. If a player owns 1 of 4 tickets, his/her probability is 1 in 4 but his/her odds are 3 to 1. That means that there are 3 chances of losing and only 1 chance of winning. To convert odds to probability, take the player’s chance of winning, use it as the numerator and divide by the total number of chances, both winning and losing. For example, if the odds are 4 to 1, the probability equals 1 / (1 + 4) = 1/5 or 20%. Odds of 1 to 1 (50%) are called “evens,” and a payout of 1 to 1 is called “even money.” Epidemiologists use odds ratios to describe the risk for contracting a disease (e.g., a particular group of people might be 2.5 times more likely to have cancer than the rest of the population).
In gambling, “odds” rarely mean the actual chance of a win. Most of the time, when the word “odds” is used, it refers to a subjective estimate of the odds rather than a precise mathematical computation. Furthermore, the odds posted by a racetrack or bookie will not be the “true odds,” but the payout odds. The true odds are the actual chances of winning, whereas the payout odds are the ratio of payout for each unit bet. A favourite horse might be quoted at odds of 2 to 1, which mathematically would represent a probability of 33.3%, but in this case the actual meaning is that the track estimates that it will pay $2 profit for every $1 bet. A long shot (a horse with a low probability of winning) might be quoted at 18 to 1 (a mathematical probability of 5.3%), but these odds do not reflect the probability that the horse will win, they mean only that the payout for a win will be $18 profit for every $1 bet. When a punter says “those are good odds,” he or she is essentially saying that the payout odds compensate for the true odds against a horse winning. The true odds of a horse are actually unknown, but most often the true odds against a horse winning are longer (a lower chance of a win) than the payout odds (e.g., payout odds = 3 to 1; true odds = 5 to 1). The posted odds of a horse actually overestimate the horse’s chance of winning to ensure that the punter is underpaid for a win.
Equally Likely Outcomes
Central to probability is the idea of equally likely outcomes (Stewart, 1989). Each side of a die or coin is equally likely to come up. Probability, however, does not always seem to be about events that are equally likely. For example, the bar symbol on a slot machine might have a probability of 25%, while a double diamond might have a probability of 2%. This does not actually contradict the idea of equally likely outcomes. Instead, think of the 25% as 25 chances and the 2% as two chances, for a total of 27 chances out of 100. Each of those 27 chances is equally likely. As another example, in rolling two dice there are 36 possible outcomes: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1) . . . (6, 6); and each of these combinations is equally likely to happen. A player rolling 2 dice, however, is most likely to get a total of 7 because there are six ways to make a 7 from the two dice: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1). A player is least likely to get a total of either 2 or 12 because there is only one way to make a 2 (1, 1) and one way to make a 12 (6, 6).
