Probability, a cornerstone of mathematics, is the foundation on which the entire structure of lottery odds rests. It provides a quantitative measure of the likelihood of a specific event occurring within a given set of circumstances. In the context of lotteries, probability serves as the guiding principle that dictates the chances of an individual ticket holder to win the jackpot. The odds of winning a lottery depend on a fundamental comparison between the total number of potential outcomes and the subset of favorable outcomes. This ratio establishes a numerical expression that reflects the probability of a ticket matching the winning combination drawn during the lottery. As such, the calculation of odds serves as a crucial determinant in understanding the feasibility of achieving victory in these games of chance. Consider a widely played lottery game characterized by a specific set of rules and parameters. Within this framework, the odds of securing the jackpot can be meticulously computed by dividing the singular winning combination by the total number of possible combinations.
Consider a lottery game with n balls, where k balls are drawn. The odds of selecting the correct numbers can be calculated using the formula:

Odds = $\frac{1}{\text{C(n,k)}}$; where the total number of possible combinations is given by C(n, k).

It represents the number of combinations of n items taken k at a time, and the number of winning combinations is simply 1.

For example, if a lottery requires players to select six numbers from a pool of fifty, the odds of a single ticket matching all six numbers would be calculated as:

Odds = $\frac{1}{\text{C(50,6)}}$; with C(50, 6) = $\frac{\text{50!}}{\text{6!(50-6)!}}$ = $\frac{50\times 49\times 48\times 47\times 46\times 45}{6\times 5\times 4\times 3\times 2\times 1}$ = 15,890,700.

Another example, if a lottery requires players to select five numbers from a pool of fifty, and two numbers from a pool of twelve, the odds of a winner ticket matching would be calculated as:

Odds = $\frac{1}{\text{C(50,5)}}x\frac{1}{\text{C(12,2)}}=\frac{1}{\mathrm{139838160}}$; with C(50, 5) = 2,118,760 and C(12,2) = 66.

The Gambler's mistake, a cognitive bias deeply rooted in human psychology, is a common trap among lottery players. This fallacy revolves around the erroneous belief that past outcomes influence future results in random events like lottery drawings. In reality, each lottery draw operates independently of its predecessors, devoid of any memory or influence from past outcomes. Despite this, many individuals succumb to the temptation of believing that a streak of losses increases the likelihood of a subsequent win. The notion of certain numbers being "hot" or "cold" in a lottery is a prevalent misconception that permeates the minds of many players. This concept suggests that certain numbers have a higher likelihood of being drawn based on their recent frequency in previous draws. However, the truth lies in the statistical principle of independence, which dictates that each lottery draw is entirely independent of its predecessors. Therefore, the idea of hot or cold numbers holds no merit in the realm of lottery probabilities, as the outcome of each draw is determined purely by chance. Luck and superstition wield considerable influence over the psyche of lottery players, shaping their perceptions and behaviors in the pursuit of fortune. While acknowledging the psychological impact of these beliefs, it is crucial to juxtapose them against the statistical reality of lottery play. While luck may play a role in individual outcomes, the overarching framework of probability governs the collective outcomes of lottery games. Understanding this duality allows players to navigate the realm of lottery play with a balanced perspective, embracing the allure of luck while grounding themselves in the statistical truths that rule the game.

Lottery has yield multiple interests in research field along the past years, occasionnaly concluding on contradicting results. In 2010, a paper called "Lottery Gambling: A Review" concluded young people play different forms of lottery and the best predictor of their behavior is their parents' loterry participation. Besides, it redute the fact winning a big lottery ruin the winners' lives by describing a better life quality. It also described that the poor are still the leading patron of the lottery and even the people who were made to feel poor buy lotteries. In the other hand, in 2019, an other paper named "Lottery Wins and Satfisfaction: Overturning Brickman in Modern Longitudinal Data on Germany" disprove a correlation between happiness and the act of winning a big lottery even if statisfication levels are indeed achieved.

Concerning statistics and related strategies, a bunch of articles are interesting. In 2010, an article called "A Statistical Analysis of Popular Lottery "Winning" Strategies" has developed statiscal hypothesis around three common strategies: a random strategy in which people use quick picks, a low frequency strategy in which people pick the numbers that occur less frequently and a high frequency strategy in which people picl the numbers that occur often historically. This paper concluded that commonly used strategies are no better than random guessing. Although the low frequency strategy may seem to be better than the others as more time passes, in reality the slight increase in number of matches does not come close to resulting in big lottery winnings. It must be remembered that statistical significance is not the same as practical importance. That is, one would have to play lottery forever, or for a very long period of time, in order to have some minor gains over other strategies which yield very low return anyway. In 2008, a paper named "The Statistics of the National Lottery" studied the randomness hypothesis of iterative draws from UK data and describe the fact that certain combinations are much more popular than average. Therefore the skill to identify unpopular combinations can increase the mean return.