Gambling mathematics entails applying mathematical laws to analyze and forecast betting results, odds, and gaming strategies. According to mathematical principles, the games of chance create sequences of random events, the probability of which can be assessed and calculated. Therefore, by applying a scientific approach, gamers can identify the likelihood of specific outcomes, evaluate risks, and measure potential rewards.
How exactly can the mathematical methods help you increase your revenue and minimize the role of chance in your gaming strategy? I’ll guide you through the basic elements of gambling mathematics to help address this question.
Table of Contents
Probability in online gambling
Probability theory is the core pillar of gambling math. This mathematical principle helps gamers estimate their chances of winning by gauging the likelihood of a particular event. For instance, the probability of rolling a 6 on a fair six-sided die is 1/6, or approximately 16.67%.
If applied in casino gaming, the probability demonstrates the gambler’s likelihood to win a hand. It ranges from 0 to 100, where 0 means no chance to win. As the number grows, the chances of triumph increase correspondingly.
Whether it’s a slot machine, poker, or roulette, every game is characterized by a combination of possible outcomes, each with its respective probability. A probability space in gambling is the mathematical framework that shapes all the possible results and identifies probabilities of each. Understanding probability in the context of the game’s probability space empowers players to justify their decisions, identify mutual exclusivity in particular events, control risk, and assess the expected value of their bets in online gambling strategies.
The expected value and its calculation
Expected value (EV) qualifies the average outcome of a bet based on the bet amount and the likelihood of the event to occur. This parameter is utilized to understand the long-term average of the results and, consequently, whether a bet promises profits or not. Thus, a positive EV means the bet is favorable in the long run, while a negative EV indicates potential losses over time.
Use the following formula for calculations:
EV = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost)
Let’s assume that you are going to bet on a coin toss, where:
- Heads bring you $10 (with a 50% or 0.5 probability of winning),
- Tails result in losing $10 (with a 50% or 0.5 probability of losing).
Incorporating these numbers in the formula, we’ll get:
EV = (0.5×10) − (0.5×10) = 5−5 = 0
Here, the expected value is $0, meaning that with numerous flips, you would neither gain nor lose money on average. This is an example of a fair bet, where the odds are perfectly balanced, and the anticipated outcome is neutral, like with even money betting.
Now, let’s consider the example of an unfavorable bet:
For instance, you have a lottery ticket that costs $5, and you have a 1% (0.01 probability) chance to win $100.
Let’s calculate the EV:
- Probability of winning: 0.01
- Amount won: $100
- Probability of losing: 0.99
- Amount lost: $5
EV = (0.01×100 − (0.99×5) = 1−4.95 = −3.95
As we can see, the expected value is negative in this case, meaning that on average, you would lose $3.95 for every ticket you buy. Therefore, this is an unfavorable bet since it is anticipated to produce a loss over time.
House edge: Does the casino always win?
The concept of house edge implies the mathematical advantage of the casino or a bookmaker over the player. In fact, it’s the percentage of a wager that a house anticipates to retain in the long term. For instance, in American roulette, the house edge is about 5.26%. Therefore, for every $100 bet, the casino expects to keep $5.26 over time.
The house edge, also referred to as a vigorish, can vary depending on the game. Thus, the games with the lowest edge include poker, baccarat, craps, and blackjack.
Admittedly, the casino/bookmaker has a long-term advantage over the players. How does this happen from a scientific standpoint? The underlying mathematical principle is the law of large numbers. Namely, it states that the more attempts are taken, the closer the resulting average approaches the expected value. Therefore, if the casino has at least a tiny benefit of the game’s odds, the outcomes of all wagers and chances will eventually reflect the odds. Although each trial has its own probabilities, the long-term average tends to bring winning results.
Knowing this fundamental principle, you’ll avoid falling into the trap of representativeness heuristic, a common misconception in casino games. It refers to a cognitive bias where people make forecasts based on their stereotypic impression of what is likely to happen in gambling, rather than relying on the actual probabilities or odds. Such misjudgments often lead to faulty decision-making.
An illustrative example of the representativeness heuristic is the gambler’s fallacy, the belief that after a series of losses, a win must occur to balance the results. For instance, if several consecutive roulette spins result in black, a gambler might have exceeded expectations about the likelihood of red in the next spin. The truth is, however, that each spin is independent, and the probability remains the same.
Mathematical models in sports betting
Apart from online casinos, mathematics also takes its part in sports betting. Bookmakers apply mathematical models to set odds that reflect the probability of a particular result. At the same time, just like with casinos, bookmakers ensure those odds provide a profit margin, or vigorish. Mathematical principles and laws, including the previously explained concepts of probability theory and expected value, are also applicable in sports betting to determine whether a bet delivers value.
For example, bookmakers and gamers often analyze past performance data, like team scores, player statistics, or point differentials, to forecast future results. If the performance metrics of a team or player follow a normal distribution, the most likely outcomes will group close to the average, within a standard deviation. The outcomes that fall beyond these limits are less likely to occur. Thus, if a team consistently hits an average of 24 points per game, this average represents the mean, and a normal distribution can anticipate their probability of getting significantly more or fewer points.
Various sports betting strategies rely on math. Gamblers may choose among the more conservative ones, like the Maria Staking Plan, or aggressive ones, like the Martingale Strategy. The primary thing is to research the options and identify which model suits your style.
Final word: How to use gambling math in your favor?
Whether you are applying mathematical methods in casino games or sports betting, you should recognize the winning opportunities the scientific approach can provide.
Advantage gambling includes the legal methods used to gain an edge over other players or the house. The sets of respective knowledge and skills will benefit gamblers in different games.
For instance, card counting empowers players to overcome the casino house edge by continually counting high and low-valued cards dealt. Card counters typically increase their bets when they have an advantage and minimize them when the dealer has an advantage. Besides, they adjust gaming decisions according to the cards remaining in the deck.
Slot machines and lotteries, like Keno, may have progressive jackpots, which accumulate over time and grant an extremely high return. However, obtaining such significant payouts requires a deep knowledge of statistics and probability and a sufficient bankroll to sustain long-term betting.
Generally, the understanding of probability, expected value, and odds will give you a solid background to succeed in gambling. Prioritize games and bets with a positive expected value, handle your bankroll responsibly, and avoid emotional decisions. Applying mathematical methods consistently will raise your chances of long-term profitability.
