How Gambling Works – The Casino Theory


The mathematics involved in gambling are an intriguing collection of probability and its applications that are encountered in games of chance and form a significant part of the game theory concept. From the point of view of mathematics, a game of chance involves experimental generation of various kinds of distinct events with their probability being calculated on the basis of properties of probability around a finite event space. This is the basis of the entire casino theory.


Understanding the Probability Model


A probability model is based on an experiment with a mathematical structure being attached to that experiment – for example, the space or field of events. This event is the main unit based on which the entire casino theory of probability works. Gambling has a number of different categories of events with each of them having a textual predefinition attached to it. Based on the choice of game in a casino, three different event types may be found.

  • Events that are related to a person’s play or to the play of their opponents

  • Events relating to an individual’s play or that of a number of players

  • Occurrence of immediate events or long-shot events



Every category may be divided further into a number of subcategories and this depends on the game being played. It is possible to have a literal definition of the events but care must be taken while framing a problem based on probability. These events are no more than subsets with the space of events being a Boolean algebra when looked at from a mathematical point of view. The events can be from a choice of independent and non-independent events, exclusive and non-exclusive events, or elementary and compound events.


Setting Expectations and Building Strategies


Games that are based on chance are more than just mere applications of probability calculus while gaming situations are not limited to isolated events that have a numerical probability calculated based on well-known mathematical methods. These are games that progress upon the influence of human actions. The human elements have a significant role to play in the casino theory. The interests of the players are not limited to the mathematical probabilities of the numerous gaming events but also involve their expectations from the games in the event of considerable amount of interaction. For obtaining favorable results out of these interactions, gamblers take into consideration all possible available information for building their gaming strategies.


The predicted gain or loss of the future is known as expected value or expectation and is the summation of probabilities of every possible outcome of the experiment multiplied by its value or payoff amount. Thus it is a representation of the average amount every individual expects to win for a bet provided bets of identical odds are repeated over a number of times. In casino theory, a game that gives an expected value of zero to a player is referred to as a fair game, meaning that it involves neither a gain nor loss for the individual involved.


Edge or House Advantage


With casino games, players are usually afforded a predictable, long-term casino advantage which is also referred to as a “house.” It also offers the player the possibility of getting a short-term payout of a large sum. There is an element of skill associated with some casino games where the players are required to make decisions. These games are referred to as “random with a tactical element.”


Though skillful play allows the house advantage to be minimized as far as possible, it is not a common sight to find a player who possesses sufficient skills that can completely eliminate the inherent long-term disadvantage associated with a casino game. Developing a skill set to this extent would require many years of training, an extraordinary grasp over numeracy, a sharp memory to match, and acute visual observation.


House edge is defined as the profit made by the casino expressed as a percentage of the original bet made by the player. For such games as Spanish 21 or Blackjack the final bet could turn out to be several times more than the original bet in case the player chooses to split or go for a double.


If we take an example of American roulette, it involves two zeroes alongside 36 non-zero numbers – 18 blacks and 18 reds. When a player bets $1 on a red, he has an 18/38 chance of winning the $1 and a 20/38 chance of losing the same. So for the player concerned, his expected value will work out to EV= (18/38 x 1) + (20/38 x 1) = -5.26%. So the house edge is measured at 5.26%. Following ten rounds of play with $1 played at every round, the average house profit comes to 10 x $1 x 5.26% = $0.53. While it is not possible for a casino to earn the exact sum of 53 cents, this is the average profit made by the casino from every player assuming that it had a million players with each of them betting 10 rounds at the rate of $1 on every round.


House edges of the various casino games tend to vary considerably with the choice of games. It can be as high as 25% on Keno and 15% on slot machines while some of the Australian pontoon games do not cross more than 0.3% to 0.4% with their house edges.


While calculating the house edge for roulette may seem like a trivial exercise, the same cannot be said while establishing a casino theory for the other games that often require computer simulation or combinatorial analysis to figure out the solution.


Finding the Right Casino Strategies to Be a Winner on All Fronts


Casino strategies are the crucial aspects that can help beat all the odds at any given casino – whether a land-based one or an online setup. Being able to successfully master every move in a casino game is what will allow a player to counter the strategies put in place by the casino for with the aim of protecting their own advantages. Casino strategies typically refer to the correct decisions that should be taken over the course of a game to ensure favorable results for the player. A person should be well informed of the odds of the game before getting started while also having the necessary skills in terms of money management.


Thus, these casino strategies play a crucial role in determining the fortunes of the individual playing the game. Irrespective of whether they play roulette, craps, blackjack, or slots, by choosing the right strategy the person can emerge victorious in their gambling endeavors. For instance, while playing roulette it is very important for the players to manage their funds and place their bets appropriately so that the house edge gets considerably reduced. The right knowledge of placing bets is imperative for those involving in a game of craps at a casino. Applying the right casino strategies to a game of blackjack can be crucial for guaranteeing success in the long run.


Not Following the Right Casino Strategies Is Not an Option


For those who choose to shy away from following the correct casino strategies, they put themselves at a considerable risk of incurring significant losses. In such scenarios, the casinos end up making a fortune thanks to the lack of knowledge and information on the part of the player as far as placing their bets is concerned. The correct casino strategies are a path to success and this holds true for both online casinos as well as land-based casinos. It is a common belief among most gambling enthusiasts that the chances of winning are the same for every casino game but that, unfortunately, is far from the truth. There is an individual house-edge percentage on every game which causes the probability of a win to vary for every bet placed. In order to win, it is important that a player plays the right kind of games and makes use of the right kind of moves.


Where and When Casino Strategies Are Applicable


Every kind of casino game requires that casino strategies be needed for them – this holds true for skill-based games such as blackjack and poker as much as for luck-based games likes roulette and slots. For the latter, players typically do not get to exercise complete control over their fortunes though they can find ways by virtue of which they can improve their chances of registering a win. For those keen on registering consistent wins, their focus should typically be on the former category of games that involve more of skill and less of chance. The odds tend to be better for those who have the necessary skill and experience, and are also capable of implementing the appropriate casino strategies. For some variations of the game of blackjack, players tend to hold an edge over the dealer from the casino.


Strategies involved in winning a game of blackjack are easy to come across online. These guides can be helpful for individuals who wish to master the necessary gambling skills so that they do not end up sending all their hard-earned money down the drain. Poker involves playing other individuals and not the house. Here, having better casino strategies than one’s rivals can improve an individual’s chances of securing a win. Strategies for winning a game of poker can also be found on online guides.


Money Management in Casino Strategies


An extremely crucial aspect of gambling online is being extremely careful about money management. For those who are not familiar with this term, this is the ability that helps players monitor exactly how much money they are shelling out for their gambling activities. Being reckless with this expense is one of the biggest problems in the world of online gambling and also highlights the fact that most players are not well aware of the very basic principle involved in gambling.


Money management may also be defined as the ability of an individual to play as per the limits of their bankroll which ensures a highly efficient use of the person’s monetary resources. Money management may or may not come naturally to an individual so some amount of self-training may be necessary.

It is important to determine the gambling bankroll for the season before placing the first bet on any casino game. People often get caught up and spend more than what they had planned for but this is something that should be avoided at all costs. Discipline is the mantra to follow in this regard. It also helps when a person is wise and realistic about choosing their bets. A good strategy is one where the $100 bankroll is spent in $1 or $5 bets to give more number of hands rather than on $25 bets that can make for a short, bitter experience. A sense of proportionality often holds the key to developing good casino strategies as much as alertness and sharpness of mind. Long hours of gambling tend to make people fatigued and prone to mistakes so it is always wise to quit when still ahead in the game.


Every individual who goes out to play in a casino harbors a dream of getting their hands on the ultimate jackpot. While a few common tricks and gambling techniques are well known to most people, expert guidance comes in handy for those who are serious about making it big with their wins. The right choice of casino strategies comes in equally handy to help in the realization of this dream.


When At the Casino Beat the Odds with These Tips and Tricks


Beating the odds while at the casino may not seem like the easiest thing to do except for those who are highly talented and possess immense gambling skills. However, a close analysis shows that casino beat the odds is not as difficult as it is made to sound provided a person knows what tricks to use and how to go about their business inside a casino.

Identifying the clumsiest dealers


An ultimate gambling insider, Bill Zender believes that the world does not have any more than 100 professional blackjack card counters. Simply by being at one of them a person can buy himself an advantage of 1.5 percentage points. This energy can be better directed elsewhere, perhaps in keeping an eye out for the sloppy blackjack card-dealer who accidentally gives the players a glimpse of the face-down card. This is known as card-holing and can give the player and edge by 6 to 9 percent over the performance of the house. Moreover, this is something that is recognized by the law so the casino cannot have the player arrested even if they decide to throw him out of the establishment.


Keeping an eye on the prize



Casino-goers may have observed the sexing up techniques implemented by most casinos with resident pole dancers and bikini-clad dealers at the table games. These areas inside a casino are known as the Party Pits and are iconic symbols of Vegas – sin, skin, and a whole lot of booze. However a closer look may reveal the actual picture. While players remain focused on the gyrating hips and twirling legs, casinos take full advantage of the distraction and reduce the payouts at the tables. This results in the house edge going up considerably and is not a beneficial point for the players.


Knowing when to say “enough”


While playing roulette, there is always a 5 percent edge that the house gets to enjoy. Players have a decent chance of securing a winning hand on the first spin and this can continue for the second and third hands as well. However a player who carries on playing roulette forever is likely have his chips taken away by the house at some point of time or the other. The point at which casinos are guaranteed victory in a game of roulette has been calculated and found to be 30,000 hands. No wonder they keep luring clients back with the promise of luxury suites and lobsters. People who are on a winning streak should therefore learn when and how to say “enough” and quit with their wins.


Either going big or going broke


Zender says that an average slot machine tends to be two or three times costlier to the players than other table games at a casino. As a result they should be avoided as far as possible. However for those adamant about cranking the handle, their focus should be only on slots of $5 or more with the maximum bet being played. On penny slots, this tends to hike the odds in favor of the house by a minimum of 15 to 20 percent. So if a player loses, he loses everything at one go but when he wins, he comes away with a fortune in terms of rewards.


Avoiding Keno


The fact that Keno offers a terrible chance of winning should be reason enough for a player to shy away from it. Some casinos tend to have a house edge as high as 35 percent on the Keno games. History suggests that no gambler has ever managed to match all 20 numbers present on a 20-point ticket. The odds of such an occurrence stand at one in 3.5 quintillions.


The old adage of practice makes perfect


It is not always true when people say that the house always wins, especially for those who are playing video poker. For this game the house is typically offered a 0.46 percent advantage over the player. The pay table is present on the machine while the payoff is on the higher end of the scale. The catch is that cashing out is only possible for those playing at an advanced level. The main profit of casinos from video poker is in the lack of skills of the persons who play this game. It is advisable that people do a small amount of research on the game before starting out to play with it.


Investing in a nice watch


There is a good reason why the casinos house floors don’t ever feature windows or clocks. This is because the casinos wish its patrons to lose track of time and continue playing for as long as it is humanly possible. This is also the reason why watches for the dealer are not allowed at a number of casinos. As soon as a person starts raking in the profits, it would be a good idea to call for a break and then get hold of an elegant new timepiece.


Those who want to drink should buy them on their own


Though the world has become accustomed to hearing the word “free” it should be understood that nothing in this world comes for free – this also includes the free booze that is provided at most of the casinos. Every casino manages something that they refer to as a fund for “player reinvestment.” It makes a prediction on the amount of money a person is likely to lose and then reimburses these people with a portion of that money in the form of comps that are a real other-worldly delight for those who are casual visitors on the casino floor. Worse the odds of winning a casino game, better will be the person’s ability to land a free drink!




Online casinos and games in the modern scenario have become a significant money-spinning business that attracts participants from all across the world. As a word of caution, it is important that people stay safe against cyber crime while accessing online games for casinos so that they don’t fall prey to fraudulent hacks. This is something that falls under the ambit of effective casino beat the odds as they help individuals stay focused on their game rather than worrying about being at a threat to cyber-attacks on the vast Internet network.


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