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Introduction

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The first mechanical slot machine was invented in the late 1800's by a Bavarian imiagrant named Charles Fey (1862-1944) in San Francisco. In order to understand the history of the slot machine though we need to jump back a little in time.

Poker Machines

Before Fey’s invention there were other coin-operated games of chance. The most popular one, invented by Sittman and Pitt of New York, was a 'poker machine' that was similar to a slot machine and used 5 reels with 10 poker cards on each reel. These machines were very profitable and were used in hundreds of locations (mainly in cigar stands) in the 90's (the 1890's that is). The machines paid out prizes, like a free cigar or free drinks, which were distributed manually by an attendant.

Charles Fey

When Charles began building machines, he initially built ones that were similar the popular poker machines and called them by various names, like the 'Duke' and the 'Klondike'. After building a few of them, placing them in locations, and doing very well with them, he then opened a factory in San Francisco to work on his machines full-time.

But Fey wanted to build a machine that would pay out automatically. This wasn't possible at the time due to the difficulty of calculating the vast number of winning combinations of a machine with 5 reels and 10 cards on each reel. So, in 1898, Fey designed a poker machine called the 'Card Bell' machine that retained the card symbols of the earlier poker machines but had only 3 spinning reels and only 5 symbols printed on each reel. The automatic prize-payout allowed the machine to be the first to pay out coins.

The 'Liberty Bell'

About a year later, in 1899, he created the 'Liberty Bell' machine, which added horseshoes and bells to the suit symbols on the reels. Lining up three bells would win the top prize (hence the name). Fey's design became the standard design for slot machines going forward and was so popular that all 3-reel slot machines were referred to as 'Bell Machines'.

Fey rented his machines to saloons and bars and split the profits 50/50. The demand for Liberty Bell slot machines was huge and allowed Fey to monopolize the slot machine market. Many gambling supply manufacturers wanted to buy the manufacturing and distribution rights to the Liberty Bell but Charles Fey didn't want to sell them.

But Fey could not keep up with the demand so in 1907 he partnered with Mills Novelty Company to manufacture a cast-iron machine called the 'Mills Liberty Bell'.

Unfortunately for Fey, patent laws of the time did not protect gaming devices because a Federal Judge ruled the slots could only be used for gambling and had no useful purpose. So a few years later, in 1910, the Mills Novelty Company introduced a slight variation to the Mills Liberty Bell called the 'Operator Bell'. The machines from Mills Novelty were the first to use the fruit symbols like lemons and cherries that you see on some slot machines today.

1910-1933

Part of the growth of slot machines was due the wide open nature of San Francisco during the early 1900's. The climate started to change quickly though in 1909 when San Francisco outlawed all gaming machines. Nevada did the same a year later and the state of California created a statewide ban on slot machines in 1911.

These laws did not have much of an effect on slot machine sales because slot machine manufacturers were able to find ways to alter the games to avoid getting them classified as gambling devices.

For example, the 'Liberty Bell Gum Fruit' model dispensed a package of gum, which allowed the machine to be classified as a vending machine. The Caille Brothers slots created machines that had a Swiss music box located in the bottom of the cabinet so the machine was classified as a musical device. Another popular strategy was to have slot machines dispense items like mints or gum in order to have them classified as vending machines.

Slot machines reached their peak sales during the Great Depression and the lawless days of prohibition, which began in 1919. They were popular in the speakeasies as well as the many respectable businesses that needed the profitable machines in order to stay in business during the tough economic times.

1933-1945

After prohibition ended the government decided to target slot machines since they were looked at as tools for organized crime. Raids began to increase as well as laws prohibiting the possession of slot machines or a sale of a slot machine to an illegal state. Despite these efforts, the popularity of slots machines was difficult to stop and slots were still able to operate in some places.

Post WWII

After World War II, governments started to become friendly to the slot machine industry because it now looked at it as a source of tax revenue.

Computer Technology

In 1963, Bally developed the first electromechanical slot machine, called Money Honey, that used electronic micro-processors to decide the outcome of the game.

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The first fully-electronic slot machines were introduced in Las Vegas in 1975. They were built by the Fortune Coin Company and used simulated reels on a monitor. The electronic machines caught on slower than expected because many players did not trust the fairness of the machines. In 1978, the company that would later be known as International Game Technology bought out the Fortune Coin Company.

In 1984, a Norwegian scientist named Inge Telnaes received a patent for a device titled, 'Electronic Gaming Device Utilizing a Random Number Generator for Selecting the Reel Stop Positions.' International Gaming Technology (IGT) bought the patent in 1988 and now all slot manufacturers his technology must license the patent from IGT.

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HPG ADMIN on February 27, 2013

Games available in most casinos are commonly called casino games. In a casino game, the players gamble cash or casino chips on various possible random outcomes or combinations of outcomes. Casino games are also available in online casinos, where permitted by law. Casino games can also be played outside casinos for entertainment purposes like in parties or in school competitions, some on machines that simulate gambling.

Categories[edit]

There are three general categories of casino games: gaming machines, table games, and random number games. Gaming machines, such as slot machines and pachinko, are usually played by one player at a time and do not require the involvement of casino employees to play. Tables games, such as blackjack or craps, involve one or more players who are competing against the house (the casino itself) rather than each other. Table games are usually conducted by casino employees known as croupiers or dealers. Random number games are based upon the selection of random numbers, either from a computerized random number generator or from other gaming equipment. Random number games may be played at a table or through the purchase of paper tickets or cards, such as keno or bingo.

Some casino games combine multiple of the above aspects; for example, roulette is a table game conducted by a dealer, which involves random numbers. Casinos may also offer other type of gaming, such as hosting poker games or tournaments, where players compete against each other.

Common casino games[edit]

Notable games that are commonly found at casinos include:

House advantage[edit]

Casino games typically provide a predictable long-term advantage to the casino, or 'house', while offering the players the possibility of a short-term gain that in some cases can be large. Some casino games have a skill element, where the players' decisions have an impact on the results. Players possessing sufficient skills to eliminate the inherent long-term disadvantage (the house edge or vigorish) in a casino game are referred to as advantage players.

The players' disadvantage is a result of the casino not paying winning wagers according to the game's 'true odds', which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1 in 6 chance of any single number appearing, assuming that the player gets the original amount wagered back. However, the casino may only pay 4 times the amount wagered for a winning wager.

The house edge or vigorish is defined as the casino profit expressed as the percentage of the player's original bet. (In games such as blackjack or Spanish 21, the final bet may be several times the original bet, if the player double and splits.)

In American roulette, there are two 'zeroes' (0, 00) and 36 non-zero numbers (18 red and 18 black). This leads to a higher house edge compared to European roulette. The chances of a player, who bets 1 unit on red, winning is 18/38 and his chances of losing 1 unit is 20/38. The player's expected value is EV = (18/38 × 1) + (20/38 × (−1)) = 18/38 − 20/38 = −2/38 = −5.26%. Therefore, the house edge is 5.26%. After 10 spins, betting 1 unit per spin, the average house profit will be 10 × 1 × 5.26% = 0.53 units. European roulette wheels have only one 'zero' and therefore the house advantage (ignoring the en prison rule) is equal to 1/37 = 2.7%.

The house edge of casino games varies greatly with the game, with some games having an edge as low as 0.3%. Keno can have house edges up to 25%, slot machines having up to 15%.

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The calculation of the roulette house edge was a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.

In games which have a skill element, such as blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting), on the first hand of the shoe (the container that holds the cards). The set of the optimal plays for all possible hands is known as 'basic strategy' and is highly dependent on the specific rules and even the number of decks used. Good blackjack and Spanish 21 games have house edges below 0.5%.

Traditionally, the majority of casinos have refused to reveal the house edge information for their slots games and due to the unknown number of symbols and weightings of the reels, in most cases it is much more difficult to calculate the house edge than that in other casino games. However, due to some online properties revealing this information and some independent research conducted by Michael Shackleford in the offline sector, this pattern is slowly changing.^[1]

In games where players are not competing against the house, such as poker, the casino usually earns money via a commission, known as a 'rake'.

Standard deviation[edit]

The luck factor in a casino game is quantified using standard deviations (SD).^[2] The standard deviation of a simple game like roulette can be calculated using the binomial distribution. In the binomial distribution, SD = √npq, where n = number of rounds played, p = probability of winning, and q = probability of losing. The binomial distribution assumes a result of 1 unit for a win, and 0 units for a loss, rather than −1 units for a loss, which doubles the range of possible outcomes. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold.^[3]

SD (roulette, even-money bet) = 2b√npq, where b = flat bet per round, n = number of rounds, p = 18/38, and q = 20/38.

For example, after 10 rounds at 1 unit per round, the standard deviation will be 2 × 1 × √10 × 18/38 × 20/38 = 3.16 units. After 10 rounds, the expected loss will be 10 × 1 × 5.26% = 0.53. As you can see, standard deviation is many times the magnitude of the expected loss.^[4]

The standard deviation for pai gow poker is the lowest out of all common casino games. Many casino games, particularly slot machines, have extremely high standard deviations. The bigger size of the potential payouts, the more the standard deviation may increase.

As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played. As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is impossible for a gambler to win in the long term. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win.

It is important for a casino to know both the house edge and variance for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the variance tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts. Casinos do not have in-house expertise in this field, so outsource their requirements to experts in the gaming analysis field.

See also[edit]

References[edit]

1. ^'Michael Shackleford is the wizard of odds'. Observer. Retrieved 13 October 2015.
2. ^Hagan, general editor, Julian Harris, Harris (2012). Gaming law : jurisdictional comparisons (1st ed.). London: European Lawyer Reference Series/Thomson Reuters. ISBN978-0414024861.
3. ^Gao, J.Z.; Fong, D.; Liu, X. (April 2011). 'Mathematical analyses of casino rebate systems for VIP gambling'. International Gambling Studies. 11 (1): 93–106. doi:10.1080/14459795.2011.552575. S2CID144540412.
4. ^Andrew, Siegel (2011). Practical Business Statistics. Academic Press. ISBN978-0123877178. Retrieved 13 October 2015.