In Stud Hi/Lo, players compete to make their highest or lowest five-card combination from a deal of seven. Four cards are dealt face-up, three face-down. The players with the highest and lowest hands split the pot. If no player has a qualifying low hand (8 qualifier), the player with the highest hand wins the entire pot. Compared with other blackjack counts, Hi Lo card counting does lack precision. Hi-Opt 1 and 2: These systems were developed by Lance Humble, though they can be traced back to the 1960s. There are many more“neutral”cards compared to the Hi-Lo Count. Hi-Opt 1 uses aces, twos, sevens, eights and nines as zero for the count.

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%.

The calculation of the roulette house edge is 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.

Poker Games

Texas Hold'em

One of the most popular poker games in the world. Players must make the best five-card hand possible from a combination of five community cards and two hole cards. The player with the highest hand wins the pot.
GEGA-001313 (Limit) & GEGA-002254 (No Limit)

Omaha

A variation on Texas Hold'em in which players compete to make the best five-card hand from a combination of four hole cards and five community cards. Players must use exactly two of the cards in their hand and three of the community cards
GEGA-001307

Omaha Hi/Lo

In Omaha Hi/Lo, players make their highest and lowest hands from a combination of four hole cards and five community cards, using exactly two cards from their hand and three cards from the board. Once the showdown is complete, players show their cards; the players with the highest and lowest hands split the pot. If no player has a qualifying low hand (8 qualifier), the player with the highest hand wins the entire pot.
GEGA-001308

Big O

Big O is a variation on Omaha Hi/Lo in which players are dealt five hole cards instead of four. Players must make their best hand from exactly two of their hole cards and three board cards. Once the showdown is complete, players show their cards; the players with the highest and lowest hands split the pot. If no player has a qualifying low hand (8 qualifier), the player with the highest hand wins the entire pot.
GEGA-002898 & GEGA-002899

Stud

The game that made poker famous. In Stud, there are no community cards; players must make the best five-card combination from the cards in their own hands. Players are dealt four cards face-up, and three cards face-down. The best five-card combination wins the pot.
GEGA-001316

Stud Hi/Lo

In Stud Hi/Lo, players compete to make their highest or lowest five-card combination from a deal of seven. Four cards are dealt face-up, three face-down. The players with the highest and lowest hands split the pot. If no player has a qualifying low hand (8 qualifier), the player with the highest hand wins the entire pot.
GEGA-001324

Lowball

Lowball is a variation on 5-Card Stud where the player with the lowest ranked hand wins. The most common form of Lowball is known as 'ace-to-five' or 'California lowball.' In ace-to-five, aces are low, with the best possible hand being a straight of 5-4-3-2-A.
GEGA-001322

Mixed Games

Step up to the next level of poker and try your hand at Mixed Games. The games usually change/rotate every 8 hands or a half hour depending on the players’ requests.

Razz

Similar to Lowball, Razz is a variation on 7-Card Stud, in which the lowest hand wins. The player with the best ace-to-five low hand wins the pot.
GEGA-001891

Badugi

Badugi is a combination of Lowball and Draw Poker in which players compete to have the lowest four-card hand of different suits with no pairs. The top hand is 4-3-2-A, with each card in a different suit. (This is called a 'Badugi.') The player with the best four-card hand wins.
GEGA-000212

2-7 Triple Draw

2-7 Triple Draw is a variation on Draw Poker in which players compete to have the lowest five-card combination. Unlike in ace-to-five Lowball, aces are high with straights and flushes counting against your hand. The best hand therefore being 7-5-4-3-2. The player with the lowest five-card hand takes the pot
GEGA-000211

Chinese Poker

In Chinese Poker, a maximum of four players compete to make their three best hands from thirteen cards. Each player is dealt thirteen cards which they must separate into one hand of three cards ('the front') and two hands of five cards each ('the middle' and 'the back'). The bank hand must be the highest hand with the front hand as the lowest. The pot is divided according to who takes each hand, with a possibility of multiple winners within a single game.
GEGA-001304

Cal Games

EZ Baccarat

In EZ Baccarat, as in standard Baccarat, the goal is to get as close to nine as a banker or player with two or three cards. Aces count as 1 and 2-9 cards hold their face value. 10-K each count as zero. If cards add up to more than ten, the 'tens' digit is ignored – a 4 and a 9 would count as 3 not 13, for instance. The hand totaling closest to nine wins the pot.
GEGA-002539

21st Century Blackjack

In 21st Century Blackjack Aces on the initial two card has a value of 11.5. The object is to get as close to 21.5 without going over. Should the dealer receive a 7, 8, 9 of spades all busted hands are considered a push. Additional bonus bets such as Buster Bet and Perfect Pair are added for bigger payouts.
GEGA-003514

21st Century Blackjack Switch

In 21st Century Blackjack Switch, players compete with the Player / Dealer to get as close to 21 as possible without going over. In this variation, players are dealt two hands, while the Player / Dealer is only dealt a single hand. Players may switch cards between their hands to build the best hand possible.
GEGA-003444

Pai Gow Poker

Pai Gow Poker is played with a standard poker deck plus one Joker, which is a wildcard. Players build their best two-card and five-card hands from a seven card deal. The object is to have both sets rank higher than the corresponding sets of the Player / Dealer for that hand.
GEGA-001309

Hi-lo Card Counting Strategy

Fortune Pai Gow Poker

Fortune Pai Gow Poker is a variation on Pai Gow Poker with a bonus bet, known as the 'fortune bet.' Players can wager extra that their hand contains a winning combination. The better the hand, the higher the payout on the fortune bet.
GEGA-002157

Pai Gow Tiles

The rules of Pai Gow Tiles are similar to the rules of Pai Gow Poker. Instead of cards, players are dealt four dominos that they must separate into front and back combinations. Players win if both of their combinations beat the combinations of the Player / Dealer.
GEGA-002968

Ultimate Texas Hold'em

In Ultimate Texas Hold'em, players compete to form a higher five-card poker hand than the Player / Dealer from two hole cards and five community cards. Gameplay is similar to standard Texas Hold'em, with a number of additional side bet options
GEGA-002362

3 Card Poker

In 3 Card Poker, players must make the best 3-card hand possible. Players receive their cards face-down, while the Player / Dealer receives two face-down and one face-up. Player / Dealer requires a Q high or better to qualify. Five unique bets are possible on each hand, including a 6 Card Bonus, in which players wager whether a combination of their cards and the Player / Dealer's cards will contain a winning five-card hand
GEGA-003645

Mississippi Stud

Mississippi Stud is a progressive poker game in which two hole cards and three community cards are all dealt face-down. As each community card is turned over, another round of betting commences. Player with a pair of 6’s – 10’s push and J’s or better wins.
GEGA-003665

Crazy 4 Poker

In Crazy 4 Poker, players compete against the Player / Dealer to build the best four-card hand from a five-card deal. After all players have set their hands, the Player / Dealer's cards are revealed. Players with better hands than the Player / Dealer win. Player / Dealer requires a K high or better to qualify.
GEGA-003964

Let It Ride

In Let It Ride, players make their hands from a combination of three hole cards and two community cards. Any hand containing a pair of 10s or better wins.
GEGA-002362

Casino War

Hi Lo Card Counting Method

It doesn't get much easier to learn than Casino War, a variation on the classic game War. Players set their wagers, then compare their card with that of the Player / Dealer. All players with higher cards win. In case of a tie, players who choose to play must match their original wager.
GEGA-003391

Pan 9

Pan 9 is a variation on Baccarat in which 7s-10s are removed from the deck. Players start with 3 cards and may have the option to stay or receive an additional card. As in Baccarat, the object is to get as close to nine as possible.
GEGA-003806

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