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Pai Gow

Pai gow is a Chinese gambling game that is played with a Chinese dominoes tile set. Pai gow is played in unsanctioned casinos in most Chinese communities.[citation needed] It is played openly in major casinos in Macau, China, Las Vegas, Nevada, Atlantic City, New Jersey, in many California cardrooms, and in some Australian and New Zealand casinos. It dates back to at least the Song Dynasty, and is a game steeped in tradition.

The name “pai gow” is sometimes used to refer to a card game called pai gow poker (or “double-hand poker”), which is loosely based on pai gow.

Rules

Starting the Game

Tiles are randomized on the table, and are stacked into eight stacks of four tiles each in an assembly known as the woodpile. Various ritualistic “shuffles” are made, rearranging the tiles in the woodpile in standard ways that result in a new woodpile. Bets are then made.

Next, each player (including the dealer) is given four tiles with which to make two hands of two tiles each. The hand with the lower value is called the front hand, and the hand with the higher value is called the rear hand. If a player’s front hand beats the dealer’s front hand, and the player’s rear hand beats the dealer’s rear hand, then that player wins the bet. If a player’s front and rear hands both lose to the dealer’s respective hands, the player loses the bet. If one hand wins and the other loses, the player is said to push, and gets back only the money he or she bet. Generally seven players will play, and each player’s hands are compared only against the dealer’s hands.

Evaluations of three basic hands.

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Craps

Craps is a casino dice game. Craps is a simplification of the Old English game hazard. Its origins are complex and may date to the Crusades, later being influenced by French gamblers. What was to become the modern American version of the game was brought to New Orleans by Bernard Xavier Philippe de Marigny de Mandeville, scion of wealthy Louisiana landowners and a gambler and politician. The game, first known as crapaud (a French word meaning “toad”) reportedly owes its modern popularity from its being spread through the African-American community.

In craps, players wager money against the casino on the outcome of one roll, or of a series of rolls of two dice. Craps can also be played in less formal settings and is said to be popular among soldiers. In such situations side bets are more frequent, with one or several participants covering or “fading” bets against the dice.

The rules of play

Craps is a game played by 1 or more players. Players take turns rolling two dice. The player rolling the dice is called the “shooter.” The game is played in rounds, with the first roll of a new round called the “come-out roll.”

On the come-out roll, if the total of the two dice is 7, 11, 2, 3 or 12, the round ends immediately and the shooter must roll another come-out roll. A result of 2, 3 or 12 is called ‘craps’ while a result of 7 or 11 is called a ‘win’ or a ‘natural.’ When any other number (4, 5, 6, 8, 9, or 10) is rolled on the come-out roll, this number becomes what is called the point. If a point is established, then the shooter will re-roll the dice continuously until either a 7 is rolled or the point is rolled again. If the shooter rolls the point again, the round ends and the game starts over with the same shooter rolling another come-out roll. If the shooter rolls a 7 instead of the point, this is called a ’seven-out,’ the round ends, and the dice pass to the next player to the left, who becomes the new shooter.

Players can make any of a large number of bets. Most of these are betting on the way the round will end (point comes or a seven out). Other betting can include betting on a specific total being rolled, or a specific total being rolled before a 7. In a casino players will make bets with chips on a specially made craps table.

A casino craps table is run by four casino employees: a boxman who guards the chips, supervises the dealers and handles coloring out players; two base dealers who stand to either side of the boxman and collect and pay bets; and a stickman who stands directly across the table from the boxman and announces the results of each roll and then collects the dice with an elongated wooden stick. He is also in charge of managing the bets made on the center of the table (hardways, yo, horn, etc).

A new shooter, who must bet the table minimum on either the “pass” line or the “don’t pass” line to play, is presented five dice by the stickman and picks two.

The dealers will usually insist that the shooter roll with one hand and that the dice bounce off the wall surrounding the table. These requirements are meant to prevent cheating attempts by players switching the dice or making a “controlled shot.” If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request using the same die if it passes the boxman’s inspection. This requirement is used in an effort to reduce cheating the game by players substituting loaded dice for the regulation dice.

Types of wagers
Player bets

Fire Bet: Before the shooter begins, some casinos will allow a bet known as a fire bet to be placed. A fire bet is a bet for between 1-5 dollars (the Rio in Las Vegas allows up to $10) in the hopes that the next shooter will have a hot streak of setting and getting many points of different values. As different individual points are made by the shooter, they will be marked on the craps layout with a fire symbol. The first three points will not pay out on the fire bet, but the fourth, fifth and sixth will pay out at increasing odds. The fourth point pays at 25-1 (a maximum of $125 for a $5 bet), the fifth point pays at 250-1 (a maximum of $1,250 for a $5 bet) and the 6th point pays at 1,000-1 (a maximum of $5,000 for a $5 bet). Note that the points must all be different numbers for them to count towards the fire bet. A shooter who successfully hits a point of 10 twice will only garner credit for the first one on the fire bet.

The fire bet is only avaliable for play in some casinos. Example: Mohegan Sun

Line bets

The shooter is required to make either a Pass Line bet or a Don’t Pass bet if he wants to shoot. Line bets are based around points.

Pass line: The fundamental bet in craps is the pass line bet, also called the win line in some countries. A pass line bet is won if the come-out roll is a 7 or 11. If the come-out roll is 2, 3 or 12, the bet loses. If instead the come-out roll establishes a point, and that point is rolled again, the bet wins. If a point is established and a 7 is rolled before the point is re-rolled, the bet loses.

Don’t pass: The opposite of the pass line bet is the don’t pass bet. The don’t pass bet is opposite in that it loses if the come-out roll is 7 or 11 and wins if the come-out roll is 2 or 3. A 12 will draw (this depends on the casino); either way a player cannot lose if 12 is rolled. A draw (the word “BAR,” printed on the Craps layout, means “Standoff”) on 12 is done to ensure the casino maintains a house edge regardless of whether players are betting pass or don’t pass. If a point is established and that point is rolled again, the don’t pass bet loses. If a 7 is rolled instead of the point being re-rolled, the don’t pass bet wins. Betting on don’t pass is often called “playing the dark side,” and it is considered to be in poor taste, or even taboo, because it goes directly against conventional play.

Pass odds: If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll (i.e., if a point is set), most casinos allow pass line bettors to take odds by placing from one to five times (and at some casinos, up to 100 times) the pass line bet behind the pass line. This additional bet wins if the point is rolled again before a 7 is rolled (the point is made) and pays at the true odds of 2-to-1 if 4 or 10 is the point, 3-to-2 if 5 or 9 is the point, and 6-to-5 if 6 or 8 is the point.

Don’t pass odds: If a player is playing don’t pass instead of pass, they may also take odds by placing chips behind the don’t pass line. If a 7 comes instead of the point coming, the odds pay at true odds of 1-to-2 if 4 or 10 is the point, 2-to-3 if 5 or 9 is the point, 5-to-6 if 6 or 8 is the point. For most players the perceived disadvantage of putting up the long side of the bet makes the don’t pass odds less desirable, however putting up the long side reduces variance.

Come bet: The rules for the come wagers are the same as for the pass line except that they can only be made after the come-out roll. If the roll the come bet is made on is a 7 or 11 it wins, if it is a 2, 3 or 12 it loses, just like a pass bet. If instead the roll is 4, 5, 6, 8, 9, 10 then the come bet will be moved by the base dealer onto a box representing that number. If the number is rolled again before a seven, the bet wins. If the seven comes before the number (the come-bet), the bet loses. Odds can also be placed on a come-bet just like a normal pass point; in this case the dealer (not the player) places the odds bet on top of the bet in the box, because of limited space, slightly offset to signify that it is an odds bet and not part of the original come bet.

Because of the come bet, if the shooter makes their point, a player can find themselves in the situation where they have a come bet (possibly with odds on it) and the next roll is a come-out roll. In this situation odds bets on the come wagers are presumed to be not working for the come-out roll. That means that if the shooter rolls a 7 on the come-out roll, any players with active come bets waiting for a come-point lose their initial wager but will have their odds money returned to them, if the come-point is rolled the odds do not win but the come bet does and the odds are returned. The player can tell the dealer that they want their odds working, such that if the shooter rolls a number that matches the come point, the odds bet will win along with the come bet, and if a seven is rolled both lose.

Don’t come: There is also a don’t come box which is the opposite of a come bet in that the player is betting that craps will come on the next roll instead of 7 or 11, or that if a come point is made, that value won’t be rolled again before a 7. It pays just as don’t pass and also has odds in the same way.

Single roll bets

Single Roll bets have a result in a single shooter roll. They include:

Yo: Wins if the shooter rolls 11.

3 (ace-deuce): Wins if the shooter rolls a 3.

2 (craps aces): Wins if shooter rolls a 2.

12 (craps): Wins if shooter rolls a 12.

2 or 12 (hi-lo): Wins if shooter rolls a 2 or 12. The stickman places this bet on the line dividing the 2 and 12 bets.

Craps: Wins if the shooter rolls 2, 3 or 12.

C & E: A combined bet, a player is betting half their bet on craps and the other half on yo (11). One of the two bets will always lose, the other may win.

Any seven: Wins if the shooter rolls a 7. This bet is also nicknamed Big Red, since the 7 on its betting space on the layout is usually large and red.

Field: This bet is a wager that one of the numbers 2, 3, 4, 9, 10, 11, or 12 will appear on the next roll of the dice. This bet typically pays more 2:1 or 3:1 if 2 or 12 is rolled, and 1:1 if 3, 4, 9, 10 or 11 is rolled. Unlike the other proposition bets which are handled by the dealers or stickman, the field bet is placed directly by the player.

The Horn: This is a bet that involves betting on 1 unit each for 2, 3, 11 and 12 at the same time for the next roll. The bet is actually four separate bets, and pays off depending on which number is actually rolled, minus three units for the other three losing bets. Many players, in order to eliminate the confusion of tossing four chips to the center of the table or having change made while bets are being placed, will make a five-unit Horn High bet, which is a four-way bet with the extra unit going to one specific number. For example, if you toss a $5 chip into the center and say “horn high yo,” you are placing four $1 bets on each of the horn numbers and the extra dollar will go on the yo (11).

Whirl or World: bet is a five-unit bet that is a combination of a horn and any-seven bet, with the idea that if a seven is rolled the bet is a push, because the money won on the seven is lost on the horn portions of the bet.

Multi roll bets

These are bets that may not be settled on the first roll and may need any number of subsequent rolls before an outcome is determined.

Hard way: You may bet that the shooter will throw a specific hard way (either 4, 6, 8 or 10), before he throws a seven or the corresponding easy way. A hard way is when both dice show identical values, also known as “doubles,” so 2 2 is hard way 4.

Easy way: Opposite of hard way is a bet that the shooter will throw a specific easy way (either 4, 6, 8 or 10), before he throws a seven. An easy way is a value that does not have two dice identical, so 3 1 is easy way 4.

Big 6 and Big 8: These wagers are considered by craps players as sucker bets because they pay even money while a player can bet on the same proposition (that the number will be rolled before a 7) by making place/buy bets on the 6 or the 8, which pay more money. Veteran craps players avoid these bets, and some casinos do not even offer them. The bets are located in the corners behind the pass line, and bets are placed directly by players.

Place and buy: Players can buy or place certain individual numbers (4, 5, 6, 8, 9, 10) by placing their wager in the come area and telling the dealer, “place the 6″ or “buy the 8″. Both place and buy bets are bets that the number bet on will be rolled before a 7 is rolled. Place bets are paid at odds worse than the true odds, while buy bets are paid at true odds, but a 5% commission is charged. Traditionally, the buy bet commission is paid no matter what, but in recent years a number of casinos have changed their policy to charge the commission only when the buy bet wins. Most casinos usually charge only $1 for a $25 green-chip bet (4% commission), or $2 for $50 (two green chips), reducing the house advantage a bit more. Where commission is charged only on wins, the commission is sometimes deducted from the winning payoff–a winning $25 buy bet on the 10 would pay $49, for instance.

Lay: A lay bet is the opposite of a buy/place bet, where a player bets on a 7 to roll before the number that is laid. The lay bets pay true odds, but a 5% commission is charged. In some casinos the commission is only charged if the bet wins. Like the buy bet the commission is adjusted to suit the betting unit such that fraction of a dollar payouts are not needed.

Most multi-roll bets are similar to the Come bet above in that the round may be won by the shooter making point before the outcome of the bet is decided. As with the Come bet, these bets are considered “not working” until the next point is established, unless the player calls the bet as “working.” Casino rules vary on this; some of these bets may not be callable, while others may be considered “working” during the come-out.

Bet odds

Note: Individual casinos may pay some of these bets at different odds than those listed below. The payoff odds listed are the most common throughout North American casinos.

Note: Actual odds do not vary.

Bet Actual Odds Odds Paid House Edge
Pass / Come 251:244 1:1 1.41%
Don’t Pass / Don’t Come (Bar 12) 244:251 1:1 1.36%
Pass Odds / Come Odds Same as paid 2:1 on 4 or 10
3:2 on 5 or 9
6:5 on 6 or 8 0%
Don’t Pass Odds / Don’t Come Odds Same as paid 1:2 against 4 or 10
2:3 against 5 or 9
5:6 against 6 or 8 0%
Yo (11) 17:1 15:1 11.11%
3 17:1 15:1 11.11%
2 35:1 30:1 13.89%
12 35:1 30:1 13.89%
Hi-Lo 17:1 15:1 11.11%
Craps 8:1 7:1 11.11%
C & E 5:1 3:1 on craps
7:1 on 11 11.11%
Any 7 5:1 4:1 16.67%
Field 5:4 1:1 on 3,4,9,10 or 11
2:1 on 2 and 12 5.56%
Field 5:4 1:1 on 3,4,9,10 or 11
2:1 on 2, 3:1 on 12 2.78%
The Horn 5:1 27:4 on 2 or 12
3:1 on 3 or 11 12.5%
Whirl/World 2:1 26:5 on 2 or 12
11:5 on 3 or 11
0:1 (push) on 7 13.33%
Hard way 4 / Hard way 10 8:1 7:1 11.11%
Hard way 6 / Hard way 8 10:1 9:1 9.09%
Big 6 6:5 1:1 9.09%
Big 8 6:5 1:1 9.09%
Place 4 / Place 10 2:1 9:5 6.67%
Place 5 / Place 9 3:2 7:5 4%
Place 6 / Place 8 6:5 7:6 1.52%
Buy 4 / Buy 10 2:1 2:1 + 5% commission 5%
Buy 5 / Buy 9 3:2 3:2 + 5% commission 5%
Buy 6 / Buy 8 6:5 6:5 + 5% commission 5%
Lay 4 / Lay 10 1:2 1:2 + 5% commission 5%
Lay 5 / Lay 9 2:3 2:3 + 5% commission 5%
Lay 6 / Lay 8 5:6 5:6 + 5% commission 5%

The expected value of all bets is negative, such that the average player will always lose money. This is because the house always sets the paid odds to below the actual odds. All bets have a negative expectation except for the “odds” bet that the player is allowed to make after a point is established on a pass/come don’t pass/don’t come bet (the odds portion of the bet has a long-term expected value of 0). However, the “free odds” bet cannot be made independently, so the expected value of the entire bet, including odds, is still negative. Since there is no correlation between die rolls, there is no possible long-term winning strategy in craps.

Maximizing the size of your odds bet in relation to your line bet will reduce, but never eliminate the house edge, and will increase variance. Many casinos have a limit on how large the odds bet can be in relation to the flat bet, with single, double, and five times odds common. Some casinos offer 3-4-5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively. During promotional periods, a casino may even offer 100x odds bets, which reduces the house edge to almost nothing, but dramatically increases variance, as the player will be betting in large betting units.

Since several of the multiple roll bets pay off in ratios of fractions on the dollar, it is important that the player bets in multiples that will allow a correct payoff in complete dollars. Normally, payoffs will be rounded down to the nearest dollar, resulting in a higher house advantage. These bets include all place bets, taking odds, and buying on numbers 6, 8, 5, and 9, as well as laying all numbers.

Optimal betting

Since all bets have a house advantage, and a negative expected value, the optimal strategy is to be the house. Failing that, one can reduce one’s average hourly losses by only placing bets with the smallest house advantage.

The pass/don’t line, come/don’t line, place 6, place 8, buy 4 and buy 10 (only under the casino rules where commission is charged only on wins) are the bets with the lowest house edge, and all other bets will on average lose money between three and twelve times faster because of the difference in house edges.

An important alternative metric is house advantage per roll (rather than per bet), which may be expressed in loss per hour see reference. The typical pace of rolls varies depending on the number of players, but 102 rolls per hour is a cited rate for a nearly full table see reference. This number then permits calculation of rate of loss per hour, and per the 4 day/5 hour per day gambling trip:

$10 Pass line bets .42% per roll, $4.28 per hour, $86 per trip

$10 Place 6,8 bets 1.46% per roll, $14.89 per hour, $298 per trip

$10 Place 5,9 bets 1.32% per roll, $13.46 per hour, $269 per trip

$10 Place 4,10 bets 1.19% per roll, $12.14 per hour, $243 per trip

$1 Single Hardways 2.78% per roll, $2.84 per hour, $56.71 per trip

$1 All hardways 2.78% per roll, $11.34 per hour, $227 per trip

$5 All hardways 2.78% per roll, $56.71 per hour, $1134 per trip

$1 Craps only on come out 3.29% per roll, $3.35 per hour, $67.09 per trip

$1 Eleven only on come out 3.29% per roll, $3.35 per hour, $67.09 per trip

This runs counter to the notion that hardways and C/E on come-out roll are necessarily bad bets, since, although their house percentages are poor, they have lower minimum bets and happen less frequently. Therefore, they do not lose money as quickly as the pass line bet.

Also, by this metric, other betting patterns are shown to be costly, for example placing $10 on all point numbers, which has a much higher loss of $40.49 per hour or $810 per trip.

Etiquette

Besides the rules of the actual game, certain unwritten rules of etiquette exist while playing craps and are expected to be followed. Many consider these guidelines as important as the actual rules themselves. New players should familiarize themselves with them before approaching a craps table.

Rules related to casino security

* Players are not supposed to handle the dice with more than one hand (such as passing them from hand to hand before rolling) nor take the dice past the edge of the table. The only way to change hands when throwing dice, if permitted at all, is to set the dice on the table, let go, then take them with the other hand. This reduces or eliminates the possibility of the shooter switching dice by sleight-of-hand.
* When throwing the dice, the player is expected to hit the farthest wall at the opposite end of the table. Some casinos refer to throws that do not hit the opposite wall as “Mellenberg Rolls.”[citation needed] Some casinos will allow rolls that do not hit the opposite wall, while in others it is a “no roll” due to the more controllable nature of such a roll. The dice may not be slid across the table and must be tossed. Typically, players are asked not to throw the dice higher than the eye level of the dealers.
* The dice cannot land in the boxman’s bank or on any of the dealers’ working stacks of money. Dice that land in the chip tray also constitutes a “no roll”. If the die or dice leave the table, it is also a “no roll” and the boxperson will examine the dice before letting it come back into the game. However, the player may request the same die or dice.
* When either of the dice land on chips or markers not in the boxman’s bank or the dealers’ working stacks, the number that would be on top if the object the die is leaning on were removed, is the number that is used to make the call.
* If one or both dice hits a player or dealer and rolls back onto the table, the roll counts as long as the person being hit did not interfere with either of the dice, though some casinos will rule “no roll” for this situation.
* In most cases the shooter may “set” the dice to a particular configuration, but if they do, they are often asked to be quick about it so as not to delay the game. Some casinos have “no setting” rules.
* Dealers are not allowed to touch the players or hand chips directly to a player. Players are expected to lay the cash down on the layout, which the dealer will take and then place chips in front of the player.
* Many craps table layouts state “NO CALL BETS”. This means a player is not allowed to call out a bet without having at least the right amount of chips on the table. If the chips exceed the bet, for example a $100 chip is placed and bets called out of “$25 on five and nine”, the dealer will say “it’s a bet” and return $50 change to the player. The dealer doesn’t have to actually place the bet in the proper place on the table to constitute a valid bet. This method is consistent with the fast action of the game, allowing a player to make a last-second bet while the dice are about to be thrown. The NO CALL BET rule may exist to prevent confusion on the amount bet, possibly going back to the days of 25 cent tables. For example “three fifty” could mean $3.50 or $350. If the dealer is not clear about the intention of the player he may state “no bet” and push the chips back to the player.

Commonly observed etiquette
This section does not cite any references or sources.
Please improve this section by adding citations to reliable sources. Unverifiable material may be challenged and removed. (September 2007)

* It is generally preferable to place chips on the board rather than tossing them. Tossed chips may roll on edge out of the dealer’s reach and/or upset other stacks of chips. When chips must be tossed it is polite to gain the dealer or stickman’s attention and toss as few chips as necessary to cover the bet (a $25 chip is preferable to a stack of five $5 chips).
* When offered the dice to shoot, a player may pass the dice to the next player without fear of offending anyone; however, keep in mind that at least one player must always be a “shooter” betting on either the pass line or don’t pass line for the game to continue.
* When tipping, the most common way is simply to toss chips onto the table and say, “For the dealers,” “For excellent service” or “For the boys” (the latter is considered acceptable even though dealers often are women). Another method is to place a bet next to your bet and call out “dealers.” A “two-way” bet is one that is part for the player and part for the dealers. Usually, the dealers’ bet is smaller than the player’s bet, but it is appreciated. The part of the bet for the dealer is called a “toke” bet; this is from the $1 slot machine coins or tokens that are sometimes used to place bets for the dealers in a casino. Most casinos require the dealers to pick up their winning bets, including the original tip, rather than “let it ride” as the player may choose to do.
* After the come-out roll, it is considered bad luck to say the word “seven”. A common “nickname” for this number is “Big Red”.
* It is considered bad luck to change dice in the middle of a roll.
* Center bets are made by tossing chips to the center of the table and calling out the intended bet; the stickman will then place the chips correctly for the player. As mentioned above, care should be taken when tossing chips. Players furthest from the stickman can often elect to place a center bet with a dealer who will relay the bet to the center.
* It is considered rude to “late bet,” or make wagers while the dice are no longer in the middle of the table. While entirely permissible, excessive late betting will generally garner a warning. At their discretion, dealers can disallow a bet made after the dice have left the center.
* Food, drinks, and other items should remain off the chip rail.
* Players feel it is bad luck for the shooter to leave the table after a successful come-out roll.
* While it is mathematically a slightly better bet, “wrong bettors” (people who bet “don’t pass”) are considered to bring bad luck to the table.
* When the shooter is ready to roll, players should remove their hands from the table area in order to avoid interfering with the dice. The stickman will often say “hands high, let ‘em fly” or “dice are out, hands high”.
* When making bets in the field or on the Big 6 or Big 8, it is the player’s responsibility to track his or her bet. Place bets and Come Line bets will be tracked by the dealer, who will pay you directly. Hardway and other proposition bets are tracked by the stickman and will be paid by the dealer to you directly based on instructions from the stickman.

Systems

Martingale system

No wagering system can consistently beat casino games of pure chance such as craps, but that does not stop hopeful gamblers believing in them. One of the best known systems is the Martingale System, in which the player starts by betting $1 and doubles his bet whenever he loses. Upon winning, he starts over at $1. The idea is to realize a net win of $1 after every eventual win. This system fails because the player will either run out of money after having to double his bet several times in a row after a streak of losing bets, or he will be unable to bet the amount dictated by the system because it would exceed the maximum bet allowed by the casino.

Free Odds Basic Strategy

The free odds bets are continuation bets that you can make on pass/don’t pass & come/don’t come bets. These bets are paid at true odds and are the best bets available in the casino. Hence the player can reduce the casino edge by taking full odds on their pass/don’t pass & come/don’t come bets. The amount by which the player can reduce the casino edge depends on the allowed multiple on the free odds. But even with a conservative triple odds on the pass line, the casino edge can be reduced to 0.471%.

The Iron Cross

The Iron Cross is a bet pattern that allows the player to win on every roll that is not a seven. The Iron Cross is made by a field bet and place bets on the 5, 6 and 8. This strategy will not create a mathematical advantage for the player but is fun to play when the table is hot.

Gambler’s fallacy

Other systems depend on the gambler’s fallacy, which in craps terms is the belief that past dice rolls influence the probabilities of future dice rolls. For example, the gambler’s fallacy indicates that a craps player should bet on eleven if an eleven has not appeared or has appeared too often in the last 20 rolls.

In reality, each roll of the dice is an independent event, so the probability of rolling an eleven is exactly 1/18 on every roll, even if eleven has not come up in the last 100 rolls, or if eleven has come up 5 times in the last 5 rolls. The common term to describe this is “dice have no memory”.

Parity hedge system

The parity hedge system is a hoax promulgated by Quatloos. Despite the fact that no such system exists (indeed, it is a mathematical impossibility), several gambling-related web sites have retold the ‘parity hedge’ story without attribution.

Dice setting or dice control

Another approach is to “set” the dice in a particular orientation, and then throw them in such a manner that they do not tumble randomly. The theory is that the dice will be more likely to show certain numbers. Unlike other systems, this one is mathematically plausible, because if it were possible to alter the probabilities of each outcome, then winning systems could be devised.

Casinos do take steps to prevent this. The dice are required to hit the back wall of the table, which makes controlled spins more difficult. Whether it is possible for human beings to consistently exercise the precise physical control necessitated by the theory is a source of controversy. A small but dedicated community of controlled shooters maintain records and claim proof of dice influencing in casino conditions. Frank Scoblete, Stanford Wong and Jerry L. Patterson, authors of books that feature dice control techniques, believe that it is possible to alter the odds in the player’s favor by dice control.

Chris Pawlicki, a mechanical engineer who (under the pseudonym “Sharpshooter”) wrote a book on dice setting called Get The Edge At Craps: How to Control the Dice as a part of the Frank Scoblete “Get the Edge Guides,” defined the math and science behind dice control.

In addition, some people offer to teach dice-setting skills for a substantial fee. Currently there has been no independent conclusive evidence that such methods can be successfully applied in a real casino.

Two-up

Two-up is a traditional Australian gambling game. It is also widely known as swy (also spelt swei), and this is usually explained in terms of the German word zwei, “two” (on the basis that swy uses two coins).

History

The exact origins of Two-up are obscure, but it seems to have evolved from pitch and toss, a gambling game involving tossing a single coin into the air and wagering on the result which was popular amongst poorer English and Irish citizens in the 18th century. The predilection of the convicts for this game was noted as early as 1798 by the colony’s first Judge Advocate, as well as the lack of skill involved and the large losses. By the 1850’s, the two-coin form was being played on the gold fields of the Eastern states and it was spread across the country following subsequent gold rushes.

Two-up was played extensively by Australia’s soldiers during World War I and games, to which a blind eye was cast, became a regular part of ANZAC Day celebrations for returned soldiers.

As time passed, increasingly elaborate illegal “two-up schools” grew around Australia, to the consternation of authorities but with the backing of corrupt police. The legendary Thommo’s Two-up School, which operated at various locations in Sydney from the early years of the 20th century until well after World War II, was one of Australia’s first major illegal gambling operations. The popularity of Two-up declined after the 1950s as more sophisticated forms of gambling like Baccarat gained popularity in illegal gaming houses and poker machines (slot machines) were legalized in clubs.

Legal Two-up arrived with its introduction as a “table” game at the new casino in Hobart in 1973 and it is still offered in some Australian casinos. Two-up has also been legalized* on ANZAC Day, when it is played in Returned Serviceman’s Leagues (RSL) clubs and hotels. Several tourist “Two-up schools” in the Outback have also been legalized. According to the NSW Gambling (TWO-UP) Act 1988, two up in NSW is not unlawful on ANZAC day.

Rules

Two up is played by players who surround a ring and take turns at being the ’spinner’; ‘come in spinner’ being the call for another spinner to come forward into the ring. The game is managed by a ‘boxer’ who oversees the game and betting and a ‘ringy’ or ringkeeper who looks after the coin tosses in the ring. The spinner offers a bet, which is matched. He then tosses two coins up into the air using a paddle known as a ‘kip’. If the coins are both heads (Heads) he wins, if they are both tails (Tails) he loses and if they are one of each (Odds) he throws again. The boxer takes a commission out of the kitty that the spinner wins. The other punters place side bets.

M. G. Heuston, a WWI veteran, described a game that he ran. The spinner needed to toss Heads three times to win, with his bet having to be matched before each throw. Side bets were held on whether the spinner would toss Heads or Tails and ‘tail betters’ would bet 3/1 against two Heads. The spinner could choose to bet for Tails instead or play sudden death with three coins so that there were no Odds.

In casino play the players gamble against the house and the rules vary along a similar theme. At Star City in Sydney, two-up was removed in October 2003 due to budget cutbacks brought in by Tabcorp, leaving one of Australia’s largest casinos without the iconic game. The spinner needed three Heads to win and was paid 7.5/1. Tails or five Odds in a row was a loss. Other players could place side bets on Heads or Tails. The five Odds are the odds in favor of the House which are 3.4% against the Spinner and 3.1% against side bets. At Conrad Jupiters on the Gold Coast, the spinner is required to get five heads in a row to win. A loss is three Odds in a row, or Tails. With Odds, all bets are frozen, which means that no-one can change or remove their bets, and new players are not permitted to join. Conrad Jupiters no longer advertises two-up, and is now owned by Tabcorp as well.

Three card poker

Three card poker (trademark name) or tricard poker is a poker-based game that is played in casinos. It actually consists of two separate games, pairplus and ante-and-play. The players can choose to play either or both of the games.

The History and Strategy of Three Card Poker

Poker in its purest form, has been around for centuries, dating all the way back to 900 A.D., when Chinese Emperor Mu-tsung is said to have played domino cards with his wife.

These “domino cards” set the stage for what we now call poker, using a ranking system of cards or dominos combined with the skilled art of bluffing one’s opponents to win the game.

3 Card Poker (or tri-card poker as it’s also called) is an American version of a British game called Brag. This game originated over three hundred years ago as a game known as Primero, a fast-moving betting game using only three cards. As the game evolved, it became known as Post-and-Pair and then again as Brag. This game made it to the States as Casino Brag and Brit-Brag, but eventually evolved again into the game we now know as 3 Card Poker.

Pairplus

Pairplus is a simple bet on the cards with a payout for all hands of a pair or better. Below are probabilities and six examples of actual payout tables used by some casinos.

Probabilities - Three Card Poker
Ways to draw 3 cards out of 52 = 22100

Hand

Combinations

Percentage
Straight flush 48 0.22%
Three of a kind 52 0.24%
Straight 720 3.26%
Flush 1096 4.96%
Pair 3744 16.94%
High card 9720 43.98%
None 6720 30.41%

Payoff Tables for Pairplus

Hand

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6
Straight flush 40 to 1 40 to 1 35 to 1 50 to 1 40 to 1 40 to 1
Three of a kind 30 to 1 25 to 1 25 to 1 30 to 1 30 to 1 30 to 1
Straight 6 to 1 6 to 1 6 to 1 6 to 1 5 to 1 6 to 1
Flush 4 to 1 4 to 1 4 to 1 3 to 1 4 to 1 3 to 1
Pair 1 to 1 1 to 1 1 to 1 1 to 1 1 to 1 1 to 1
House advantage 2.32% 3.49% 4.58% 5.10% 5.57% 7.28%

Ante-and-play

Normal ante-and-play gameplay

For ante-and-play, the player places an ante bet before receiving his cards. The player is then dealt his cards and after seeing them, the player can fold his cards and lose the ante bet, or raise by placing out a bet of equal money to the ante bet. If he chooses to play, there are three possibilities. The first is that the dealer does not ‘qualify’. To qualify, the dealer must have a hand of a queen high or better. If the dealer does not qualify, the ante bet is paid out even money, but the play bet is simply returned. If the dealer does qualify, the player wins if his hand is of higher value than the dealer’s, and gets paid out even money on both his ante and play bets. If the dealer’s hand is of higher value, the dealer takes the Ante and Play bets. Rules vary on what happens when the hands are of exactly equal value: some say that the player simply gets his money back, but others say that the player is paid even money on his bet.

The ante bonus

In addition to normal ante-and-play gameplay, there is a bonus payout on the ante bet for especially good hands.

Ante Bonus Payouts

Hand

Table 1

Table 2

Table 3

Table 4
Straight flush 5 to 1 5 to 1 4 to 1 3 to 1
Three of a kind 4 to 1 3 to 1 3 to 1 2 to 1
Straight 1 to 1 1 to 1 1 to 1 1 to 1
House Edge 3.37% 3.61% 3.83% 4.28%

These bonus payouts are paid only on the ante bet for any player who chooses to play, regardless of whether the dealer qualifies or whether the player wins or loses.

Texas Hold’em Bonus Poker

Texas Hold’em Bonus Poker is a gambling card game is owned and licensed by Mikohn Gaming/Progressive Gaming International Corporation. The game is based on traditional multi-player Texas Hold’em poker.

Rules

* The game is played with a standard 52 card deck.
* Each player makes an ante bet of 1 unit and may make an optional bonus bet.
* The player and dealer are both dealt two cards (face down).
* After checking his/her cards, the player may decide to fold with no further play losing the ante bet or make a flop bet of two units.
* Three cards are then dealt to the board.
* The player may decide to check or make a turn bet of one unit.
* Another card is dealt to the board (making four cards in total on the board).
* The player may decide to check to make a river bet of one unit.
* One more card is dealt to the board (making five in total).
* The player and dealer make their best five card poker hand from their own hand and five board cards.
* If the dealer’s hand is better than the player’s hand the player loses all bets.
* If the dealer’s hand is equal to the player’s hand, all bets are a push.
* If the player’s hand is better than the dealer’s hand, the player wins even money on the flop, turn and river bets. The player also wins even money on the ante bet if his best hand is a straight or better, otherwise the ante bet pushes.
* A separate side bet may be wagered on the player’s starting hand. If a player’s hole cards are a pair, A-K, A-Q, or A-J, the player wins the side bet according to the pay table. This bet pays even if the player does not beat the dealer’s hand.

Notes

* Unlike in traditional Texas Hold’em poker, there is no bet after the river.
* In Atlantic City, New Jersey, there is a variation on the rules above. The player only wins even money on the ante bet if his best hand is a flush or better.

Strategy

The optimal strategy for the flop bet, assuming optimal play thereafter, is to call all hands except for 2-3 offsuit, 2-4 offsuit, 2-5 offsuit, 2-6 offsuit and 2-7 offsuit. However, said optimal “postflop” strategy for the turn and river bets, while easy for a computer to solve, is extremely complicated, because of the large number and variety of possible card combinations. No concise explanation of optimal postflop strategy, or even a simplified version thereof, has been published.

Spanish 21

Spanish 21 is a variant of blackjack owned by Masque Publishing Inc., a gaming publishing company based in Colorado. Unlicensed, but equivalent, versions may be called Spanish Blackjack. In Australia and Malaysia, an unlicensed version of the game, with no dealer hole card and significant rule differences, is played in casinos under the name “Pontoon”.

Rules

Spanish 21 is generally played on a standard Blackjack table and uses the following rules:

* The game is played with four, five, six, or eight decks dealt from a shoe, or from a continuous shuffling machine (CSM). Spanish 21 is played with 48-card Spanish decks, which are standard 52-card decks with the 4 ten-spot cards removed. All cards have the same values as in blackjack.
* The dealer gets a hole card.
* In most venues, the dealer hits soft 17 (abbreviated as H17), and in some venues, the dealer stands on soft 17 (abbreviated as S17). Compared with H17, S17 lowers the dealer’s average unbusted final total, and lowers the dealer’s chance of busting. The effect of the former is greater than the latter, with the result that S17 is much better for the player than H17. The house edge for 6-deck H17 Spanish 21 is 0.78%, but the house edge for 6-deck S17 Spanish 21 is only 0.37%.
* Blackjack pays 3:2, and always wins regardless of whether or not the dealer has a blackjack.
* Insurance is paid 2:1, just like in Blackjack, despite the fact that there are four fewer ten-valued cards per deck. As 3 cards in 12 are worth ten, the chance of the dealer getting a Blackjack when showing an Ace is only 25%. Therefore, for insurance to be an even bet, it would have to pay 3:1, not 2:1. Consequently, the insurance bet in Spanish 21 ties with Keno as being the worst bet in any casino.
* Hitting, standing, and splitting all follow similar rules to Blackjack. Doubling after splitting (DAS) is always permitted, and, in most venues, players are allowed to draw as many cards as they wish after splitting Aces, or may double down after receiving second or subsequent cards. The Mohegan Sun casino does not allow drawing on split Aces.
* Players can split to a maximum of four hands, including Aces (abbreviated as SPL3)
* In most venues, if the dealer doesn’t have blackjack, players may surrender, and get half their bet back in exchange for relinquishing the right to play on. This type of surrender is known as a “late surrender” (LS).
* Players can surrender after doubling (a k a forfeit, double-down rescue, or concede). The dealer takes the double portion of the bet, and the player retains the original bet.
* Once the initial two-card hands are dealt, if the dealer is showing an Ace or face card, he peeks underneath the hole card to check for a blackjack, before playing actually commences. If he has blackjack, all players automatically lose, unless they also have a Blackjack.
* The player may double down on any total, even after taking hit cards.
* In some casinos, players may redouble up to two times after doubling down. For example: The player bets one unit and is dealt 2-3, giving a hand total of 5; the dealer is showing a 6. The player doubles the first time and draws a 3. The hand total is now 8 and the total amount wagered is two units. The player doubles a second time and draws a 3. The hand total is now 11 and the total amount wagered is four units. When the player doubles a third time on 11, the total amount wagered will be eight units. Redoubling is a profoundly player-advantageous rule, when optimally executed. The house edge for 6-deck H17 without redoubling is 0.78%, and with redoubling is 0.42%.
* A total of 21 always wins for the player. It never pushes against the dealer’s 21.
* A five-card 21 pays 3:2, a six-card 21 pays 2:1, and a 21 with seven or more cards pays 3:1. A 21 composed of 6-7-8 or 7-7-7 of mixed suits pays 3:2, of the same suit pays 2:1, and of spades pays 3:1. These bonus payouts apply even if the hand was the result of a split. However, these bonus payouts do not apply if the 21 was the result of doubling.
* A “super bonus” of $1000 for bets under $25, and $5000 for bets of $25 and over, is paid on a suited 7-7-7 against any dealer 7. All other players at the table receive a $50 “envy bonus”. The super bonus is not paid on split hands.
* The Meskwaki casino in central Iowa pays 3:2 on blackjacks obtained after splitting Aces or face cards, in addition to the 3:2 payout on regular blackjacks.

The removal of the four tens in each deck gives roughly a 2% advantage to the dealer. This is almost fully compensated by the liberal Spanish 21 rules.

Masque Publishing maintains a list of venues that offer the superior S17 or redoubling rules.

Beating Spanish 21

Spanish 21 is not as easy to beat with traditional card counting methods, although it is possible . However, many other advantage play techniques, such as hole carding and ace sequencing are possible. Because many casinos don’t perceive card counters as a threat on Spanish 21, it is easier to get away with a large betting spread.

Red Dog

Red Dog, also known as Red Dog Poker or Yablon, is a game of chance played with cards. It is a variation of acey-deucey or in-between. While found in some land casinos, its popularity has declined, although it is featured at many casinos online.

The deck used to play Red Dog is the standard, fifty two card variety. The game may be played with anywhere from one to eight decks, with an increasing number of decks decreasing the house edge — the house’s advantage begins at 3.155% with one deck, but falls to 2.751% when eight decks are used. This is in contrast with some other casino card games, such as blackjack, where a higher number of decks used will increase the house edge.

The game only uses three cards at a time, which are ranked as in poker, with aces high. Suit is irrelevant. A wager is placed, and two cards are placed face up on the table, with three possible outcomes:

* If the cards are consecutive in number (for example, a four and a five, or a jack and a queen), the hand is a push and the player’s wager is returned.
* If the two cards are of equal value, a third card is dealt. If the third card is of the same value, then the payout for the player is 11:1, otherwise the hand is a push.
* If the two cards difference is greater than one place (for example, a three and an eight), then a spread is announced which determines the payoff, pending the outcome of a third card which will be dealt. If this third card’s value falls between the first two, the player wil receive a payoff according to the spread, otherwise the bet is lost. Before dealing the third card, the player has the option to double his bet.

The spread table is as follows:
Spread Payout
1 card 5 to 1
2 cards 4 to 1
3 cards 2 to 1
4+ cards 1 to 1

Even when using eight decks, Red Dog does not offer favorable odds for the player in comparison with other games of chance common to casinos. There is little strategy involved; raises should only be made when a spread statistically favors a player (which is at seven cards or more, regardless of the number of decks used).

[edit] References

Pai gow poker

Pai Gow poker (or Double-hand poker) is an Americanized version of Pai Gow, in that it is played with playing cards using poker hand rankings, while Pai Gow is played with Chinese dominoes. The games of Pai Gow poker and Super Pan-9 were co-created by Sam Torosian and Fred Wolf.

The game is played with a standard 52-card deck plus a single joker. It is played on a table set for six players plus the dealer.

Each player is playing against the banker, who may be the casino dealer or one of the other players at the table.

Object of the game

The object of the game is for a player to create two poker hands out of the seven cards in his hand: a five-card poker hand and a two-card poker hand. The five-card hand must rank higher than the two-card hand. The two-card hand is often called the hand “in front” or “on top”, and the five-card hand is called the hand “behind” or “bottom”, as they are placed that way in front of the player when he is done setting them.

The deal

The cards are shuffled, and then dealt to the table in seven face-down piles of seven cards. Four cards are unused regardless of the number of people playing.

Betting positions are assigned a number from 1 to 7, starting with whichever player is acting as banker that hand, and counting counter-clockwise around the table. A number from 1 to 7 is randomly chosen (either electronically or manually with dice), then the deal begins with the corresponding position and proceeds counter-clockwise. One common way of using dice to determine the dealer starting number is to roll three six-sided dice, and then count betting spots clockwise from the first position until the number on the dice is reached.

If a player is not sitting on a particular spot, the hand is still assigned, but then placed on the discard pile with the four unused cards.

Hand rankings

The only two-card hands are one pair and high cards.

Five-card hands use standard poker hand rankings with one exception: in most Nevada casinos, the hand A-2-3-4-5 ranks above a king-high straight, but below the ace-high straight A-K-Q-J-10. At most casinos in California and Michigan this rule doesn’t apply; the A-2-3-4-5 is the lowest possible straight.

The joker plays as a bug, that is, in the five-card hand it can be used to complete a straight or flush if possible; otherwise it is an ace. In the two-card hand it always plays as an ace, except in several southern Californian casinos where the joker is completely wild.

Determining a win

If each of the player’s now-separated hands beat the banker’s corresponding hand then he wins the bet. If only one of his hands beats the banker then he pushes. If both of his hands lose to the banker then he loses.

On each hand, ties go to the banker (for example, if a player’s five-card hand loses to the banker and his two-card hand ties to him then he loses); this gives the banker a small advantage. If the player fouls his hand, meaning that his low hand outranks his high hand, or that there are an incorrect number of cards in each hand, there will be a penalty: either re-arrangement of the hand according to house rules or forfeiture of the hand.

In casino-banked games, the banker is generally required to set their hand in a pre-specified manner, called the “house way”, so that the dealer does not have to implement any strategy in order to beat the players. When a player is banking, he is free to set the hand however he chooses; however, players have the option of “co-banking” with the house, and if this option is chosen then the player’s hand must also be set in the house way.

Californian casinos typically charge a flat fee per hand (such as 5 cents or one dollar) to play, win or lose. Other casinos take, out of the winnings, a 5% commission (usually known as the rake). While this may seem high, a hand of Pai Gow poker takes a long time to play compared to a game like blackjack, and there are many pushes; therefore the house doesn’t collect that 5% as often as it would collect the house percentage on other games.

Basic strategy

Generally speaking, players should try to set the highest two-card hand that they can legally set: the best two-card hand that still leaves a higher five-card hand behind. More specifically, players should expect an average hand to be something like a medium-to-high pair behind in the five-card hand and an ace-high in front. Detailed computer analysis has been done to determine the ideal strategy, but this requires memorizing large tables; a close approximation can be done with only a few rules of thumb: when playing in a casino and in doubt, a player can always ask that his hand be set house way. Most house strategies are quite reasonable and can be quite close to optimal strategy.

* If a player has no pairs, straights or flushes, he can set the second- and third-highest cards in his two-card hand. For example, with K-Q-J-9-7-4-3 he can play Q-J and K-9-7-4-3. There are a few minor exceptions to this, for example, with A-Q-10-9-5-4-2 it is slightly better to play Q-9 and A-10-5-4-2, but these situations are rare and do not affect a player’s win rate much.
* If a player has nothing but a single pair, he can set it in his five-card hand and put the two highest remaining cards in his two-card hand. For example, with A-Q-Q-9-6-5-3 he can play A-9 and Q-Q-6-5-3. There are no exceptions to this rule. This and the above rule will cover approximately 90% of played hands.
* Two pair is the most common case where strategy isn’t obvious. A player can either play high pair behind and small pair in front, or else two pair behind and high cards in front. The smaller the high pair and higher the remaining cards, the more inclined he should be to play two pair behind. If his side cards are small or his larger pair is large, he should split the pairs. He should always split the pairs if his high pair is of aces, and should almost always split if his high pair is of kings or queens: they are high enough by themselves. With cards like J-J-4-4-A-Q-5 he can consider playing A-Q and J-J-4-4-5- since A-Q in front is not much worse than 4-4; however, two pair behind is much better than a single pair of jacks. A player with jacks and tens might be more inclined to split, because tens in front is much better than A-Q. With pairs as small as 7s and 8s, a player might consider playing two pair behind if he can play a king-high or better in front. With 2s and 3s he may even play as little as a queen-high in front. If he has no side cards higher than a jack, he should always split pairs, even 2s and 3s (most house ways split if there’s a pair of 6s or higher, and split small pairs if there’s no ace for the low hand).
* Three pair is a very good hand. A player should always play the highest pair in front with no exceptions. For example, with K-K-7-7-4-4-A he should play K-K and 7-7-4-4-A.
* If a player has three of a kind and nothing else, he should play three of a kind behind and the remaining high cards in front unless they are aces. He should always split three aces, playing a pair of aces behind and ace-high in front. Occasionally, he can even split three kings if his remaining side cards are not queen-high; for example, with K-K-K-J-9-7-6 it is slightly better to play K-J and K-K-9-7-6 than to play J-9 and K-K-K-7-6. Most house ways only split three aces.
* If a player can play a straight or a flush or both, he should play whichever straight-or-better five-card hand makes the best two-card hand. For example, with K?-9?-8?-7?-6?-5?-4? playing the flush would put 8-6 in front, playing the 9-high straight would put K-4 up front, but the correct play is K-9 and 8-7-6-5-4. Occasionally the player will have a straight or flush with two pair; in that case, he should play as if it were two pair and ignore the straight or flush. This rule applies even if a player can play a straight flush; if a straight or flush makes a better hand in front, play it that way.
* With a full house, a player should generally play the three of a kind behind and the pair in front. The exception is if the pair is very small and the side cards are very high; for example, with 5-5-5-3-3-A-Q it might be better to play A-Q with the full house behind. However, these cases are rare, and a player will never be making a big mistake if he never play a full house behind. House ways will always split the full house.
* With two three of a kinds, a player should play the higher as a pair in front and the smaller three of a kind behind. For example, with Q-Q-Q-7-7-7-A he should play Q-Q and 7-7-7-A-Q — no exceptions.
* With four of a kind, a player should play as if it were two pair, but should be slightly less inclined to split. For example, with 10-10-10-10-J-5-4 he should play 10-10 and 10-10-J-5-4, and with 3-3-3-3-K-Q-7, K-Q and 3-3-3-3-7. Most house ways always split the four of a kind.
* With three pair and a straight or flush (only possible with the joker), a player should play his hand as three pair (with aces in front).

The cases below rarely happen, but deserve mention:

* With four of a kind and a pair, a player should play the pair in front unless it is very small, and the four of a kind is very large. For example, with 9-9-9-9-7-7-K he should play 7-7 and 9-9-9-9-K, but with K-K-K-K-3-3-9 he might play K-K and K-K-3-3-9. House ways always put the quartet in back and the pair in front.
* With a full house and a pair, a player should play the higher pair in front and a full house in back.
* With four of a kind and three of a kind, a player should split the four to play a pair in front and full house behind, unless the three of a kind has a higher rank than the four of a kind; in that case he should play the four of a kind, with a pair from the three of a kind in front.
* With all four aces and the joker, a player should play a pair of aces in front and three aces (or a full house) behind, unless the back pair is of kings.

History

In addition to being a games inventor, Fred Wolf was the casino manager of the Commerce Casino in the early 1980’s. Fred Wolf decided to sublet a third of the casino floor space of the Bell Club, in the city of Bell, California, to introduce his new Super Pan-9 game. Fred Wolf needed to innovate new gaming structures in order to overcome the competition of the larger Los Angeles area card casinos, such as the Bicycle Club and Commerce Casino. The games of Pai Gow Poker and Super Pan-9 became immediate crowd favorites, quickly spreading to the entire Californian gaming market, and then, worldwide.

Subsequently, Fred Wolf invented, and obtained U.S. patents on, several new gaming devices which included “Three-special-dice”, and games such as “Sweepstakes Blackjack”, “Fast-action hold ‘em”, “Lucky Pan-9″ and “Pai Gow jokers”.

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