Lotteries are the most popular form of gambling. The basic premise is straightforward: the player buys a ticket and wins if the numbers on the ticket match the numbers that are drawn. In most lotteries, players can win smaller prizes by matching only some of the numbers drawn In lotteries with predetermined ticket numbers (e.g., raffles), the probability of a win is determined by how many tickets are sold. In lotteries where players pick their own numbers, the odds are determined by how many unique combinations of numbers are possible.

In Lotto 6/49 in Ontario, the player picks 6 numbers from a pool of numbers ranging from 1 to 49, which results in approximately 14 million possible unique combinations of the 49 numbers. The winning numbers are drawn without replacement from the same ball cage so that a particular number can only occur once on a ticket. Note that each draw begins with all 49 balls, so all draws are independently random of each other. In other lotteries (e.g., Ontario’s Pick 3), each number might be drawn from a separate cage of balls so that the same number might appear more than once on the same ticket.

In many lotteries, the top prize changes with each draw. If no one wins, the prize money is rolled over so that the prize on the next draw is larger. If the Lotto 6/49 prize, for example, reaches greater than 14 million, the expected return is positive and long-term profit is theoretically possible. However, lotteries make most of their money during the long runs when the prize value steadily increases. Since these lotteries usually allow more than one person to buy the same ticket number, there is a chance that the prize will have to be split between multiple winners. The larger the prize, the more tickets are sold and the greater the chance that the prize will be split. As a result, even when the prize exceeds the odds against winning it, the players may still be playing against a negative expected return.

Keno is a type of lottery in which a player buys tickets made up of between 1 to 15 numbers chosen from a total of 80 numbers. That is, a player’s ticket might consist of 3, 4, or even 15 numbers. Twenty numbers are drawn randomly from either ball cages or a computer generator. The player wins if some of their numbers are drawn. The more of a player’s numbers that are drawn, the higher the prize. The more numbers the player bets on, the more numbers he/she must match in order to win a prize. A player who bets on only one number triples his/her money if it is drawn. But if a player selects 6 numbers, matching 1 number pays nothing. Matching 15 numbers pays a very large prize.

Instant lotteries are sold as tickets on which the player matches 3 symbols or prize values by scratching off a removable plastic coating. Nevada tickets, pull tabs and break-open tickets are essentially the same as instant lottery tickets, but the symbols are hidden by a cardboard flap and the symbols are similar to slot machine symbols (e.g., lemons and cherries).

An instant bingo ticket has a “caller” box of hidden numbers and up to four player cards whose numbers are visible. The player scratches to reveal the hidden caller numbers and then scratches matching numbers on the player cards, which are also covered by a scratchable coating.

Instant crosswords are essentially the same as instant bingo cards except that the player matches a series of hidden letters in one box with visible letters in a crossword puzzle to form words.

In Ontario, Instant Keno is a ticket that essentially mimics live keno. On one side is a pre-set selection of 3, 4, 5, 6 and 10 numbers. On the other side of the ticket is a set of hidden numbers that represent the numbers drawn. The player can win by matching some or all of the numbers. The more numbers matched, the bigger the prize.

With instant bingo, keno and crossword tickets, the player can see the numbers or letters on the game card area before buying the ticket (but not the hidden numbers or letters). The visible numbers may feed an illusion of control by encouraging the player to look for lucky numbers or numbers that are due to win, or to search for biases.

Bingo involves matching randomly drawn numbers to numbers printed on a card in a 5 by 5 grid. Before the game, the caller announces the pattern that must be completed for a win. The pattern is most often a line, 2 lines, or a completed card, but it could also be an X, T, Y, Z or box pattern. The caller draws bingo balls one at a time, each of which is marked with a number, and these numbers are posted on a board. Players stamp or cover the matching numbers on their card(s) until the matched numbers form the required pattern. The first player to complete the pattern yells “Bingo!” to claim the prize. A prize might be given out for the first line completed after which the game continues until someone completes the entire card. If more than one player completes the pattern or card at the same time, the prize is split.

A player with well-developed memory and attention skills is able to play more cards simultaneously; the cognitive exercise of playing multiple cards may even be beneficial to some players. The first author reports having difficulty keeping up with the caller with only 3 cards in front of him and was quite impressed by the little old ladies who were happily playing 9 or more cards. Although playing more cards increases the frequency of wins, it does not improve the long-term payback for these “skilled” players. Winning at bingo is merely a matter of random chance. A player who attempts to monitor 18 bingo cards but can not keep up with the caller would actually decreases his/her payback percentage compared to a less ambitious player with only 3 cards. Recent advances in electronic bingo may allow people to play more cards, but might also remove the beneficial effect of bingo on memory and motor skills.

A bingo session is a series of about 10 individual games. A session usually takes 2 to 3 hours, depending on breaks and on how long it takes to find and verify the winners. Bingo is a social game that often serves an important social function for women and older adults; most socializing occurs between games.

Games with progressive (growing) jackpots and networked games with super jackpots are now available; however, the players’ odds of winning in these games are lower.

The following is a brief introduction to the nature of slot machines. For a more comprehensive discussion of slots, see Turner and Horbay (2004).

The basic game of a slot machine involves setting 3 or more reels into motion by pressing a “spin” button, a spin icon on a computer screen or, on older machines, pulling a lever. When the reels stop spinning, if matching symbols from all 3 line up on a payline, the player wins. Some machines have 5 reels or multiple paylines. Common symbols include lemons, cherries, lucky sevens, and diamonds. The amount of the win varies depending on the rarity of the symbol.

The wins are recorded on an LED readout (or on a video screen) that notifies the player how many credits he/she has won. If the player wins more credits than the machine can pay out, a light on top of the machine goes off notifying the casino of a big win. The payout of the machine is determined by the odds against winning, not by how recently the machine has paid out.

A slot machine can either have actual physical reels or a video display. The game play is essentially the same on either reel or video slots; however, the video display allows the programmer to incorporate a much greater variety of gambling experiences (e.g., bonus features) into the game than is possible with physical reels.

A video lottery terminal (VLT) is a gambling machine that provides a variety of games, including simulated slot machine games, video poker and blackjack. It is called a terminal because the random numbers are often generated by a central system, rather than within the machine itself. The central determination system allows such machines to be legally classed as lotteries rather than slots, but from the players’ perspective this distinction is irrelevant.

There is no skill in slot play, but VLTs often include blackjack and video-poker games that do involve some degree of skill. Accordingly, in a treatment situation, it may be important to find out what types of games the player actually plays (e.g., line games or video poker) to determine which of the client’s beliefs are erroneous. Laws in some states in the U.S. encourage or require skill elements in slot games. Most of these are pseudo-skill elements so that the game provides no real opportunity for skilled play (Griffith, 1993, 1999). Because of bonuses and progressive jackpots, the payback percentage will vary, but, in general, there is simply no way to beat a slot machine.

When slot machines were first invented over 100 years ago, they consisted of 3 flywheels that were set in motion by the pull of the lever. The force of the spin would, to some extent, determine how far the reels would turn. It was possible to manipulate the outcome by carefully controlling (or tampering with) the lever. Some players still believe that it is possible to win by controlling the lever. Modern slot machines are computers. The reels themselves only serve to tell the player if they have won or not; they do not determine if the play wins.  A random number generator (RNG) determines the wins and losses on a slot. Before the reel is even set in motion, the computer uses a number drawn from its RNG to determine where the reel will stop. The computer predetermines that the reel should land on the symbol for, say, a cherry, and it spins it to that location.

A slot machine reel might have 22 pictures on it (oranges, cherries, diamonds, blanks between the pictures, etc.), and some pictures appear more frequently on the reel than others. There is, however, no way to tell how likely a symbol will occur based on looking at the reel. The odds of a reel landing on a particular picture do not depend on how many pictures there are, but on how many “stops” are associated with the picture in the computer’s memory. Programmed into the computer is a table called the virtual reel that maps the numbers selected by the RNG to particular symbols.

Suppose the RNG was programmed to generate a number from 1 to 64. Each of these 64 possible numbers is related to a stop on a virtual reel, and the stops on the virtual reel are mapped onto the 22 symbols of the actual reel. The actual reel might have 2 double diamond pictures on it out of 22 total pictures. The virtual reel, however, might map only 2 of its 64 numbers onto double diamonds. Virtual reel weighting ensures that low paying symbols and blanks come up more often than high paying symbols. The apparent probability of a double diamond on the reel might be 1 in 22, but the actual probability of a hit might be 2 in 64. This means that instead of a jackpot coming up 1 in 10,648 spins, a jackpot’s actual probability would be 1 in 32,000 spins (assuming that all 3 reels have the same probability). To make things more complex, there is no particular reason why a symbol should have the same frequency on the 3 reels, virtual or otherwise. It is important to understand that the outcome on the payline is still random, but the placement of the images on the reel itself and the neighbours above and below the payline give the player a distorted picture of his/her chances of winning.

There are numerous myths about slot machines. For example, many people believe they have to stay at a particular machine because it is due to win. Each spin is an independent random event. The history of the machine’s play is irrelevant. A machine is never due to win. In addition, because a computer, not the spinning of the actual reels, determines the outcomes of a slot, there is no such thing as a near miss. A near miss is simply a loss (see Turner & Horbay, 2004, for a discussion of other myths about slots).

The roulette wheel consists of a fixed outer rim and a rotating inner wheel. The wheel is rotated in one direction and the ball is thrown in the opposite direction around the inside of the outer rim. As the ball starts to slow down, the ball drops down off the rim, rolls around the inner wheel and eventually comes to rest on one of the numbered slots. On an American-style roulette wheel, there are 38 slots numbered 1 to 36, as well as two slots numbered 0 and 00. Eighteen of these numbers are red, eighteen are black; 0 and 00 are painted green. The numbers are scattered around the wheel in an apparently random order; however, the arrangement ensures that black and red, high and low, and odd and even alternate around the wheel. A European wheel (available in Quebec) is essentially the same, but has only one 0, giving it slightly better odds for the player. Apparently, some wheels have a third green number, often with an Indian head (Wong & Spector, 1996), giving slightly worse odds for the player, but neither authors have seen one of these wheels.

Players bet by placing their wages on a green felt betting table. The numbers on the betting table are arranged in order from 1 to 36 in 12 rows of 3 columns. At one end are the zeros (0 and 00). Bets placed on individual numbers are called inside or straight-up number bets. These bets pay 35 to 1. A player can bet on a single number or several numbers. A player also has the option of placing a single chip across two numbers, four numbers (a corner), 3 numbers (a street) or six numbers (a double street). A player can increase his/her chance of winning by covering more spaces, but will win less. A $10 bet on a single number pays $350 (plus the player keeps the $10 bet). A $10 bet covering 4 numbers pays $80 (plus the player keeps the $10 bet). Around the outside of the betting table are spaces for betting on multiple numbers such as all of the red, black, high, low, odd or even numbers, which pay even money (that is, the payout odds are 1 to 1; the win equals the amount bet, plus the player keeps his or her bet). Bets on a 12-number column pay 2 to 1.

Roulette is unique in that it is the only game where the house edge is clearly marked (i.e., 2 green spaces out of 38 spaces). The math behind roulette is quite clever in that there are many different types of bets, but nearly all have the same house edge.

Craps or dice, like roulette, is a table game that gives the player a wide range of betting options, and a very slim house edge. Craps is one of the fastest, most exciting and noisy casino games. There is no skill involved in winning, but because of the complexity of the game and the fact that the player gets to hold the dice, there is a strong illusion of skill. A unique aspect of craps is that a single bet, of say $10, can last for several rolls of the dice.

There are several types of bets, but the main ones are called pass-line, don’t-pass, come and don’t-come bets. The payback percentage in craps varies from 98.6% for pass-line, don’t-pass, come and don’t-come bets to as low as 83.3% for a bet on the numbers 2 or 12. Players can place a bet with no house edge whatsoever, called free-odds bets, but these are only available after the player has placed an initial pass-line, don’t-pass, come, or don’t-come bet.

We will illustrate how the game works by using the pass-line bet, or betting with the shooter, as an example. Players take turns being the shooter, that is, rolling the dice. Any player can bet on the shooter’s throw by placing money on the pass line. The number that wins changes from the first roll to the second. On the first roll, if the shooter rolls a 7 or 11, he/she wins. If the shooter rolls a 2, 3 or 12 (a craps), he/she loses. However, all others numbers (4, 5, 6, 8, 9 and 10) are neither winners nor losers. If the player rolls one of these numbers, this number becomes the shooter’s “point” number. In order to win, the shooter now has to roll this same number again. However, if the player rolls a 7 before rolling the point number, he/she loses. For example, if the shooter rolls a 6 on his/her first roll, then 6 becomes the shooter’s point. If a 6 comes up before a 7, the bet wins; if a 7 is rolled, the bet loses. The shooter keeps rolling until he/she rolls either a 6 (wins) or a 7 (loses). If the shooter wins, he/she has another turn rolling the dice. If the shooter loses, the dice are passed to the next player.

A don’t-pass bet is the opposite of the pass-line bet. Essentially a don’t-pass bet is a bet that the shooter will lose either by rolling a 2 or 3 on the first roll or by rolling a 7 before his/her point number. Note that, in order to ensure the house’s edge for don’t-pass bets, rolling a 12 on the first roll is a standoff (neither win nor lose). Two other bets, come and don’t-come, follow the same rules as pass and don’t-pass bets, but are placed after the shooter establishes a point. A player can make only one pass-line bet at a time, but can have several come bets going at the same time.

Adding to the complexity of the game, after a point number has been established, the player can increase the size of his/her bet with a free-odds bet. Free-odds bets are an increased wager on a pass-line or don’t-pass bet. Free-odds bets, however, are paid out according to the true odds against winning, so there is no house edge on them (payback is 100% on the free-odds bet). Some casinos allow free-odds bets of double or even ten times the original bet. If a player has placed a pass-line bet, the free-odds bet wins if the shooter rolls his/her point number before a 7; the opposite is true for a player who placed a don’t-pass bet. Free-odds bets give the player a strong illusion of skill. The addition of free-odds bets has no net effect on the player’s long-term losses; they continue to lose at a rate of 1.4% of their initial pass-line bet. Free-odds bets, however, increase the player’s potential short-term gain or loss. The volatility produced by these free-odds bets also enhances the roller-coaster feel of the game.

There are numerous other betting options in craps, including placing a bet that 6 or 8 will come up before a 7, betting that the next roll will be a 7, betting that a 6 will come up as a double 3 (“hardways”), or betting that a specific number (e.g., 12) will come up on the next roll. The players, including the shooter, can place several different types of bets at the same time. Most of these other bets have a lower payback percentage than the pass-line and come bets. Incidentally, the shooter does not actually have to place a pass-line bet. He/she could instead place a don’t-pass bet (betting against the shooter). In this case, the shooter would run the risk of winning the roll (hitting a 7 on the first roll or making the point), but losing his/her bet, and feeling a little silly as the dice are pushed back to him/her to roll again (personal experience of the first author).

Baccarat, as well as its variation mini-baccarat, are card games that have attracted a fair degree of prestige. Baccarat is often shown in James Bond movies. There is no skill involved in winning on most versions of this game, but a strong illusion of skill. The object is to obtain a hand closest in value to 9. Face cards and tens are worth 0, aces are worth 1 and all other cards are worth their face value. If a hand goes over 10, the 10 is dropped and only the remaining units are counted. A card value of 3, 13 or 23 is worth 3, a card value of 8, 18 or 28 is worth 8.

Two hands are dealt, called the “player” and the “banker” hands. Bets are placed before any cards are dealt. In mini-baccarat, the gambler can bet on either the player or banker hands. Each hand is dealt 2 cards face up. Depending on the total value of the hands, a third card may be dealt. The player hand is played out first, and then the banker hand is played. In most forms of baccarat, the casino follows rigid rules to determine if a third card is to be drawn, and neither the player nor dealer has any say about this. Because the rules for drawing cards for the banker’s hand take into account the player’s third card, the banker hand has a slightly better chance of winning. To ensure a house edge for bets on the banker hand, a punter must pay a 5% commission to place such a bet.

A win pays even money. The payback percentage in baccarat is 98.8% for betting on the banker hand and 98.4% for the player hand—one of the highest payouts of any casino game. The player can also place a bet for a tie between the two hands, but ties are very rare, so it is not a very good bet. Card counting in baccarat is theoretically possible in single-deck games, but with multi-deck games counting provides no advantage (see the discussion of card counting in “Part 5: Blackjack” below). Some European high-stakes forms of the game (e.g., where a punter stakes his own cash to bank the game) may involve some degree of skill, but most do not.

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