In this section we describe one POD game, Lucky Clover, to give the reader an in-depth look at a POD game. A schematic of the computer touchscreen for Lucky Clover is shown in Fig. 1. The game is based on North American Bingo, where each card has 25 squares including the ‘free’ middle square. Under the “B” the numbers are 1–15, under the “I” they are 16–30, under the “N” they are 31–45, under the “G” they are 46–60, and under the “O” they are 61–75. The patron plays from one to four cards at a time, which are shown in the middle of the screen. In Fig. 1 the player is playing four cards and can wager $0.25, $0.50, $0.75, or $1.00 per card. In Fig. 1 the player is wagering $1.00 per card, for a total wager of $4.00.
There are 15 winning patterns, named in the paytable on the right-hand side of the screen in Fig. 1. If one or more of the 15 winning patterns is achieved, the prize corresponding to the highest paying pattern is awarded. Many of the 15 patterns can occur in multiple places on the card. For example, the pattern “One Line Any Way” occurs 12 times (i.e., 5 horizontal lines, 5 vertical lines, and 2 diagonal lines much like the Aztec Game). In total there are 53 different ways the 15 patterns can be arranged, and thus there are 53 possible ways of winning. The maximum prize per card is $10,000, which is achieved when the player has wagered $1.00 on a card and has covered all 12 squares of the highest paying “Clover” pattern.
After the player selects the number of cards and wager per card, the player presses the button labelled “4 Cards Selected—Total $4.00—Buy” to initiate the game. There is no button labelled “Play”. As described in the POD brochure, “The cash display on the lower right section of the screen shows your current balance, which increases with winnings and decreases with purchases.”. Using this terminology, expenditures are not referred to as losses but rather as the purchase price of playing, and so any outcome can be presented either as a “non-win” or a “win”.
When play is initiated, 24 random numbers are drawn by the computer and virtually dabbed on all cards in approximately 2 s. The 24 drawn balls are shown on the left-hand side of the screen.
Here we explain the outcome of each of the four cards shown in Fig. 1.
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The top left card has 12 squares dabbed including the numbers 1, 66, and 69, which form an “Any 3 Corners” win that pays $1.00. In Lucky Clover, any winning pattern is highlighted in green (these are shown with thick borders in Fig. 1).
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The upper right card has nine numbers dabbed, but none are part of a winning pattern. In Lucky Clover, any winning patterns that are missed by one square have that missed square shown in flashing red (these are shown as circles in Fig. 1). For example, in the upper right card, the number 19 is displayed in flashing red to indicate that the horizontal line formed by 13, 19, Free, 49, and 66 would have been a “One Line Any Way” win if the number 19 had been picked.
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The bottom left card has 12 numbers dabbed, but no win. It has two squares in red: the 27 in the top left to indicate that the player just missed the “Stamp in Corner” and the 5 in the bottom left to indicate the “Stamp in Corner” in the bottom left was just missed.
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The card in the bottom right has nine numbers dabbed, and no wins. It has the number 7 in red to indicate there would have been a “Stamp in Corner” win if the number 7 had been called. It has the numbers 12 and 65 in red to indicate that an “Any 3 Corners” win would have occurred if either 12 or 65 had been called.
The result of the play in Fig. 1 is that there are winning sounds, the winning card flashes, the winning pattern flashes, and the screen displays “WINNER! You win $1.00.” The player has wagered $4.00 and “won” $1.00—even though the net loss of that play is actually $3.00. In reality the player has not won a profitable prize; what they got was an LDW and six near misses.
Table 2 provides the paytable for Lucky Clover, which was provided to us by OLG. Table 2 shows that the player has a 0.000025 % probability of winning the jackpot of $10,000. In gambling, when the win is equal to the wager it is called a “push.” Table 2 shows that the probability of getting a push when wagering a single card is 7.19 %. We have calculated the column “Plays per Win,” which shows that when playing one card the player wins something, on average, on every 6.08 plays.
Table 2 Lucky clover paytable
When playing four cards on Lucky Clover, the four cards are independent of one another. Each card has a hit frequency of 16.44 %, which means that 83.56 % of plays on a card are losses. We defined the hit frequency as a win on at least one card (i.e. LDWs are included as hits because players typically misinterpret them as wins). So if one were to put wagers on four cards then it would be a hit if 1, 2, 3, or 4 of the cards has a win of any size. We calculated the hit frequency broken down by cards wagered and the results are that playing 1 card has a hit frequency is 16.44 %, for 2 cards it is 20.18 %, for 3 it is 41.66 %, and over half of the outcomes when playing all 4 cards will be a win or LDW (51.25 %).
We wrote a computer program to simulate the playing of one million cards on Lucky Clover. The payback percentage we obtained was 91.94 %, which means an estimated hold of 9.06 %, which differs only slightly due to sampling error from the stated hold of the game which is 8.90 % (see Table 1). In the program we considered the 1,000,000 outcomes as if the player were wagering on four cards at a time, thus yielding 250,000 plays. The 250,000 plays in our simulation had a hit frequency of 51.34 % broken down as follows:
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48.66 % regular losses
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19.13 % LDWs
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32.21 % regular wins
The manner in which the balls are drawn in Lucky Clover is different than in regular/live bingo. In regular bingo, the 75 balls (numbered 1–75) are in one physical drum, and balls are randomly drawn one at a time. The numbers on Lucky Clover are drawn randomly but from five separate arrays, as if from five different drums, with one drum for each of the five letters in B-I-N-G-O. In Lucky Clover there are always five balls drawn between 1 and 15, five between 16 and 30, four between 31 and 45, five between 46 and 60, and five between 61 and 75. The player is not informed about this difference between Lucky Clover and regular bingo. When the 24 balls are shown to the player, as in Fig. 1, they are presented in random order so it is not obvious to the player that the balls are drawn differently than in regular bingo. No explanation is provided as to why the balls are drawn differently than in regular bingo but displayed randomly as in regular bingo.
Fast and continuous play
Like slot machines, Lucky Clover and other POD Bingo games can be played at a much faster rate than paper Bingo. Players are able to complete a play in as little as 2 s, or 30 plays per minute if playing continuously. The high frequency of small wins and LDWs reinforces continued play. For example, assume a player arrives with $20 and plays until broke by betting $1.00 per play with $0.25 on each of four Lucky Clover cards. That player may lose an average of 8.90 cents per spin because the hold of the game is 8.90 %, and it may take an average of 225 spins (20 divided by $0.089) for the player to go broke. Such a session would have the player wagering a total of $225 and at 30 plays per minute it would take approximate 7.5 min for the player to go broke. The player’s original bankroll of $20 is only a small fraction of the total amount wagered. The other $205 is won mostly as LDWs and small wins, with perhaps a few larger wins. With wagers placed on four cards, the hit frequency in Lucky Clover is 51.34 %, so the player would have an average of 116 positively reinforcing hits (225 * 51.34 % equals 116), made up of an expected 73 regular wins and 43 LDWs—even though the player ends up going broke.
Players control the frequency and size of wins
Our computer simulation of Lucky Clover found that players have the choice to increase the hit frequency from 16.44 % with one card played up to 51.34 % with four cards, and that approximately 19.13 % of plays result in an LDW when playing all four cards. Although LDWs are obviously losses, the celebratory sights and sounds that occur during play serve to camouflage this fact (Dixon et al. 2015a) and may positively reinforce continued play (Dixon et al. 2010; Wilkes et al. 2010). The choice of how many cards per play gives the player the ability to control how often they ‘win’, much like slots players can control the hit frequency by their choice of the number of paylines (Harrigan et al. 2011). They can also adjust the nominal size of prizes by a factor of 4 by betting from $0.25 up to $1.00 per card. Giving players control over these parameters has no effect on the hold, but may nevertheless give players a sense that they can improve their odds of turning a profit if they play skilfully. These superfluous controls are therefore likely to support cognitive distortions such as illusion of control and gambler’s fallacy that are common among problem gamblers (Goodie and Fortune 2013).
Near misses
Near misses in games of chance are objectively equivalent to an outright miss, but appear similar to wins and subjectively motivate continued risk taking. This may happen in slots games by heightening the anticipation of imminent reward (Clark et al. 2013; Dixon et al. 2013), by increasing excitement and physiological arousal (Dixon et al. 2011), and possibly by suggesting to the player that they are becoming skilled at the game (Griffiths 1991; Reid 1986). The fact that Lucky Clover highlights the near-misses with flashing red graphics means that players are frequently reminded of near-misses, which occur on over 30 % of cards.
List of past wins
Lucky Clover provides the player with a list of the past ten wins, but not the losses. This feature increases the salience of past wins compared to past losses and makes the wins more memorable (Scoboria and Wilson 2011). Problem gamblers might use this information in their vain attempts to predict future outcomes according to distorted heuristics like the gambler’s fallacy (Tversky and Kahneman 1974) or hot hand fallacy (Gilovich et al. 1985). The game could easily be designed not to have this listing of wins, and its only purpose appears to be to stimulate poor decision making among players who have a tendency toward cognitive distortions that are typical of problem gamblers.