The widespread implementation of free slot play awarded on the basis of a player’s theoretical or actual gambling loss has created two camps regarding the cost of awarding free slot play to a casino player—a payback camp and a free camp. The payback camp argues that the cost is the payback percentage of the slot machine that the player chooses to redeem the promotional credits on. For example, if the game is a 95 percent payback game and the player is given $10, the cost is $9.50. The free camp argues that the longer the customer plays, the less the cost of the promotion and assumes that if a player plays for a very long time, the cost to the casino is nothing. This argument finds a base in the fundamental theorem of gambling: The longer a slot player gambles, the greater the chance that the casino will win all of the money available to the player.
This view is best expressed by Robert De Niro, who plays a casino boss in the movie Casino. The cardinal rule of gaming, according to De Niro’s character, “… is to keep them playing, keep them coming back. The longer they play, the more they lose. In the end, we get it all.”
No player, however, can or will play forever. Play may end when she runs out of time or when she runs out of money. Play may also end when her win reaches a certain threshold. In these cases, a player may leave with some or all of the free play she was awarded in addition to any win or unspent amount from her money budget.
This study quantifies the cost of free slot play by simulating different types of players awarded different amounts of free play while playing machines with different characteristics. In our simulations, players with equal money budgets are distinguished by their time budgets, free play awards and jackpot win quitting thresholds. Machines are distinguished by their hold percentages and volatilities. The simulator runs each player type through 50,000 sessions on four types of slot machines, a volatile and a non-volatile machine with a high and a low hold percentage. A random number generator that is commonly used in the gaming industry for slot machines determines the outcome of each game within each session.
Our simulations confirm that free slot play costs the casino nothing when players play without limit, accomplished by simulating 50,000 players without time budgets or jackpot win thresholds. If a player plays forever, the cost of free slot play is zero.
We simulate outcomes for a player with a money budget of 500 tokens, where each token affords her a single pull on a popular 3-reel slot playing maximum bet. Play is simulated for 50,000 sessions for each of 48 scenarios, unique combinations of machine characteristics and player characteristics: machine volatility (low or high); machine hold (5 or 15 percent); the player’s free play award (15 or 30 tokens); the player’s win threshold (2,500 or 5,000 tokens, i.e., five to 10 times the player’s money budget); and the player’s time budget (240, 480, or 720 minutes, i.e., 2,400 pulls, 4,800 pulls or 7,200 pulls, assuming 10 pulls per minute). The free play amounts of 15 and 30 tokens reflect 10 and 20 percent rebates on expected theoretical win on a 5 percent hold slot machine for a player with a 300 minute time budget and 500 token money budget. A player’s session ends when her money budget plus free play award runs out, when she runs out of time, or when she hits a jackpot or wins an amount that carries her bankroll, including the tokens she started with and the free play award she received, over her threshold to walk. When these events occur, the simulator totals the player statistics and sums them for the entire scenario.
Cost of Free Play
We found that neither the payback camp nor the free camp is right. The cost of free slot play declines the longer a slot customer is willing and able to play on her visit to a casino. The long-run cost, in theory, is zero—in the end, the casino gets it all back. In practice, however, the expected cost depends on complicated interactions between the amount of the bonus relative to the customer’s gambling budget, the customer’s quit behavior upon winning a sizable amount of money, and the hold and volatility characteristics of the game the customer plays. Computer simulations of 48 scenarios reveal the following dynamics associated with the cost of free slot play:
• The cost decreases when the hold percentage increases
• The cost increases when the volatility of the game increases
• The cost decreases with the length of time a customer is willing to play
• The cost decreases with the customer’s win threshold, i.e., the amount of winnings at which the customer quits playing
• The cost increases with the amount of bonus relative to the player’s own budget
The costs of free play in terms of numbers of tokens is summarized in Table 1. In later tables, the costs are shown as percentages of the 15 and 30 token bonuses given.
Impact of Hold Percentage
The simulations revealed that an increased hold percentage substantially reduces the cost of awarding free play. Games with a 200 percent increase in hold percentage, from 5 percent to 15 percent, reduce the cost of free slot play by 46 percent (41 percent vs. 76 percent). The trend is similar at both the 15 and 30 token award levels. For a 15 token award, a 200 percent increase in hold percentage decreases the cost of free slot play by 46 percent (40 percent vs. 76 percent), and at the 30 token award the decrease is 43 percent (43 percent vs. 76 percent).
Hold percentage impact on the cost of free slot play is due to several factors. All other things being equal, a higher hold percentage reduces the amount of games a player can play for a given budget, thus lowering the odds that a player will hit the threshold that will cause her to leave with his winnings.
Impact of Game Volatility
In general, as machine volatility increases, so does the cost of awarding a player free slot play. The less volatile game in our simulations reduced the cost of free slot play by 29 percent compared with the cost of the more volatile game (66 percent vs. 52 percent). In simulations where players were awarded 15 tokens, the cost of the bonus was 30 percent greater on the volatile machine than on the non-volatile machine (65 percent vs. 50 percent). This remained true when players were given a 30-token bonus, where the average cost on the volatile machine was 29 percent greater than on the non-volatile machine (67 percent vs. 52 percent). The higher the volatility index, the larger the top pay values in a pay table and the greater their associated probabilities of occurrence. Hit frequency was reduced, however, so the machine’s hold percentage remained constant. High volatility increases the cost of free slot play because a player is more likely to hit a jackpot and quit. Pay table distribution plays a role in the cost of free slot play based upon how it impacts the length of player sessions. The longer sessions on non-volatile machines reduce the cost of free slot play and conversely, the shorter sessions on volatile machines increase the cost of free slot play.
Impact of Game Volatility and Hold Percentage
We next compared the cost of free slot play on a high volatility, low hold percentage machine with the cost on a low volatility, high hold percentage machine. The results were dramatic. The low volatility, high hold percentage game cost of awarding free slot play is 61 percent less expensive than the high volatility, low hold percentage game (31 percent vs. 80 percent). In addition, the cost on a high volatility, high hold percentage game is 28 percent less expensive than the cost on a low volatility, low hold percentage game (52 percent vs. 72 percent).
We also found that on a 5 percent hold machine, a low volatility game reduces the cost of free slot play by 15 percent compared with a highly volatile game (72 percent vs. 80 percent); and on a 15 percent hold machine, the low volatile game reduces cost by 40 percent compared with the high volatile game (31 percent vs. 52 percent). For a high volatility game, 15 percent hold reduces the cost of free slot play by 35 percent compared with the cost of a 5 percent hold game (52 percent vs. 80 percent), while for a low volatility game, 15 percent hold reduces the cost by 56 percent compared with a 5 percent hold game (31 percent vs. 72 percent).
Our simulation results thus suggest that a large difference in hold percentage has a greater impact on the cost of free play than volatility. Tighter machines are more effective in reducing the cost of free play on non-volatile machines than on volatile machines, because big jackpots that cause the player to quit are less frequent. The longer she plays, the better the chance a casino will recoup any free slot play a player is given.
Impact of Player Win Threshold
We found the percentage cost of an award was roughly the same for both the 2,500 and 5,000 token win thresholds. We also found that a higher win threshold has little effect on the percentage cost of an award, whether on a volatile or non-volatile machine. Our simulation results again highlight the impact of volatility on the cost of an award: The volatile game is 26 percent more expensive at the 2,500 token threshold (53 percent vs. 67 percent) and 30 percent more expensive at the 5,000 token threshold (50 percent vs. 65 percent). The increasing cost at the 5,000 token threshold results from the paytable distribution inherent in the volatile game. Simply put, a player is more likely to hit that threshold and quit on a volatile game than a non-volatile game.
A casino can expect to win back more of a free slot play award than the hold percentage of the machine being played. It cannot, however, expect to win it all back. Thus, neither the payback nor the free camp is right. Our simulation results establish that the cost of free slot play to a casino depends on player behavior and machine characteristics. Too-generous awards can be unprofitable when other costs of servicing a guest are considered. Care should be taken when determining the percentage of player bankroll or expected player loss awarded as free play. Our simulation results suggest that awards can be most generous to players who prefer non-volatile to volatile machines and, quite obviously, to players drawn to high hold rather than low hold games, as well as to players willing to play a reasonably long time. Our results also suggest that the cost of free slot play to a player who shoots for a very large win before she quits, and hence plays a long time, is not much less than the cost of the same award to a player with a lower win threshold.
Professor Malamud, a graduate of Polytechnic University, Carnegie-Mellon University and New School University, has taught a wide variety of courses since joining the UNLV faculty in 1968. He recently served on the Clark County Planning Commission and consults to the legal profession and the gaming industry.
Jeff Jordan has worked for 16 years in a variety of roles in the gaming industry, most recently as IGT’s Director of Product Strategy and Marketing Research. He also served IGT as Director of Corporate Strategic Planning and Strategic Business Development. He also was an executive at Acres Gaming where he served as a Corporate Development and Operational responsibilities.