Casino Enterprise Management

Discounting Player Losses

By Jim Kilby and Anthony F. Lucas

Editor’s Note: The following article is an excerpt from the book, Principles of Casino Marketing, written by Jim Kilby and Anthony F. Lucas. You can find out more about their book at www.principlesofcasinomarketing.com.

Discounts on loss were originally used to entice players to pay outstanding gambling debts. In the late 1970s and early 1980s, when few jurisdictions offered gambling, there were few premium players. Although the gaming action of these players pales in comparison to that of today’s high rollers, they were great players for their time. Consider the early 1980s, an era before gambling debts were legally collectible. In those days, casino executives had few options for dealing with players who refused to pay outstanding gambling debts.

These early high rollers were known to play for dozens of hours during a single trip, breaking only to eat and sleep. When their trip ended, casino executives could be holding in excess of $1 million in signed markers. (This was a much more considerable sum in the 1980s than it is today.) At this point, management would attempt to collect the debt, which often became a waiting game.

When a player applied for casino credit, he was asked how he planned to settle any outstanding debt. Typically, the terms of the credit allowed for a maximum of 45 days in which to settle outstanding debts. Unfortunately, players often failed to adhere to the stated terms of the collection policy. It was not unusual for a gambling debt to remain outstanding for periods in excess of one year.

As a result of these extended collection periods, the discount on loss was born. This incentive was originally conceived to encourage early settlement of outstanding gambling debts. From those humble beginnings, discounting has grown into a remarkably expensive marketing tool. The primary use of discounts has also changed, as casino marketers have transformed a collection incentive into a play incentive.

To some degree, discounts are offered by nearly all major U.S. casinos and many other casinos throughout the world. Yet, despite widespread use, it seems as though few executives understand how a discount on loss affects the underlying mathematics of casino games¹. This is a serious statement, as gaming is a core product, if not the core product, for many of these executives. Without knowledge of discount mechanics, management can severely damage the earnings of a gaming property. Therefore, understanding the potentially devastating effects of discounts is not only of vital importance, it is also a critical responsibility of casino executives.

Cost of a Discount
A discount on loss effectively reduces the casino’s advantage. Consider the following example. Let’s assume that management replaces the double-zero roulette wheels with single-zero wheels. The double-zero wheels have a 5.26 percent house advantage, while the single-zero wheels have a 2.7 percent house advantage. In effect, this exchange would reduce the house advantage by 48.7 percent ((0.0526 – 0.027) / 0.0526). Discounts on loss have the same effect, as they alter the house advantage of the games. For example, the casino can expect to win only a portion of the player’s losing wager under the terms of a discount.

Before implementing a discount on loss program, casino executives must understand how the discount affects the house advantage, the cost of the discount, and how to establish a program that encourages play. Surprisingly, many existing programs actually provide an incentive for players to minimize play. Most importantly, the program design must ensure that an acceptable amount of profit is produced.

Discount Cost Framework
A discount on loss of 10 percent seems straightforward to most gaming executives. However, math involving probabilities is often more difficult than it appears, especially with regard to setting up the problem to be solved. The math related to discounts is no exception. To demonstrate this point, consider the subtleties associated with the following cost principles:

•    Within the context of the expected value formula, the cost of the discount is dependent upon the game’s outcome probabilities and the amount of the discount.
•    The cost of the discount is dependent upon the number of hands or rounds played.
•    The cost of the discount is dependent upon the volatility of the wagering activity, with respect to the dollar amount wagered per decision.
•    The cost of the discount is affected by the bet’s payoff odds.

Game Probabilities and Discount Magnitude
If a player receives a 10 percent discount, the casino is returning 10 percent of the dollar amount lost by the player. Thus far, the cost appears to be 10 percent. However, this is where the misconception begins. The cost of a discount is not the percentage of the actual loss returned to the player. In fact, the cost of the discount should be thought of in terms of the percentage decrease in house advantage resulting from the offer. For instance, let’s assume the customer plays one hand of baccarat and wagers one unit on the player proposition. The payoff on a winning player-side wager is one to one. The probabilities associated with baccarat outcomes are as follows:

Player hand win = 0.4462466
Banker hand win = 0.4585974
Tie = 0.095156

In this scenario, the player’s expected value would be computed as follows:

(0.4462466 * 1) + (0.4585974 * -1) + (0.095156 * 0) = -0.012351

Alternatively stated, the player would be expected to lose 1.2351 cents per dollar wagered. If a 10 percent discount on loss carries a cost to the casino of only 10 percent, then a discount, after one hand, should reduce the expected value (1.2351 cents) by 10 percent. However, that isn’t the case. Per the terms of the discount, the player would only lose 90 percent of his wager on losing hands, but he would win 100 percent of it on winning hands. Remember, the player-side wager carries a one-to-one payoff. Plugging these revised terms into the previous formula, the following result is produced:

(0.4462466 * 1) + (0.4585974 * -.90) + (0.095156 * 0) = +0.03351   

Remarkably, the player would now be expected to win 3.351 cents of every dollar wagered. In summary, the bettor has gone from a disadvantage of 1.2351 percent to an advantage of 3.351 percent. A discount after one hand costs the casino its entire advantage and more! In fact, the casino suffers a 371 percent decrease in the house advantage. Of course, any decrease in excess of 100 percent turns the game in favor of the player, making this a startling result.

Principle: The cost of the discount is dependent upon the game’s outcome probabilities and the amount of the discount.

Number of Decisions
If a player were to play two consecutive hands before receiving the discount, the difficulty of the math increases. After playing two hands, the player could have won the first and lost the second, lost the first and won the second, tied/pushed the first and won the second, etc. Figure 1 shows a tree diagram that illustrates all of the possible two-hand outcomes.

Figure 1: Possible Outcomes for Two Hands of Baccarat

Table 1 summarizes Figure 1 by listing all possible outcomes, their associated probabilities, and the resulting expected value. In this case, the expected value represents the player disadvantage.

Table 1: Summary of Figure 1

The player’s expected value divided by the total wager of two units equals the player’s disadvantage. If the sign were reversed, it would represent the house advantage. That is, a player disadvantage of -1.235 percent results in a house advantage of 1.235 percent. The following equation computes the player disadvantage on the player-side wagers.

-0.02470 / 2 = -0.01235, or -1.235 percent²

However, with a 10 percent discount, the player forfeits only a fraction of the loss incurred over the two-hand period. When the player wins, he is paid the full amount. The probabilities of the outcomes do not change; only the cash flows associated with the player’s losing outcomes are revised. These revised outcomes produce an increased expected value for the player. In fact, the increase is profound, as it transforms the previous player disadvantage into a player advantage. Table 2 summarizes the effect of the discount on the player’s expected value.

 Table 2: Effect of 10% Discount

The following equation computes the player’s new expected value:

0.02609 / 2 = 0.01344, or 1.344 percent

Note that this is a positive value, reflecting a house disadvantage. That is, a 10 percent discount after two hands decreases the casino’s game advantage by 209 percent (i.e, from 1.235 percent to -1.344 percent). Of course, any decrease in the house advantage equal to or greater than 100 percent will result in negative cash flows for the casino. In fact, management must retain at least enough t-win to cover operating costs.

Remember, in the first example, the player also received a 10 percent discount but played only one hand. In the one-hand scenario, the 10 percent discount decreased the casino’s house advantage by 371 percent. By increasing the number of hands played from one to two, the same 10 percent discount decreased the casino’s game advantage by 209 percent. Although neither result is profitable for the casino, it demonstrates an important point. That is, as the number of decisions increases, the cost of the discount decreases, all else held constant.

Principle: The cost of the discount is dependent upon the number of hands or rounds played.

Wagering Volatility
In the previous example, the two-hand outcome distribution was based on the assumption of a constant wager. Such wagering behavior is often referred to as flat betting. When the amount of a player’s wager remains constant, the casino’s discount cost is minimized. However, as the player varies the amount of his wagers, the cost of the discount increases. To demonstrate this phenomenon, let’s assume the player makes two wagers: $1 on the first hand and $10 on the second hand. Figure 2 shows a tree diagram that illustrates all the possible two-hand outcomes of such a scenario.

Figure 2: Two-Hand Outcomes in Baccarat Uneven Wagering

 

Table 3 summarizes Figure 2 by listing the net gain or loss (A) along with the compound probabilities of each possible two-hand outcome (B). The products of each net gain/loss and its associated probability (A x B) are summed, producing the player disadvantage, or expected value. 

Table 3: Two-hand Outcome Distribution & Expected Value – Uneven Wagering

The following formula computes the player’s disadvantage by dividing the expected value from Table 3 by the total amount wagered over the two hands of baccarat:

-0.13586 / $11 = -0.01235, or -1.235 percent

Of course, by reversing the sign from negative to positive, this quotient also represents the house advantage. As always, before any discount, the house advantage on player-side wagers in baccarat is 1.235 percent. However, if the player is granted a 10 percent discount on loss, the player’s expected value becomes positive. Alternatively stated, the casino’s expected value becomes negative. Table 4 shows the computation of the player’s expected value.

Table 4: Effect of 10 percent Discount – Uneven Wagering


The following formula computes the player’s advantage, after the discount, by dividing the expected value from Table 4 by the total amount wagered over the two hands of baccarat:

0.32768 / $11 = 0.0298, or 2.98 percent

This player advantage of 2.98 percent is increased from 1.34 percent in the previous example. The player advantage computed from the previous example (1.34 percent) was also based on a two-hand scenario; however, flat betting was assumed. The increase to 2.98 percent was caused by the introduction of wagering volatility. That is, by varying the amount of the bets from the first to the second round, an increase in the player advantage occurred.

Principle: The cost of the discount is dependent upon the volatility of the wagering activity, with respect to the dollar amount wagered per decision.

Effect of Payoff Odds
The cost of the discount is also affected by the bet’s payoff odds. This principle is most germane to roulette play. Consider the double-zero roulette player who always wagers on propositions with 1:1 payoffs, such as red, black, odd, even, etc. All else held constant, discounting the losses of this player will cost the casino less than discounting the losses of a roulette player who always places bets on single numbers. A winning single-number wager is paid at a rate of 35:1.

To demonstrate the effect of the payoff on the cost of the discount, let’s first examine the cost of a discount when players wager on propositions that pay 1:1. These bets are also known as even-money wagers. Next, we will examine the effects of the same discount on players who place single-number wagers. Table 5 lists all possible outcomes, the probability of each possible outcome, and the resulting expected value for players who make even-money wagers.

From Table 5, the casino can expect to win 5.26 percent of every dollar wagered. How will a 10 percent discount affect this house edge? Table 6 lists all possible outcomes, the probability of each possible outcome, and the resulting expected value for players who make even-money wagers. However, in Table 6, the player’s expected value is computed after considering the effect of a 10 percent discount. Further, this revised expected value is computed after a single spin of the wheel.

Table 6: Effect of a 10% Discount – Even-money Roulette Wagers

In this case, the cost of the 10 percent discount is 100 percent of the game’s base advantage. That is, the house would relinquish its entire advantage. Management should expect to earn nothing from this player.

Next, the house advantage associated with single-number roulette wagers is computed. Table 7 lists all possible outcomes, the probability of each possible outcome, and the resulting expected value for players who make single-number wagers.

Table 7: Single–Spin Outcome Distribution and Expected Value – Single-Number Roulette Wagers

The expected value of 5.26 percent from Table 7 is common to the double-zero wheel, when no discount is applied. Table 8 also contains all possible outcomes, the probability of each possible outcome, and the resulting expected value for players who make single-numbers wagers. However, the expected value in Table 8 includes the effect of a 10 percent discount. Notice that the casino no longer wins one unit from the player. The casino now wins 90 percent of one unit.

Table 8: Effect of a 10 percent Discount – Single-Number Roulette Wagers

The 10 percent discount proves to be disastrous, as the casino’s advantage is decreased by 185 percent. Here, the discount has created a player advantage of 4.474 percent. In summary, the same 10 percent discount reduced the house advantage by 100 percent when applied to even-money wagers, but reduced the house edge by 185 percent when applied to single-number wagers. Although both cases are completely unacceptable, the effect of the payoff on the cost of the discount becomes clear.

Principle: The cost of the discount is affected by the bet’s payoff odds.

Equivalent Wagers
Whenever the casino’s advantage is decreased via changes to the game advantage or through a discount on loss, it is important to understand the effects of such actions on the casino’s profitability. For instance, if management were to exchange the double-zero roulette wheels for single-zero wheels, the game’s advantage would be reduced from 5.26 percent to 2.7 percent³ . Such a change would reduce the casino’s advantage by 49 percent. This means that a player wagering $513 on a double-zero wheel will generate the same t-win as a $1,000 bettor at a single-zero wheel. This occurs in spite of the fact that $513 is only 51.3 percent of $1,000.

Unfortunately, most casino executives would prefer the $1,000 bettor to the $513 bettor. However, the $513 bettor should be preferable, as both players will generate the same theoretical win; however, the outcome distribution of the $513 bettor will feature a much smaller standard deviation. Because the t-win is the same, the reduced outcome volatility of the $513 bettor should make him more attractive to management. Alternatively stated, why would management accept increased risk without an increased return? That is, why suffer potentially extreme outcomes for no additional t-win? Table 9 compares the t-win and standard deviation produced by the two bettors after 300 spins.

Table 9: Comparison of Outcome Distributions – Single-Zero v. Double-Zero Bettors
(Assume 300 Spins and Even-money Wagering)⁴

From Table 9, notice that the t-win is nearly identical, while the standard deviation of the single-zero player is nearly twice that of the double-zero player. Not only is the double-zero player’s outcome distribution less volatile, but it is also easier for casino marketers to find $500 bettors. Per the central limit theorem, as the number of same-sized bettors increases, the relative volatility of the collective outcome distribution decreases. That is, as the number of same-sized bettors increases, the likelihood that the casino’s actual win/loss will be near its theoretical win also increases. In the end, the more same-sized bettors casino marketers can attract, the less likely it becomes that management will suffer outcomes that are wildly divergent from the casino’s t-win.

The lesson here is that discounts not only decrease the game’s advantage, but they also retain the standard deviation of the larger bet. To this point, discounts can have further-reaching effects than most might imagine. For example, increased earnings volatility leads to missed earnings projections, which in turn leads to increased cost of capital in equity markets. As casino marketers in most public gaming companies are fond of discounts, management must be mindful of the fallout from the practice. That is, any increases in the cost of capital could certainly affect a company’s expansion and development plans, among many other things.


Structuring a Profitable Model
Aside from providing an overview of a profitable discount model, this section serves as an introduction to the specific steps of program design. As previously demonstrated , the cost of the discount is a function of the following criteria:

•    The game’s outcome probabilities and the amount of the discount.
•    The number of hands or rounds played.
•    The volatility of the wagering activity, with respect to the dollar amount wagered per decision.
•    The payoff odds of the bets placed.

To structure a profitable discount program, one must consider the effect of each of these cost components. Also, the program should be conservatively structured, assuming a worst-case scenario for the casino. For example, if constructing a baccarat program, the worst-case scenario would assume that the bettor will always wager on the banker. This wager would provide the least amount of t-win, all else held constant.

Since the cost of the discount is a function of the total number of hands played, it will be necessary to count the hands played. Further, casino marketers typically require a minimum player loss to become eligible for a discount. Therefore, it will be necessary to calculate an accurate average bet as well. This process of tracking each player’s bet is called “bet tracking.” This eliminates the task of estimating the player’s actual loss, as the amount of every bet is observed and recorded. Bet tracking provides the total number of hands played, the amounts wagered on each hand, and each proposition on which a wager was placed (e.g., banker, player or tie). From this data, management will be able to calculate the player’s actual loss, average bet and number of hands played. When offering a discount to a player, merely estimating these activity measures is not a viable option, although it is routinely practiced.

When estimating the cost of a discount prior to the player’s trip, the casino must also assume some wagering volatility. That is, players cannot be expected to wager the same amount on every hand. In an observation study performed by the management of a Las Vegas Strip casino, it was discovered that the typical discount player’s wagering variance was equivalent to a 1-to-4 spread. That is, 50 percent of the wagers were equal to one unit and 50 percent of the observed wagers were equal to four units. Based on this result/assumption, management would presume that a player with a $1,000 average bet would make half of his wagers at $400 and half of his wagers at $1,600. Obviously, the player’s actual wagering behavior could be more volatile. However, this is a reasonable assumption for use in an a priori⁵  discount program.

Table 10  demonstrates the effect of a discount program on the game advantage within the established cost framework. In fact, a baccarat player could be given a similar type of schedule as a means of describing the terms of the discount program. In the body of Table 10, the estimates of the discount’s cost to the casino are based on three assumptions. First, the bettors only place banker-side wagers. Second, discounts are awarded to players after a minimum loss of $50,000. Third, each baccarat shoe produces 78 hands.

Table 10: Baccarat Discount Schedule

Note: A minimum loss of $50,000 is required to qualify for the discount program. Table assumes all wagers are placed on banker.

A player is credited with completing one shoe after every 78 hands played, as a typical baccarat shoe will last about 78 rounds. It is much easier for players to count the shoes completed as opposed to keeping track of hands played. In addition, it is not unusual for baccarat players to skip hands. Consequently, it is important for management to count only the hands played, as opposed to hands dealt. Counting hands played is important, as the player’s discount increases with the number of shoes completed.

Table 10 shows the casino’s advantage after the effect of the discount. In baccarat, the banker bettor has a base game disadvantage of approximately 1.06 percent. After one shoe is completed (78 hands played), the casino advantage of a $1,000 bettor remains unchanged per the schedule. Although eligible for a 10 percent discount after one shoe completed, the player must also incur a minimum loss of $50,000 to qualify for the program. After only 78 hands, it is virtually impossible to lose $50,000 with a $1,000 average bet. As the average bet increases, this qualification becomes less of an issue. For example, with an average bet of $25,000 the bettor’s disadvantage is .52 percent after one shoe completed and a 10 percent discount on loss is earned. This is a 51 percent reduction in the casino’s base advantage!

The Graduated Discount
In practice, the cost of the discount becomes further complicated, as casinos frequently offer graduated discounts, which are based on a player’s actual loss. For example, let’s consider the player who places 550 wagers of $10,000 each on the player side of a baccarat game. Additionally, let’s assume management has offered him the following graduated discount terms:

10 percent on losses above $100,000
15 percent on losses above $250,000

This graduated discount will cost the casino 23.1 percent of its advantage, on average⁶.  That is, the graduated discount can be expected to reduce the game advantage from its base level of 1.235 percent to 0.949 percent. Alternatively stated, under these terms, a player with an average bet of $10,000 would be expected to generate the same theoretical win as that of a player with an average bet of $7,688 and no discount⁷.  Moreover, the lesser average bet would produce an outcome distribution with a lesser standard deviation. If given the choice, casino marketers should prefer the player who produces the lesser standard deviation. In this case, the $10,000 average bettor offers nothing but increased risk/volatility. He cannot be expected to generate any additional return. Remember, the prospect of increased risk must be associated with the possibility of an increased return.

Although meaningful, the previous example remains simplistic. That is, a player won’t always wager on the player side and he won’t always wager the same amount per hand. Let’s assume a baccarat player places the following wagers:


Wager    Bet    Number of Hands
$5,000    Player    200
$10,000    Banker    200
$2,500    Player    300
$2,500    Banker    300

Let’s also assume the player receives the following graduated discount terms:

10 percent on losses above $100,000
15 percent on losses above $250,000

These wagers along with the graduated discount terms produced the output displayed in Table 11⁸.  Note that the decrease in the base advantage is 19 percent, falling from 1.127 percent to 0.913 percent. Despite the increased complexity of the wagering assumptions, the average cost of the discount can still be computed.

Table 11: Casino Marketing Manager Output

Note: A minimum loss of $50,000 is required to qualify for the discount program.

Game-Specific Discount Terms
For management to maintain a minimum casino advantage, discounts must be game specific and dependent on the number on hands played. As demonstrated, the number of hands played and the probabilities associated with specific bets both affect the cost of the discount. If management is to control the house advantage within a discount on loss program, there is no choice but to provide individual discount schedules for each game. Further, management must not compute a player’s trip loss by combining actual losses incurred on different types of games. Such a practice would violate the game-specific mandate.

Effectively managing combined-loss discounts would be remarkably cumbersome for management and difficult for the players to understand. But if players were permitted to combine actual losses on different game types, discount offers would need to reflect the casino’s worst-case scenario. Remember, the discount is offered before the play occurs. Further, every player would have a different discount schedule based upon his game preferences and play history. This becomes problematic, as players talk to one another and compare deals. Such cross-talk would produce many awkward inquiries. That is, players will ask management why their discount is less than another player’s discount.

It is strongly recommended that casino marketers offer game-specific discount schedules. For management, combined-loss discounting greatly increases the complexity of the process. As a result, estimating the cost of the discount becomes much more difficult. With respect to the players, the inconsistent deal structures create confusion and discord.

Process Misconceptions
It is common practice for management to issue a rebate to the player immediately following that player’s discount-qualifying loss. That is, instead of the player paying his discounted debt to the casino, a second marker is often issued in the amount of the discount. The discount reduces the amount initially owed to the casino, but the second marker cancels the effect of the discount. Under such conditions, the player would be issued casino cheques⁹ in the amount of his original discount. A second marker would serve as evidence of this transaction.

In these cases, the discount does not necessarily serve as a reduction of the amount owed to the casino. That is, if the player loses the rebate cheques during the same visit, his debt to the casino would return to the pre-discount level. This turn of events is not uncommon. However, casino marketers mistakenly believe that such a loss erases the cost of the discount. This is incorrect.

Any play that occurs under the terms of a discount is subject to a reduced house advantage, whether the player wins or loses. In fact, some players will win and some will lose. However, a player’s value to the casino remains a function of the reduced house advantage whether he wins or loses. Remember, the casino does not keep the entire amount lost by losing players. All that is retained is the difference between the amount lost by losing players and the amount won by winning players. This difference represents the casino’s win.

Unfortunately, casino marketers often say, “We only pay the discount when the player loses.” This couldn’t be further from the truth. Remember, the discount reduces the game’s underlying advantage, win or lose. As an example, let’s assume you have only a double-zero roulette game available, but you want to allow a valued customer to play a single-zero game. As a remedy, you could simply place a marker in the double-zero pocket, indicating that this outcome is no longer a possibility. That is, if the ball were to drop into the double-zero pocket, it would be considered as a non-spin. No money would change hands on double-zero outcomes.

Now let’s consider the repercussions of our modified roulette wheel. The double-zero game’s advantage is 5.26 percent. The single-zero game’s advantage is 2.7 percent. What if your valued customer were to play for an hour, and over the course of this hour, the ball never fell into the double zero pocket? Could it be argued that the casino had a 5.26 percent advantage on the wagers, as the double-zero outcome never occurred? Certainly not! The double-zero pocket was excluded as a possibility on every spin, regardless of the outcome. The same condition is present when players wager under the terms of a discount. Win or lose, customers receiving discounts are playing the games with a reduced casino advantage.

Program Structure Issues
There are several design errors common to the structure of conventional discount programs. In fact, many programs used by Las Vegas casino marketers could be considered ill-conceived. For example, these programs require a customer to play for a minimum of 12 hours before becoming eligible for a discount. Such a stipulation seems responsible and prudent. However, all marketing programs should encourage additional play, as opposed to discouraging or limiting play. If management requires the customer to play 12 hours, it soon becomes obvious to the player that he should settle as soon as he reaches the 12-hour minimum. Further, whether ahead or behind, there remains an incentive for the player to settle. For instance, if the player has lost $100,000, after 12 hours of play, why should he continue wagering? His luck could change. He could win $100,000 after surpassing the 12-hour minimum. This would result in a trip loss of zero. With a trip loss of zero, he would receive no discount. Alternatively, had he settled after 12 hours of play, he would have received a discount for posting a $100,000 loss. Assuming a 10 percent discount, this player would have received a $10,000 rebate.

Let’s now consider the opposite case. That is, the player wins $100,000 after 12 hours of play. The player should settle in this circumstance as well. If the player were to continue wagering, he could lose the $100,000, resulting in a trip loss of zero. Instead, the player should settle, leave the casino, walk to another casino and commence play there. The second casino will treat this player’s arrival as a new trip. Of course, this new trip begins with a win/loss basis of zero, as opposed to a player win of $100,000. That is, the casino marketers at the second casino are not concerned with the player’s good fortune at the first casino. In fact, it is not likely that they would be aware of this previous outcome. Should the player win another $100,000 at the second casino, he should move to a third casino. If he loses his $100,000 at the second casino he should settle and accept his discount. This process is so obvious to the players, but most casino executives are seemingly oblivious to it. This conclusion is based upon the abundant availability of such policies and programs.

Quick Loss Policy
Although usually thought of as a subset of discounting, quick loss policies may represent the most costly form of such offers. In short, these policies address players who experience substantial losses before meeting the play requirement of the discount program¹⁰. That is, these players wish to be treated as though their play qualified for the maximum discount, despite their failure to reach the 12-hour play requirement. The availability of quick loss provisions decreases the average number of hands played by those receiving discounts. Not only is the cost of the discount increased for those awarded quick loss rebates, but the overall cost of the discount program is also increased by such policies. Remember, all else held constant, fewer decisions increases the cost of the discount.

Discounts and the Comp Basis
The process of awarding comps to players is also complicated by discount programs. Of course, premium players expect more than just a discount in return for their play. These players expect to receive a complimentary room, food and beverage awards, and often an airfare reimbursement as well. As the casino advantage is a function of the bets placed, amounts wagered and rounds played, most casino marketers are unable to compute the discount-adjusted casino advantage. After all, this is the casino’s true advantage, as the discount changes the game. This reduced house advantage directly affects the computation of t-win, which is used to determine the dollar amount of the comps that a player receives. If a player receives comp awards and an airfare reimbursement based on the game’s original house advantage, management will overcomp that player. The discount-adjusted house advantage must be used to compute a player’s comp basis, as it is the discount-adjusted t-win that will be available to cover these costs and provide a profit. Unfortunately, the discount-adjusted t-win is seldom computed, resulting in rampant overcomping.

Recommendations
Given the obvious complexities of the discount process, it makes sense to simplify the design and management of the discount program. In this article, we have shown that several factors can influence the cost of discounts. Further, only careful consideration of these factors can ensure acceptable profits.

Additionally, discount programs should be structured such that they encourage play, as opposed to discouraging or limiting it. To this end, the program structure must award increased play with an increased discount. Such a design will allow the player to determine the size of his discount.

Finally, management must recognize that most casino marketers are not able to effectively negotiate discounts. Consequently, they must be provided with schedules that clearly identify the program structure, including comp and airfare awards. These schedules will protect casino profits, while providing a discount program that is readily understood by casino marketers and players alike.

Footnotes

[1] Salmon, J., Lucas, A.F., Kilby, J., & Dalbor, M. (2004). Assessing discount policies and practices within the casino industry. Gaming Research & Review Journal, 8(2), 11-25. Binkley, C. (2001, September 7).  Reversal of fortune. Wall Street Journal, pp. A1, A8.

[2] Player disadvantage on player-side wagers from Kilby, J, Fox, J, & Lucas, A.F. (2004). Casino Operations Management, 2^nd ed., New York: Wiley, p.216.

[3] Kilby, J, Fox, J, & Lucas, A.F. (2004). Casino Operations Management, 2^nd ed., New York: Wiley, p. 150.

[4] T-win and standard deviation computed using Casino Marketing Manager software, version 3.3.2. This software was designed to calculate the cost of discount offers. Free trial-downloads available at JimKilby.com.

[5] In an a priori discount program, players are offered discounts before any wagering occurs. This differs in concept and purpose from a discount that is offered as an attempt to collect an existing and outstanding gambling debt.

[6] The cost of the discount was calculated using the Casino Marketing Manager, version 3.3.2. Assumptions included the eligibility requirement of a minimum player loss of $50,000.

[7] Ibid.

[8] Ibid.

[9] Casino cheques are gaming chips that carry a specified monetary value. Cheques can be wagered on different casino games or redeemed for cash. Unlike cheques, chips do not have a predetermined monetary value. Chip value is assigned at the time and place of purchase, which is the only place chips can be wagered or redeemed. Chips are most common to roulette. Unfortunately, the terms cheques and chips are used interchangeably in the industry, in spite of the aforementioned distinctions.

[10] For more on quick loss policies see Kilby, J, Fox, J, & Lucas, A.F. (2004). Casino Operations Management, 2^nd ed., New York: Wiley, pp. 308-310 & Lucas, A.F., Kilby, J. & Santos, J. (2002). Assessing the profitability of the premium player segment. Cornell Hotel & Restaurant Administration Quarterly, 43(4), 65-78. 

Anthony F. Lucas, Ph.D. has won several academic awards for his research in the area of casino marketing, while serving on the faculty at the University of Nevada, Las Vegas. Drawing on his research along with his 10 years of gaming industry experience, Lucas actively serves as a consultant to casino companies. Additionally, he co-authored the 2nd edition of Casino Operations Management, a popular text and reference book.

Jim Kilby, formerly the Boyd Professor of Gaming at the University of Nevada, Las Vegas, has over 35 years of experience in the gaming industry. He also actively serves as consultant to casinos across the globe. Kilby is the co-author of Wiley’s Casino Operations Management. He also developed “Casino Marketing Manager,” a popular software program developed to assist casinos in marketing the premium casino customer. For more information, visit JimKilby.com.

For more information, visit www.principlesofcasinomarketing.com.