“Knowledge Should Defeat Fear” – Understanding the high stakes game of Baccarat – Part I.
by Andrew MacDonald and William R. Eadington
Most people unfamiliar with the Macau gaming market who look at the revenue figures that come out of Macau’s casinos are amazed both by the volume of gaming revenues and their source, based on game type. Macau’s gross gaming revenues—which were US$5.6 billion in 2005—have almost overtaken those of the Las Vegas Strip and are widely expected to surpass the Strip in the next year or two. Furthermore, it is likely that Macau’s gaming revenues will overtake those of the entire State of Nevada (US$12.2 billion in FY2006) some time between 2010 and 2015.
The breakdown of gaming revenues by source is perhaps even more interesting, especially for analysts used to Western patterns. In Nevada, about 70% of all gaming revenues come from slot machines, with the balance coming from table games. In Macau in 2005, table games accounted for 96.5% of gross gaming revenue. Furthermore, Baccarat represents over 86% of the total of all table game revenues. In Nevada, Baccarat makes up only about 25% of table game revenues and 8% of total gaming revenues. Baccarat is not a game that is terribly familiar to most American players and operators, and its various nuances and vagaries can confuse investment analysts and operators alike when they try to comprehend the evolving gaming scene in Macau.
The issues that most often confuse and confound are not those related to understanding the game of Baccarat itself—which is a relatively simple card game—but rather the numbers and ratios associated with various metrics that are applied to the game. The main measures in question are hold percentage, also known as hold or win percentage; and house advantage, also called the win rate or the house edge. The numerator in these measures is always win (the amount retained by the house after taking losers and paying out winners). The denominator, however, is different for each measure and therein lays the root of much confusion.
Consider first the hold percentage, a classic measure that has been used by the casino industry for many years. The hold percentage at table games is the amount won divided by the drop on the table. Drop is the amount of cash and other negotiable instruments that are taken by the dealer at the game—and placed into the drop box—in exchange for chips. The total amount of funds in the drop box is counted at some interval when the drop box is removed and taken to a counting room for that purpose. This may occur at the end of a gaming day (often around 6 a.m. in the morning) or at the completion of each shift. The win for a game is calculated based on the closing chip inventory plus cash plus credits (chips removed from the table and returned to the chip bank) plus chip purchase vouchers, less the opening chip inventory and any fills in chips brought to the table during that period from the chip bank.
Until quite recently, there has been no real ability to measure the total amount wagered at a table game. Therefore, the drop at the game was used as a measure of relative activity, and served as a proxy for handle, the aggregate amount of money wagered, the summation of all wagers made at the game. The hold percentage was seen as a reasonable means to measure efficiency. It therefore became embedded as a measure within casino operations against which game performance would be compared. Unusual variations signalled possible illegal activity (from cheating or skimming, for example,) or significant changes in efficiency (possibly as a consequence of changes in floor layout or dealing procedures.)
The hold percentage on the game of Baccarat in Nevada typically ranges between 11% to 12.5%, depending on the style of game being played. In the short term however, there can be substantial variation due to the volatility of the game (i.e. the “luck” of the players relative to the house.) As long as there are only a handful of substantial players who wager very large amounts of money per hand, their specific outcomes can have a noticeable impact on a single casino’s financial performance, which can show up even for the entire market in the short term. For example, in June 2006, Nevada casinos experienced a hold percentage of 8.81% on Baccarat, whereas in April 2006, it was 14.52%; for the entire 2005-2006 fiscal year, the average hold percentage was 10.89%.
Besides luck, variations in hold percentage from jurisdiction to jurisdiction are primarily due to the relative speed and productivity of the games as well as player buy-in and cash-out behaviour, as well as accounting practices. As the underlying game rules are identical, these other factors are the only possible explanations. In Australia and New Zealand, where Baccarat is played under the same rules as the United States, the hold percentage typically ranges from 15% to 20%. In Macau the hold percentage for Baccarat is in the 15% to 17% range. These are clearly significant differences for essentially the same game.
This raises an important fundamental point regarding hold percentage. Hold percentage can be a useful empirical tool, but it relies on a denominator that is easily influenced by customer behaviour, casino procedures, and accounting practices. Furthermore, the metric is not statistically verifiable using deductive probability computations. Therefore care needs to be taken when talking about and comparing hold percentages.
The other commonly used measure for Baccarat is house advantage, or win rate. This is a statistical measure defined as win divided by handle, the total amount wagered. It is a statistic that has a corresponding parameter value in many casino games which can be determined from the underlying probabilities and pay-offs of the game. This is the case with Baccarat, which has a fixed set of rules by which it is played. The parameter—which is a single unvarying number, such as 1.06%—is often called the theoretical house advantage or the theoretical win rate; statisticians might call it the game’s expected win rate.
For the game of Baccarat, there are generally only three distinct wagers that can be made: “Player”, “Banker” and “Tie”. With respect to the “Player” and “Banker” bets, there are additional complications that occur in computing house advantage from actual play results. In these cases, the issue lies in the concept of resolved bets. In some jurisdictions or within some casinos, the computed house advantage is quoted as a function of all decisions (including Ties,) whereas in others, it is computed only with resolved decisions (Player wins and Banker wins.) The latter case is justified by the argument that, when a tie occurs, nothing happens with regard to the bets on “Player” and “Banker;” therefore these situations should be ignored. Rather than arguing for one measure over the other, it is best to understand that one will encounter both cases when reviewing casino or jurisdiction Baccarat data, and both should be considered correct. Note also that the number of decks used can also have a slight effect on the parameter values for the theoretical house advantage.
There are five distinct win rates for the game of Baccarat. Based on resolved decisions only for an eight deck game, the win rates are:
“Banker:” 1.17%
“Player:” 1.36%, and
“Tie:” 14.36%.
These are known as the relative win rates.
Based on all decisions (including Ties) for an eight deck game, the win rates are:
“Banker:” 1.06%
“Player:” 1.24%, and
“Tie:” 14.36%.
These are known as the absolute win rates.
Note that the theoretical house advantage for Tie bets is the same in either case, because the Tie bet is always resolved, i.e. it either wins or loses on each hand. Thus, there are five unique parameter values that apply to the theoretical house advantage for Baccarat.
Casinos and analysts often quote only one summary win rate or house advantage value for Baccarat, which can result in additional confusion. In effect, they are assuming a blended average between “Player” and “Banker” house advantages has been computed. If the casino is using the relative win rate standard, then the blended average would typically range between 1.26% and 1.35%. A “correct” computation would depend on the relative amounts actually wagered on the bets of “Player”, “Banker” and “Tie”. Thus, if a blended average is used, it may reflect the historical betting patterns experienced—if indeed these have been measured.
It should also be noted that even a small percentage of handle wagered on “Tie” can have a significant impact on the blended average. For example, if the amount wagered on” Banker” was 59.5% of handle, 40.0% of handle wagered on “Player” and 0.5% of handle wagered on “Tie.” then the blended average using the relative win rate would be 1.31%. On the other hand, if the percentage breakdown on handle was (respectively) 58.0%, 40.0%, and 2.0% for “Banker,” “Player,” and “Tie,” then the blended average would be 1.51%.
The theoretical house advantage is a parameter value—a fixed number that can be deduced from probability analysis for any particular game—whereas the estimated house advantage and hold percentage are both empirical measures. In the long run, the estimated house advantage must converge to the theoretical house advantage, but there is no similar anchor for the hold percentage. This is why, when both can be computed from empirical data, there is a preference to use the estimated house advantage as a monitoring metric for casino games and gaming devices.
One way of understanding the empirical relationship between estimated house advantage and hold percentage is to consider the hold percentage as a measure of the churn of the drop in relation to the handle. By definition, churn is the ratio of handle to drop, and it serves as a multiplier for how much the average player wagers based on the volume of chips that he initially purchased from the dealer in the game. This is inherently a behavioural empirical measure and, as such, there is no parameter value with which it can be associated. (The same is true for hold percentage in general.)
To illustrate this relationship, consider the following. Suppose that over a one-month period for a single casino, the blended average relative win rate (theoretical house advantage) is 1.31%; the estimated house advantage (if indeed it had been observed) was 1.22%; and the hold percentage was 16.00%. Then, by definition, the churn would be the ratio of handle to drop, which is equivalent to the ratio of hold percentage to estimated house advantage. In this case, that ratio would be 13.11 (=16.00%/1.22%), the empirical value of the churn.
The higher the churn, the higher the hold percentage, other things equal; and the higher the estimated house advantage relative to the relative win rate (theoretical house advantage,) the lower the churn. (This latter case would be consistent with the house playing “lucky” or the players playing “unlucky,” losing at a faster rate than chance would predict.) Thus, churn rates may vary based on customer behaviour, casino procedures, or vagaries of luck (volatility of outcomes) in the game. Faster game play, longer playing time, and “unlucky streaks” can all result in higher hold percentages being observed.
Everything said up to this point is generic: it applies to Baccarat as played in virtually any casino in the world. However, Macau has some unique practices that have evolved in that particular jurisdiction that add further seeds of complication to this discussion. A high proportion of Baccarat play in Macau takes place in VIP rooms, which are gaming rooms contracted out to private contractors by the casino concessionaire (historically SDTM and, since 2002, their subsidiary SJM; more recently, concessionaires have included Galaxy, the Sands Macau, and Wynn Macau.)
The VIP room contractors would purchase dead chips (non-negotiable chips that could only be used in play) from the casino concessionaire to be resold to VIP player representatives. In turn, the contractors would receive a percentage commission—say 0.7%—on the volume of dead chips they purchased. (Dead chips are also known by a number of other names. They are also called non- negotiable chips, rolling chips, or mud chips.) The representatives would then sell the dead chips to players who would use them in actual play. (The commission received on the volume of dead chips purchased by contractors is the source of profits and expenses for themselves and their VIP player representatives.) When players win a wager with dead chips, they are paid off in live (negotiable) chips, which can be redeemed at the casino cage for cash, but are more typically bought back by VIP room player representatives for dead chips; this process is called chip rolling. In order to add to their profits, VIP player representatives—working under VIP room contractors—continually purchase live (negotiable) chips from players when the players win hands. In this manner, players only make wagers with dead chips, and the VIP player representatives are continually using the acquired live chips to purchase additional dead chips.
In Macau, the metric that is typically used to measure game performance in VIP rooms is win divided by dead chip sales; the volume of dead chip sales is sometimes referred to as turnover. This measure—win divided by turnover—is conceptually different from both empirical house advantage and hold percentage because it uses a different denominator than either of the other two. The dead chips provide a simple accounting system that allows the measurement of a proxy for actual handle. Indeed, for even money (or near-even money) wagers such as Player and Banker at Baccarat, the expected life of a dead chip is just under 2.0 plays. Thus, a computation of win divided by turnover or dead chip sales (as is commonly used in Macau) is going to be just about double the computation of win divided by handle (the empirical house advantage.)
Consequently the win rate expressed as a percentage of dead chip sales (Macau style) will be about double the 1.31% previously mentioned. A blended average rolling chip theoretical win rate might be stated as being between 2.52% and 2.70%. For dead chip scenarios, there are no added complications of relative versus absolute probabilities as dead chips are only resolved on winning or losing hands and thus only relative probabilities apply. The actual rolling chip win rate will be the amount of the actual win divided by the total amount of recorded dead chip sales.
Nonetheless, the differences in definitions of hold percentage (as used on table games in Nevada), win divided by turnover (as used on table games in Macau), and empirical house advantage (not presently used for table games but now the standard for electronic gaming devices in most casino jurisdictions) point out the difficulties in keeping the various metrics regarding Baccarat straight.
The one metric that might disappear over time is hold percentage, which—because its value is affected by underlying probability parameters, casino procedures, and consumer behaviour—is an inferior measure to the other two. Hold percentage is only used because of the unavailability of empirical house advantage. Until quite recently, there was no way to measure the empirical house advantage at Baccarat except through manual recording of each wager made by each player at the table. However, with the advent of RFID (radio frequency identification), OCR (optical chip recognition) or hybrid electronic table games, there is an increasing ability to measure the actual handle at table games. Once these procedures become established, hold percentage will become an obsolete measure. This has already occurred with slot machines and other electronic gaming devices, as well as with accounting procedures for the games of keno, sports betting, and other places in the casino where handle can be precisely measured.
A further complication can occur when dead chips are in use with respect to the total drop recorded under the system, depending on where the dead chips are purchased: the table or the casino cage. If dead chips are initially purchased at the table, with buy-ins allowed for further dead chips (“chip rolling”) at the gaming table (i.e. with dead chip purchase vouchers), then drop is increased in comparison to the case where all dead chips must be purchased at the cage. This can “distort” hold percentages at the tables; in this case the resulting hold percentage would be lower because the repurchase of dead chips at the table would increase the drop. This “distortion” and subsequent lower hold percentage caused so much concern among management within the Las Vegas Hilton organisation in the late 1980s and early 1990s that the process of constantly buying dead chips at the table was prohibited; an edict was issued that dead chips could only be purchased at the casino cage. However, other casinos allowed dead chips to be purchased without mandating players return to the cage; negotiable chips won through play could be exchanged for dead chips directly at the gaming table. This absence of a standard practice across the industry led to the absence of a common measure of win divided by dead chip sales, which created a raft of difficulties regarding the interpretation of this metric for management and game monitoring purposes.
The lesson to be learned is that it is important to appreciate the distinctions among these often quoted numbers about the metrics of Baccarat play, and to be sure that what is being quoted is broadly understood by those using the information. There is a huge quantitative difference between a hold percentage of 12% and a theoretical win rate of 1.31%, and yet many senior managers in the casino industry do not have a firm grasp on how these numbers are measured or why they differ. Furthermore, there is much potential for additional confusion when dead chips and chip rolling are being used on Baccarat where the theoretical win rate might be quoted at 2.70%, but is in reality 1.36%.
Knowledge should defeat fear, and in the case of high stakes Baccarat, fear (among management) can easily abound, particularly if a full understanding of the game’s metrics is not in place when the casino suffers large losses or experiences significant deviations from stated “expected” values.
Part II of this analysis will address volatility inherent in the short run fluctuations in Baccarat, which is a more real source of fear for casino management.
