by by Andrew MacDonald and William R. Eadington
"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:
“Player:” 1.36%, and
These are known as the relative win rates.
Based on all decisions (including Ties) for an eight deck game, the win rates are:
“Player:” 1.24%, and
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.
Date Posted: 01-Feb-2007
Andrew MacDonald is founder of urbino.net and is also general manager of international business development for SkyCity Entertainment Group in New Zealand. He can be reached at Andrew.MacDonald@skycity.co.nz.
Bill Eadington is a professor of economics and director of the Institute for the Study of Gambling and Commercial Gaming at the University of Nevada, Reno. He is an internationally recognized authority on the legalization and regulation of commercial gambling, and has written extensively on issues relating to the economic and social impacts of commercial gaming. Eadington can be reached at firstname.lastname@example.org.