Knowledge Should Defeat Fear
By Andrew MacDonald and Bill Eadington

How often do we hear that results for a casino - or casino company - were impacted (positively or negatively) by high-end play associated with the game of Baccarat? Casino managers, often expected to perform to quarterly revenue or growth targets set by financial analysts, clearly do not appreciate volatility in their gaming win, and in some cases "play the man - and not the ball" as a consequence, or shy away from the high-end Baccarat business altogether.

Harrah's, for example, took the route of exiting the high-end table game business altogether a short time after they acquired the Rio in 1999. This came after a failed experiment on their part to introduce commission-based programs through the use of dead chips. (Dead chips are also known by a number of other names. They are also called non-negotiable chips, rolling chips or mud chips.) Harrah's had been, at the time of the Rio purchase, a very well respected operator of casinos throughout the US that had predominantly focused on mid-level, avid, experienced slot machine gamers. With the Rio purchase, Harrah's inherited some very high quality suites suited for premium players, along with a handful of such customers. This led to a period where the company dabbled for a period of time with high-end table game play.

Harrah's was a company that was used to being number one or number two in its particular markets, and was, to a large extent, focused on slot play. The stock market had seen Harrah's rise over the years, producing high quality earnings with good growth and little variation in results from quarter to quarter. What the Rio experiment unleashed was a period of earnings instability. No longer could Wall Street "expertly" forecast earnings per share within a penny or two and neither did they fully understand the business that Harrah's had now found themselves in. Furthermore, the new Harrah's management at the Rio was pre-occupied with getting the high-end play right, and spent considerable time analyzing this particular segment of their business, probably at the expense of the rest of their operation.

The volatility in earnings associated with being involved in high-end table game play brought about a rethink in sentiment toward the stock that was reflected in its share price. Furthermore, the Rio was not performing to the level that senior management at corporate level expected. Following several quarters of trying to work through the issues at the Rio, Harrah's leadership came to the conclusion that high-end play was not for them; the high-end Baccarat business was abandoned, and the management team at the Rio was replaced by one far more compatible with Harrah's core strategy. And over the subsequent quarters, the Rio became an important contributor to Harrah's earnings.

Gary Loveman - Harrah's President and CEO at the time - is without doubt one of the smartest operators in gaming today. So what did Loveman see that others perhaps had not? First, he recognized that there was not enough volume of high-end Baccarat play being generated at the Rio for the company to be comfortable that it would achieve anything near the statistical house advantage from the game on a quarterly basis. This meant that results for the Rio and the company were inherently going to be volatile. Furthermore, he recognized that not only was the Rio experiencing win rate volatility but also volume volatility. There was no adequate predictor of how much and when play would be generated. Several big players may come in and play during one quarter and then might not be seen for quite a period of time. Furthermore, some or all of them might win on their short visits because of the volatility inherent in the short run.

Loveman found that an inordinate amount of time was being spent by management on the issues around one or two high rollers, or on "fixing" the Baccarat problem at the Rio. Rio's management was distressed and obsessed, and the focus of the company was being distracted by the performance of this one property. He found it unusual and frustrating that he would get calls about a particular player winning or losing millions. One customer - from Harrah's customer base of around 17 million at the time - getting his and other senior management's inordinate attention just did not make sense.

Loveman also understood that the decision science tools associated with his Total Rewards program did not provide him any competitive advantage in this particular market. Furthermore, he recognized that Wall Street tended to punish bad luck on the tables to a greater extent than it rewarded good luck, so the company's stock price would drop more dramatically on a poor quarterly result than it would benefit from a quarter impacted by good luck and strong hold percentages on table games. Even analysts who followed the primary "premium play" casino companies had trouble understanding this; for those used to Harrah's consistent performance, the challenges of communication were even worse.

Finally, Loveman had come to the realization that the high-end table business was low margin that suited a "winner-take-all" outcome. With such powerhouses as MGM, The Mirage (and then MGM and Mirage together, after their merger) and Caesars dominating the Las Vegas Strip, Harrah's was not going to be number one or number two in this market. Without the facilities - palatial rooms and exclusive golf courses - hardware (i.e. private jets, fleets of limousines), and hosting infrastructure that his competitors enjoyed, and with the headaches that Harrah's had accumulated, Loveman concluded that Harrah's - at least for the time being - should not try to be a player in the high-end Baccarat market.

That left the market to be fought out between MGM Mirage and Caesars, with the Venetian playing a small but increasingly significant role. MGM Mirage was ultimately able to dominate and capture the lion's share of the high-end Baccarat market in Las Vegas at the time due largely to economies of scale. Interestingly, prior to the takeover of Mirage Resorts by MGM in 2000, it had been much more common to hear, especially from Wall Street analysts, of results from Baccarat impacting casino companies' performance. Consolidation then brought together two of the major players in the high-end VIP Baccarat market and as a consequence their volume increased to the point for MGM Mirage that quarterly volatility relative to expected win was significantly reduced. With Harrah's exit at the Rio, the demise of the Desert Inn, and little other competition at the time, MGM Mirage was able to attain over 70% of the high-end Baccarat market by 2002.

What is it that makes high-end Baccarat such a feared game? Is there something magical about this game compared to others that makes it so much more volatile? Are the players more clever or lucky, or does their inscrutable behavior work against the house? The simple answer to each of these questions is "No." To the contrary, the game of Baccarat offers no opportunity for skilled play, and is a nearly even chance game - much like flipping a coin - with a small house advantage and a low variance. Most slot machines are designed to be far more volatile - per unit wagered - than Baccarat.

As a measure of volatility, statisticians use the "yardstick" measure of standard deviation. (The formal definition of standard deviation is the "square root of the average squared distance of the actual outcome from the expected win of the game.") A single wager of one unit on an even money game such as Baccarat has a standard deviation of one unit. With Blackjack, because of 3 to 2 payouts on "naturals," doubling down, and splitting, the standard deviation is slightly larger at 1.1 units. For a single number wager at Roulette, the standard deviation is about 5.7 units. For the lottery-style game of Keno, depending on the number of spots played and the payout structure of the game, the standard deviation might exceed 40 units. For slot machines, the extent of volatility - measured by standard deviation - could be in the range of 10 or greater, depending on the configuration of possible payouts and their associated probabilities; the recent proliferation of multi-line, multi-coin games and the use of random number generators has permitted much more "lottery-style" configurations with slot machines than ever before.

More importantly for casinos, the standard deviation of a sequence of wagers is equal to the SQUARE ROOT of the number of wagers in the sequence times, the standard deviation associated with one wager. Thus, the standard deviation of 1,000 Baccarat bets of one unit each will be one unit times 31.6 (the square root of 1,000; or 3.16% of the total handle, if expressed in relative terms as a percentage.) The standard deviation of 100,000 Baccarat bets of one unit each will be one unit times 316 (the square root of 100,000; or 0.32% of the total handle, if expressed as a percentage).

Going one step further, for large enough sequences, we can predict with statistical accuracy that outcomes will fall within predictable ranges. Thus, there is about a two-thirds chance that over 1,000 equal "player" wagers at Baccarat, the actual outcome will lie within 32 units (one standard deviation,) of the expected outcome (about 12 units in favor of the house, or 1.2%), or the player has a two-thirds chance of finishing between 44 units behind and 20 units ahead. Extending this, there is about a 95% chance the player will end up within two standard deviations of the expected result (between 75 units behind and 51 units ahead), and a 99.7% chance he will end up within three standard deviations of the expected outcome (between 107 units behind and 83 units ahead).

Thus it is very rare that outcomes are beyond three standard deviations. However, if one unit is US$150,000, the "unlucky" outcome for a casino with our hypothetical Baccarat player at the two standard deviation (95% confidence) level would be a player win (or casino loss) of 51 units, or a rather painful US$7.65 million (before expenses!) This example demonstrates two things. First, the actual standard deviation increases in absolute terms as the number of hands increases. However, when expressed as a percentage, comparable to the House Advantage, the standard deviation declines relative to the expected win as the number of hands played increases.

This is known as the "Law of Large Numbers." The Law of Large Numbers is often misunderstood as implying that a game's performance must "even up" over time. In fact, there is "no gravity" in gaming and there is nothing that will push "unlucky" results back to the mean with impending "lucky" play. The game has no memory, and - for future decisions - always starts from the same statistical basis. This property is called "independence." Standard deviation as a percentage of the handle - relative to the constant House Advantage - will decrease as the number of decisions increases. The standard deviation, expressed as a percentage of the handle, will eventually converge to zero as the number of wagers in a sequence gets indefinitely large. Convergence to the House Advantage thus occurs in percentage terms as the number of decisions increases and the relative standard deviation goes to zero.

Contrast the Baccarat example above to a slot machine that has a house advantage of 5.0% and a standard deviation of 25. If the typical wager is $1 and the machine receives one million plays in a specified period of time, the expected win for the casino is $50,000, and the standard deviation of the sequence of plays is $25,000. There still is visible volatility, but one can see the Law of Large Numbers working in favor of the house. Ultimately, the number of plays will be large enough (many millions of independent plays) so that the House Advantage will dominate the standard deviation of the sequence of wagers. In the long run, the house does not gamble (i.e. risk ending up behind at the game) at slot machines because volume and independent outcomes overwhelm the volatility inherent on one or a few plays.

We can conclude that the game of Baccarat is not very volatile in its own right. There is no relatively infrequent substantial payout - as there is with a slot machine jackpot - that creates volatility. You either win or lose one unit on Player bets and you either win 0.95 units or lose one unit on Banker bets. So where does the volatility in Baccarat come from?

There are essentially three elements that contribute to volatility in high stakes Baccarat: the maximum wager made by all players, the frequency and distribution of wagers of all sizes, and the total number of large (i.e. maximum or near maximum) wagers made. Baccarat - for a variety of reasons - is the game of choice for very high stakes gamblers, especially Asians. These are players who are prepared to wager US$100,000 or more on a single bet. The maximum bet at the game of Baccarat is often the highest you will find in a casino. The maximum bet offered may be as high as US$250,000 in some cases (or perhaps higher, depending on the individual arrangements made, or the ability of the casino to reduce volatility risk through matching opposing wagers via a "differential" strategy).

It is, however, a very small population of gamblers worldwide who are prepared to make such bets and so the number of decisions that are made at that level for any particular casino is relatively small. A typical Baccarat shoe with eight decks of playing cards will provide around 70 hands of play and, depending on the player's rhythm, it may take from 30 minutes to several hours to deal through a single shoe. Therefore, in a single trip of several days, a premium Baccarat player may only generate somewhere between 500 and 1,000 decisions. With only a limited number of very high-end players playing at maximum stakes, a particular casino, such as the Rio in the late 1990s, might only generate a few thousand hands at its maximum bet for a particular financial period.

The playing cards have no memory and the shoe delivers a result independent of who makes the bet. Whoever the gamer is has no relevance to the laws of probability that govern the game of Baccarat. It is therefore not relevant to personalize a situation of wins or loses to an individual player except around decisions relating to credit or where some form of advantage play or suspected cheating may be relevant. Ironically, and mistakenly, many casinos fall into the superstitious trap of personalizing high-end play to the specific players; they do not want to be beaten by Mr. C and therefore cut him off when he is playing with "their" money.

A casino choosing to partake in the high-end Baccarat market should focus on generating the greatest number of hands at the highest wager it is willing to tolerate. Volatility in results at high-end Baccarat emanates from too few players, playing for relatively short periods, at substantial sums per individual wager. At a 1.2% House Advantage, a maximum bet of US$250,000 played for 1,000 hands will result in an expected win of US$3 million but (within two standard deviations) will vary between a loss for the casino of US$12.5 million and a casino win of US$18.5 million in 95% of occasions.

Add to this the impact of taxes on gross gaming revenue, any discounts or commissions applied based on the level of betting activity, and other marketing costs for high-end customers, it is easy to understand why the game of Baccarat can raise fear in the hearts of casino management. Normally stable results for an entire casino can be overwhelmed swiftly with such play, with even further complications arising from the issuance of credit to such players. (At the Diamond Beach Casino in Darwin in 1990, Mr. Ichiro Kasawagi happened to win A$30 million at high stakes Baccarat in one weekend, putting a significant dent in the other $25 million in gross gaming revenues the casino was winning that year for its owner John Aspinall. In 1995, Kerry Packer allegedly beat the MGM Grand out of US$20 million in a weekend, leading to a management change and a refusal to continue accepting bets from Mr. Packer.)

Furthermore, there are other risks to the game as well. One saying popular in the high stakes world of dealing with premium players is that you have to win twice, first over the gaming tables, and second in collecting the debt.

Why is this relevant today? When MGM Mirage consolidated and dominated the high-end market in Las Vegas in 2000, they were able to dissipate much of the volatility (relative to expected win) through volume. With their subsequent acquisition of Mandalay Resorts Group, MGM Mirage was able to grow revenues to such an extent that the company's quarterly revenues were now so large that even scenarios like the above would cause ripples rather than waves.

However, it is the advent of major casino operators in Macau - along with the impending competition for that market linked to the propensity of many Macau customers to bet at very large stakes - that will again make analysts think about earnings volatility related to high stakes Baccarat. With six concession holders all likely to vie for a portion of the high-end Chinese gaming market - and with that market's preference for the game of Baccarat - there will be much more focus and discussion on Baccarat performance coming out of Macau. While VIP Baccarat volumes are presently much higher in Macau than in Las Vegas, it is likely that we will see a much more competitive environment in the very near future. Furthermore, US-based companies may be restricted from competing for some portions of the market due to licensability issues around VIP room promoters and junket operators as well as their compliance initiatives linked to Nevada standards for "know your customer" and antimoney laundering protections.

Thus, when PBL/Melco, MGM/Pansy Ho, Wynn, SJM, Galaxy and Las Vegas Sands are all in full gear competing against one another for the very high-end players, it will be interesting to see how volumes will be split and who amongst the listed operators will dominate this market. With a tax rate of effectively 40% on gross gaming revenues and commissions and incentives that return to the player, VIP room promoters, junket operators and other intermediaries a further 40% of either expected or actual win - depending on the individual arrangements made - then this can clearly be a very low margin business. Add to this employee costs, promotional incentives and supporting infrastructure costs, average margins tend to converge in the mid-teens. Taking into account a run of bad luck, results in a fragmented market may put certain Macau listed companies under pressure.

As Gary Loveman put it - "It is a winner-take-all game." While the Macau and Asian highend Baccarat market is certainly large, the volatility in quarterly results may result in some operators rationally exiting the very high stakes business and finding other niche markets to cater to. Offering bets of US$250,000 per hand may not end up being to everyone's liking.
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