“Knowledge Should Defeat Fear” – Understanding the high stakes game of Baccarat – Part II.

by Andrew MacDonald and William R. Eadington

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

Harrah’s for example took the route of exiting the high-end table game business altogether after they acquired the Rio in 1999. This came after a failed experiment on their part at the Rio in Las Vegas 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 who had predominantly focussed on the mid-level, avid, experienced slot machine gamer. The Rio purchase shifted the company’s direction somewhat and with it came the experiment in high-end table game play. Harrah’s was a company that was used to being number 1 or number 2 in the markets it focussed on and was, to a large extent, focussed 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 understand the business that Harrah’s had now found themselves in. 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. Following several quarters of trying to work through the issues at the Rio, Harrah’s management came to the conclusion that high-end play was not for them.

Gary Loveman (Harrah’s President and CEO at the time) is without doubt one of the smartest operators in gaming today. So what did Gary see that others perhaps hadn’t? Firstly, he recognised that there was not enough volume of high-end Baccarat play being generated at the Rio for the company to get anything near the statistical house advantage from the game on a quarterly basis. This meant that results were inherently going to be volatile. Secondly he recognised that not only was the Rio experiencing win rate volatility but also volume volatility. That is he had no adequate predictor of how much play would be generated and when. Several big players may come in and play during one quarter and then not be seen for quite a period of time. Thirdly, he found that an inordinate amount of time was being spent on looking at the issues around one or two high rollers or fixing the problems at the Rio. The focus of the company was distracted by the performance of one property. He also found it unusual that he would get a call about a particular player winning or losing millions. One customer – from a customer base of around 17 million at that time – getting his, and others in his management team’s, sole attention. Fourthly, he understood that the decision science tools associated with his Total Rewards program did not provide him any competitive advantage in the market. Fifth, he found that Wall Street tended to punish bad luck on the tables to a greater extent than it rewarded good luck and so the stock price dropped more dramatically on a poor quarterly result than it benefited from a quarter impacted by good luck and a strong hold percentage on table games. Lastly, he felt that the high-end table business was low margin that suited a winner take all approach. Without the facilities (palatial rooms and exclusive golf courses) and hardware (private jets) of his competitors he therefore decided that Harrah’s – at that time – should not play in this market.

That left the market to be fought out between MGM Mirage and Caesars. MGM Mirage was able to dominate and take the lion’s share of the high-end Baccarat market in Las Vegas around that time. Interestingly, prior to the takeover of Mirage Resorts by MGM it had been much more common to hear and speak of results from Baccarat impacting a casino company’s performance. Consolidation brought together two of the major players in the high-end VIP Baccarat market and as a consequence volume became such at MGM Mirage that quarterly volatility was significantly reduced. With Harrah’s exit and little other competition at the time, MGM Mirage was able to attain over 70% of the high-end Baccarat market.

What is it though that makes high-end Baccarat such a feared game? Is there something magical about this game compared to others that means that it is so much more volatile? The simple answer to that question is – No. In fact, conversely the game of Baccarat is fairly much an even chance game with a very small house advantage and a low variance. Most slot machines are designed to be significantly much more volatile than Baccarat. To provide an illustration of this it is possible to use the game’s standard deviation for a single unit wagered. For Baccarat that number is close to 1, for Roulette on a single number bet that number is around 5.7 and for most slot machines it is 10 (or much higher for penny slots).

The game of Baccarat is therefore not very volatile in its own right. There is no relatively infrequent substantial payout that creates volatility. You either win or lose 1 unit if the “Player” bet wins and win 0.95 units or lose 1 unit if the “Banker” bet wins. So where does this notion of the volatility in Baccarat come from? There are essentially three other elements that make up volatility in this case. The average size of the wager, the maximum wager and the number of wagers being made at the highest amounts. Baccarat – for a number of reasons – attracts very high stakes gamblers. Predominantly from Asia these are players who are prepared to wager US$100,000 or more on a single bet. Thus 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 is some cases (or perhaps higher depending on the individual arrangements made).

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 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 may take from 30 minutes to several hours to deal. Therefore in a single trip of several days a high roller may still only experience something between 500 and 1,000 decisions. With only a limited number of very high-end players playing at maximum stakes the casino may only generate a few thousand hands a quarter at its maximum bet. To calculate the volatility associated with this it is simply a case of taking the square root of the number of hands played. For 1,000 hands the square root of 1,000 is 31.6. For 10,000 it is 100 and for 100,000 it is 316.2. The expected volatility is this number related to the expected win from that numbers of hands. As an example, at a win rate of 1.3% for Baccarat then the expected win at 1,000 hands is 13 units with an expected variation at one standard deviation of 31.6 units. Note here that the expected variation at 1 standard deviation is 2.4 times the expected win. For 10,000 hands the expected win is 130 units and the standard deviation is 100 units or 0.77 times the expected win. For 100,000 hands the expected win is 1,300 units and the standard deviation is 316.2 units or 0.24 times the expected win. From basic statistics we know that using a normal standard distribution – as is the case here – 95% of results will fall within 2 standard deviations of the mean (or expected result). This demonstrates two things. Firstly that the actual standard deviation increases in absolute terms as the number of hands increases but secondly that it falls as a relative number to the expected win or the number of hands played.

This is known as the “Law of Large Numbers” but is often misunderstood as meaning that things will even up over time. In fact there is “no gravity” in gaming and there is nothing that will pull results back to the mean. Merely variation as a percentage of the total number of decisions will decrease over time. Regression to the mean occurs only in percentage terms as the number of hands increases. Interestingly this supports the notion that if you start behind you are more likely to end behind or conversely if you start ahead you are more likely to end ahead (provided results are independent as is the case in Baccarat).

The cards have no memory and the shoe only delivers a result independent of who makes the bet. It is not relevant to personalise a situation of wins or losses to an individual except around decisions relating to credit or where some form of advantage play or suspected cheating may be relevant. Otherwise the focus should be about getting the most number of hands at the highest wager permitted. Volatility in results at high-end Baccarat emanates from too few players, playing for relatively short periods at substantial sums per individual wager. A maximum bet of US$250,000 played for 1,000 hands will result in an expected win of US$3.25M but will vary between a loss of US$12.55M and a win of US$19.05M in 95% of occasions. Add to this the impact of taxes on gross gaming revenue and any discounts or commissions applied based on activity and it is easy to understand why the game of Baccarat can raise fear in the heart of casino management. Normally stable results can move significantly with such play, with even further complications arising from the issuance of credit to such players. There is a saying that in the high stakes world of dealing with high rollers that as a casino you have to win twice. Once over the tables and the second time in collecting the debt.

Why is this relevant today? When MGM Mirage consolidated and dominated the high-end market in Las Vegas much of the volatility was dissipated. This is even more the case through the acquisition of Mandalay Resorts Group growing revenues to such an extent that the group’s quarterly revenues are now so large that even scenarios like the above cause ripples rather than waves. However, it is the advent of listed casino operators in Macau that will again make the market think about earnings volatility related to high stakes Baccarat. With six concession holders all vying for a piece 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 coming out of Macau. While VIP Baccarat volumes are much higher in Macau than in Vegas it is likely that this will be a highly competitive environment with all six operators seeking a piece of the action. US based companies may be restricted from competing for some part of that market due to their compliance initiatives following Nevada standards around “know your customer” and anti-money laundering provisions. Therefore when PBL/Melco, MGM/Pansy Ho, Wynn, SJM, Galaxy and LVSI all start competing for the very high-end players it will be interesting to see how volumes will be split and who amongst the listed operators can dominate this market. As Loveman put it – “it is a winner take all game”. While the market is certainly large, the volatility in quarterly results may result in some operators rationally exiting the very high stakes business and finding niche markets to cater to. Offering bets of US$250,000 per hand may not end up being to everyone’s liking.