by Andrew MacDonald and William R Eadington
Table Games – Optimal Utilisation: A science and an art.
By Andrew MacDonald and William R Eadington.
Many gaming executives might mistakenly believe that optimal utilisation on a gaming table is a simple function of getting as many people as possible to crowd around a single gaming table and wager as much as possible. At first glance, this might appear to be the most efficient utilisation of floor space and labour. This logic appeals even more in times when managers are being asked to trim their operating costs. This can occur when management is under short term profit pressure, and is looking wherever it can to enhance over-all performance.
The major costs in most casino operations are gaming tax, labour and complimentary benefits to players. These often make up around 80% of direct operating costs in a casino’s table game operation and, as such, come into focus in times of economic downturn when greater efficiencies are being sought. As gaming tax is generally unavoidable as a percentage of win, and player complementaries—when properly administered—are a marketing cost that helps drive business, it is often direct gaming labour that receives the greatest scrutiny. It is the “most variable” of the variable costs.
However, though it may seem counterintuitive, optimal table game utilisation is not necessarily a function of having every available position at every open gaming table occupied by customers. Indeed, that could quite possibly be a long way from the optimal outcome; the labour cost savings might be more than offset by foregone table game winnings. Targeting 100% gaming position utilization may be the best way to reduce labour costs, but it may also sacrifice the highest possible yield in profit from a given set of customers. This might be paralleled to a farmer maximizing the yield per tractor in harvesting his fields, but leaving much of the crop to rot because the few tractors in use could not get to some of the farmland.
Determining optimal utilisation per table can be approached as a scientific question. This analysis attempts to do so by applying a relatively straight-forward mathematical equation which can be estimated by carefully understanding and modelling certain important components of the mechanics of table game play.
An appropriate table games analysis needs to take into account time and motion aspects of table gaming processes, including the elements that control the speed at which dealers conduct the game. In the game of Baccarat, as it is played in Macau or Las Vegas for example, the important elements are:
• the time the dealer takes to deal the cards;
• the time taken by the players of the Player hand and Dealer hand to expose their results;
• the time taken by the dealer to take and pay individual wagers; and
• the time allowed for players to make subsequent wagers.
Issues like fills, credits, cash buy-ins, colour changes, supervisor acknowledgements and dealer changes all have some impact on the time and execution requirements at the table. However, these are usually considerably less significant and perhaps less sensitive to variations in the number of players at the game over any reasonable time frame. For our purposes, we are going to concentrate on the number of players as the key variable in seeking out optimal table allocations under varying player demand conditions.
Using empirical observations to monitor, segregate, and estimate the elements of the mechanics of the game under different playing conditions, especially with respect to the number of players at the table, will provide the basis for finding closer to true optimal solutions with respect to the table games labour question. Such data would permit baseline calculations to estimate the average speed of the game under varying circumstances, and would allow analysts to determine how changes in the number of players affect the number of decisions per player and for the entire table over any given time period.
The game of Blackjack can be used to illustrate this issue and how it might be addressed. Consider a situation where six $100 players, each planning on betting one box per round at $100 per hand, step onto the casino floor. Management’s alternatives at one extreme could be to cater to the players by having them all play at a single table with one dealer and one supervisor. At the other extreme, management could offer each player a private table with their own dealer and supervisor. Suppose that the applicable gaming tax rate is 20% and the labour cost per gaming table per operating hour is $40. Which scenario provides the better return?
To be most efficient and maintain operating costs at the lowest level, management might opt for the single table scenario. If that is the case then operating costs would be $40 rather than the alternative $240, and this is clearly more cost efficient.
But is this solution the more profitable for the casino? Suppose that empirical observations yielded the following findings for the casino’s blackjack games. The casino’s dealers can deal a total of 350 hands per hour on average (including their own hand) and this number of hands is more or less independent of the number of players at the table. House rules are such that a perfect Basic Strategy player plays to a House Advantage of 0.5% of handle. The average $100 player that the casino attracts plays a strategy about 1.0% inferior to the Basic Strategy, creating a 1.5% average House Advantage for the casino.
Under these assumptions, the single table will generate 300 player hands per hour, with a total handle of $30,000 per hour, and an expected win of $450. After labour costs are computed, the contribution to income from the single table is $410.
On the other hand, the second alternative of one player per table would permit each player to make 175 wagers per hour, resulting in a handle per table of $17,500 and an expected win per table for the casino of $262.50. For the entire six tables, the expected win would be $1,575; after labour costs of $40 per table per hour are subtracted, the contribution to income for the casino from this option is $1,335 per hour, more than three times better than the one table alternative. In addition, players may be tempted to play more than one box. This increases the yield by increasing the proportion of the 350 of dealt hands which go the player. As will always be the case with taxes on win at a fixed percentage, the after-tax results will not change the optimal solution, and the one-table-per-player option remains more than three times better than the one-table option. (If gaming taxes are accrued as a percentage of gaming win, it will not change the optimal number of players per table, but it will increase the required minimum average wager to make the game show positive income contribution.)
This type of simple example is often cited to demonstrate that optimal utilisation is not the same as 100% table occupancy. In the above scenario, optimal utilisation occurs with six box Blackjack tables when there would be a single player per table. (Given the assumptions, using three tables with two players each would result in hourly expected winnings per table of $350 and contribution per table of $310, for a total of $930, a third less profitable than the one-table-per-player option.)
Based on an algebraic model developed for the values assumed in the above situation, any average wager of $23 or more would call for one player per table. If the average wager was between $15 and $22, then the optimal number of players per table would be two; between $11 and $14 average wager, the optimal number of players per table is three; and at between $9 and $10 per average wager, the optimal number of players would be six. When the average wager per player drops below $9, the table cannot earn enough to cover its labour costs at $40 per hour.
What needs to be calculated for
Date Posted: 01-Aug-2008