Inside Asian Gaming

solution,andtheone-table-per-playeroption remains more than three times better than the one-table option. (If gaming taxes are accrued as a percentage of gamingwin,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 todemonstrate 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 each game type and for each average wager level is the number of players at which profit per player is maximised. To do this for Blackjack requires estimates of how the game’s speed of playand thenumber of decisionsdelivered to each player changes as more players join the game. For each average wager size, it is then conceptually possible to calculate the optimal utilisation for that game, taking into account gaming tax rates and labour costs. For Blackjack, it is also necessary to assess the relative average skill for each classification of player by average wager size. For example, it is conceivable that low limit players (with $10 average wagers) play with an average House Advantage (player disadvantage) of 2.0% whereas higher limit players (with $100 average wagers) might play with an average player disadvantage of 1.0%. To estimate the skill levels of different player categories, hours of observations with appropriate sampling strategies would be required to determine the average skill levels of players (based on their play strategy deviations from Basic Strategy). Existing software in the casino’s surveillance department, such as the Blackjack tracking tool “Bloodhound,” can calculate the casino House Advantage against any player, based on actual player decisions. Such a tool could facilitate determining player skill by players grouped into average wagering level categories. Calculations for the game of Blackjack will be distinct for each market depending on tax rates, labour costs, player skills and game rules. These factors, along with dealer speed and procedural efficiencies, will affect the values of the parameters in the model. It is then a relatively straightforward task to apply the logic of the model to determine an optimal utilisation rate as a function of average wager size. Of course players are not always so accommodating to be easily classified and segregated with respect to average wager size and skill level, so consideration needs Using empirical observations will provide the basis for finding closer to true optimal solutions INSIDE ASIAN GAMING | September 2008 32