Table Game Minimums and Profitability

A couple of years ago, the table games manager of the Sahara Hotel and Casino, Steve Mann, decided to spread a four-table pit that offered $1 minimum blackjack games. Mann had been receiving pressure from upper management to develop more table games players, and their solution was to advertise blackjack games available for a wager of $1. Mann is sharper than most table games managers and realized that $1 games would not make enough revenue to overcome direct table operational expenses. He knew that he needed to modify the rules on these games in order to give himself a chance of breaking even, at minimum. What did he do?

Mann invited me to the Sahara to take a look at his blackjack adaptation. What I found was a pit of four six-deck shoe blackjack games with standard dealing rules and a shuffle point of approximately 84 percent (cutting off about one deck). Mann had compensated for the lower limit by utilizing a reduced payout for a player two-card blackjack. If the player wagered any amount under $5 and received a blackjack, the player received an even-money (1:1) payoff. If the player wagered in increments of $5, the player received $6 for every $5 wagered (6:5). If the player wagered an amount different from $5 increments, such as $6, the player received a 6:5 payout for the $5 and a 1:1 payoff on the dollar change; in this situation a $6 blackjack paid $7. Using a 6:5 blackjack payoff increases the house advantage by 1.38 percent in a six deck game, although a blackjack payoff of 1:1 changes the house advantage even more; by 2.32 percent. Did Mann’s blackjack payoff strategy raise the mathematical house advantage high enough to overcome direct table game cost?

First, let’s establish what Mann’s direct table game operating costs would be to operate a four-table pit for one hour. At that time, between the dealer’s hourly salary, benefits and the related taxes paid by the employer, the expense per dealer was approximately $12 per hour. Mann spread a four-table pit that utilized five dealers working on an 80-minute rotation; total cost for the dealers would be 5 X $12 or $60 per hour. What about the cost of supervision? The cost of the supervisor (benefits and taxes) was estimated at approximately $25 per hour. The cost of the equipment per hour was nominal, and is not included in the calculation. Based on the previously stated costs, the hourly operational expense for the $1 minimum pit was approximately $85 per hour.

Second, how much money would the four tables “handle” in action in one hour at the reduced minimum limit? Observations of the games indicated that the bets were primarily $1, with a couple of players wagering $2 and one bold individual wager of $5. After a short period of observation, it was noted that the average wager per player was $2 with an average of five player hands per table. In addition, observations indicated that the dealers were producing an average of 60 dealing rounds of the table per hour. Based on this input, the hourly handle for the tables could be safely calculated to be $2,400 ($2 average bet X 5 hands X 60 rounds).

Third, we need to determine the new and improved mathematical house advantage. The modified H/A percent is a combination of the six-deck game’s natural mathematical advantage, the effect of the 1:1 blackjack payoff and the effect of individual player hand errors. You will note that I only considered the effect of the 1:1 blackjack payoff (2.32 percent) due to the overwhelming majority of wagers made under $5 (and the 6:5 payoff) threshold. The estimated house advantage on the Sahara $1 games was calculated to be 3.92 percent (see Table 1).

* The “player error” is estimated at 1 percent of every dollar wagered. The average player gives back approximately 0.8 percent, while the better player approximately 0.6 percent. The players on a low minimum game can be considered “novice” and are subject to a slightly high error percentage.

Last, we take the calculated handle and multiple it by the estimated mathematical house advantage in order to establish a theoretical win for the four games during the course of an hour’s play. The product of these factors provides us with a theoretical hourly win of $94.08. If we take this number and subtract the hourly cost, we can determine if Mann had been able to reach the break-even mark.

Based on Mann’s game modifications, he was able to make his $1 blackjack pit marginally successful, even with the low average wagers of $2. But as he pointed out; after the first round of complimentary drinks were served at these tables, “all bets were off.”

If the $1 modified blackjack game is a break-even, what about the $3 minimum game and other minimums? Let’s look at the $3 blackjack game. Using the same model in Table 2, we’ll compare the $3 wager average theoretical win with the same costs established in the Sahara example. The calculated handle will be greater because of the higher average wager, but the estimated mathematical house advantage will be much lower due to the removal of the 1:1 blackjack payoff restriction. It should also be noted that we will be using a $3 average bet on a $3 minimum table. I’m using the “basement” or lowest possible average wager to conduct the calculation.

Eliminating the blackjack payoff restriction has become a “revenue game changer” with the $3 minimum model. If the casino offers a $3 minimum game, and everyone at the game plays only $3 per hand, the game is an overall loser for the house. Even if we “pack” the table with seven player hands, the tables still do not make money under this model structure.
What if we ratchet up the average bet? Will the new model present us with a break-even situation? It’s not until the table experiences an average wager of $5 that the games can expect to break even.

Do these examples show that under normal game rules the $3 minimum game will lose money? Not necessarily. It is a money drain under this model’s structure. In most cases, the $3 minimum game will be subject to an average wager of $5. However, there are other factors that can contribute to an increase in theoretical win or the decrease in operational expenses. They are as follows.

More wagering positions can be added to the layout. The seven spot tables would be ideal because it would increase the number of wagers without increasing direct operational expenses. While additional player hands reduce rounds dealt per hour, the total amount of wagers handled increases, i.e., an increase in theoretical win.
Deck penetration could be increased in order to achieve more rounds dealt. Increasing penetration on the six-deck game to 92 percent (cutting off 26 cards) would increase hourly hand production greatly, especially in manually shuffled games. Don’t balk at the deep shoe penetration. Card counting should be the least of your worries on a lower limit game.
Add side wagers if the games don’t already offer them. Side wager utilization has a high impact on lower limit games because any wager on the side bet will create more revenue than from the main game. Why? Because the mathematical advantages of the side bets are much greater that the main game. Even side bets subject to lower mathematical advantage such as the “Lucky Lucky” (2.7 percent) are higher that the main game. Most side bets’ H/A percent is 4 to 5X higher.
Eliminate player benefit rules such as resplitting aces and doubling down on split hands. Removing these rules will increase the house advantage by approximately 0.1 to 0.2 percent, raising the mathematical house advantage to 0.7 to 0.8 percent.
In today’s gaming industry, it’s rare for floor supervisors to watch only four tables. The supervisor cost in this model can be cut in half if the supervisor is required to watch eight table games.
$3 minimum games should be used sparingly. $3 games will place the customers into $1 chip increments. When wagering in $1 chips, the players will raise their bets by the same increments, a dollar at a time. $3 minimum raises will go up to $4, $5 and $6. Placing the customers in $5 chips on $5 minimum games forces them to rise in like increments. Raises go from $5 to $10, $15 or possibly $20. Anytime you can raise any table game’s average wager, you increase the game’s theoretical win.
Unless your casino operation is considered a “destination/resort,” you need to refrain from using blackjack payoff restriction such as 6:5 or 1:1. These restrictions reduce the games’ gambling entertainment appeal by greatly increasing the house edge. When the house edge increases too much, i.e., doubling or tripling the blackjack game’s mathematical advantage, customers don’t receive “bang for their entertainment buck.” If the players don’t perceive a return in table time from their initial buy-in at the table, you may lose them to the competition where they feel their gambling experience is more positive.