After submitting a casino evaluation report to the targeted operations executive committee, I explained why I advised my client to start hitting soft 17 on all of the blackjack games. I commented that the rule change from stand on all 17s to requiring the dealers to hit the soft combinations would increase their games’ advantage by 0.2 percent, which in turn would increase blackjack revenue and hold percentage. “By how much?” they asked. Now I’m in a spot. How can I project a reasonable, accurate estimate based on limited information about this operation’s blackjack games? From experience, I know that hitting soft 17 will increase revenue and hold percentage based on the present levels of game handle, but how can I calculate handle when I only have access to management’s drop, win and hold percentage figures for the last year? As most readers probably know, I’m an avid believer in hitting soft 17 after my experience at the Aladdin Hotel Casino in the ’90s. I think everyone should use this rule. Regardless, I still need to convince management that the gains from hitting soft 17 are well worth the change. How can I provide a projection that shows the committee the benefits of hitting soft 17 over the next year?
Projecting the Effect of Hitting Soft 17
In the August issue of Casino Enterprise Management, I introduced readers to the concept of live game buy-in churn in “The Effect of Buy-in Churn on the Live Game Hold Percentage.” Readers should remember that “churn” is equal to the number of times the initial buy-in is wagered across the tables. Wagers made on each hand of play are also referred to as “handle.” If a customer buys in for $500 and wagers $25 per hand, once his total amount of handle is equal to the $500 buy-in, he has churned his buy-in one time. Readers may also remember that the greater number of times the customer churns his buy-in, the more money the casino will make in theory. I’ve been reminded many times that theoretical win “does not pay the light bill”; however, the casino executive must think in the long-term, and it’s in the long-term where theoretical win will reach parity with actual, i.e., “what we calculate we can win, we’ll win.”
One good use for the theory of “churn” is for calculating game handle over a period of time. If I know the drop, win and house advantage for a specific game, I can calculate the approximate amount of money handled in order to achieve that win. Also, over a long period of time (a year, for example), I can safely calculate the number of times the average customer churns his money and how much he will wager.
In the situation mentioned before, I had the casino’s drop, win and hold numbers for the previous year in front of me. I then made the following assumptions:
• Blackjack drop over the last year was approximately $115,000,000
• Blackjack win was approximately $16,100,000
• The average house advantage for the blackjack games was calculated to be 1.3 percent (0.4 percent for BJ rules and numbers of decks; 0.9 percent for player basic strategy errors)
By dividing the win by the house advantage, I was able to calculate the total wagering handle it took to win $16 million ($16,100,000 / 1.3% = $1,238,461,538). Next, I divided the total handle by the buy-in to calculate the number of times the buy-in was churned ($1,238,461,538 / $115,000,000 = 10.8). I can use the churn number as a simple multiplier to determine total handle under various situations (see Table 1).
Given the previous situation, management’s interests lie in the effect of changing the dealer 17 rule only on the casino’s main floor, not in the high-limit area. To be able to calculate the effect under this limited situation, I first had to establish an important assumption. I like to believe the 80/20 rule works well in gaming. In this situation, the 80/20 rule would dictate that 80 percent of the casino’s drop/revenue comes from 20 percent of its blackjack players. That means that 20 percent of the total drop is contributed by the lower-end customers that make up 80 percent of the total number of blackjack customers. With this logical frame of mind on the table, I made a new list of assumptions:
• The main casino floor blackjack drop is estimated to be $23,000,000 (20 percent of $115,000,000)
• Average churn is approximately 10.8 times the buy-in (drop)
• Total low-end handle is $248,400,000 (drop times churn)
• The increase to the house advantage by hitting soft 17 is 0.2 percent
By hitting soft 17 on the main casino floor, management could expect to add an additional $496,800 in blackjack revenue per year based on the previous year’s blackjack numbers (see Table 2). The results of these calculations not only gave management an incentive to start hitting soft 17 on their main casino floor, but it also got them thinking about extending the policy to the rest of the casino as well. It doesn’t take much to estimate how much blackjack revenue could increase by hitting soft 17 on the high action games: “Five times $496,800 … now how much is that?”
Projecting the Effect of a Single-Zero Wheel
Recently, I had another situation where I could use the churn theory to show one casino’s management team that putting a single-zero roulette wheel head on the casino floor might not be the best strategy. This casino offered four double-zero roulette tables for play by their casino customers. One game was open around the clock and was accountable for 50 percent of the roulette drop and win. The remaining three tables were open in the evenings and on weekends and contributed the other 50 percent of drop and win. Management was considering replacing their most active double-zero wheel with a single-zero version, and the casino manager wanted to know what I thought of the idea. My first response was “Why?” He advised me that the casino’s marketing department believed the casino would generate more revenue with roulette by offering a single-zero wheel. He also stated that marketing felt safe with an estimate of increasing the present drop on that specific game by 25 percent. How well would management’s roulette marketing strategy succeed?
First, let’s set up a list of assumptions to work with. Roulette numbers from the previous year indicated that all roulette games recorded approximately $2,000,000 in drop, $500,000 in win, and held 25 percent. If approximately half the action in roulette fell to this one particular wheel—let’s call it “Roulette A”— it can be assumed that Roulette A dropped $1,000,000, won $250,000, and held 25 percent. Now let’s list our assumptions:
• Roulette A dropped $1,000,000
• Roulette A won $250,000
• Double-zero roulette is subject to a house advantage of 5.26 percent
Using similar calculations as the previous example, we can determine with great confidence that the churn on Roulette A is 4.8. This indicates that the total handle or amount wagered on Roulette A over the last year was close to $4,752,852.
Next, we need to determine the variables that come into play when we remove the double-zero wheel head and table from the casino floor and swap it with a wheel head and table configured with only one zero. Since removing one zero reduces the numbers on the table and wheel, it is accepted that the house advantage will decrease as well. Because the player will lose one chip for every 37 wagered, the house advantage drops to 2.7 percent. Not bad, but compared to 5.26, the decrease is just a little less than 50 percent.
In addition, I decided to use the 25 percent expected increase as a null hypothesis measurement since the belief is that a single-zero wheel will increase business and bring more revenue to the casino. Now we can list the other assumptions needed to estimate the success of this final proposition:
• The adjusted drop for Roulette A is estimated to be $1,250,000
• The churn remains 4.8
• The calculated handle would be $5,941,065
• Single-zero roulette has a house advantage of 2.7 percent
Based on these assumptions the single-zero wheel will win approximately $160,409 based on the anticipated 25 percent increase in table drop. Whoa! That’s less revenue than the double-zero wheel earned with the original amount of table drop (see Table 3).
One thing management didn’t anticipate was the effect of the greatly decreased house advantage. Even though their promotion would attract more play, the lower house advantage left most of the intended profits sitting in the players’ pockets.
Of course, it would be reasonable to assume that the lower house advantage would allow the roulette customers to play longer on their buy-ins, a factor that would increase the rate of churn. But by how much? In addition, the single-zero roulette might attract some play from the other roulette wheels on the casino floor. But wouldn’t that be a negative, too? After showing the casino manager this exercise, he was very reluctant to accommodate casino marketing’s wishes.
Final Comments
Through these two examples, I’ve offered readers another method for using buy-in churn. In this article, churn is used to determine total bet handle for a game type by simply multiplying the churn number by the drop figure. Total bet handle can be calculated through a second method. This method requires the casino executive to take the win figure and divide that number by the specific game’s house advantage. Once total game handle is determined, the executive can easily calculate and project the theoretical win by multiplying the change in house advantage by handle. Understanding the logic and math behind these calculations will assist the casino executive in making critical decisions regarding projection of game rule changes.
Bill Zender is a former Nevada Gaming Control agent, casino operator, professional card counter and present gaming consultant. He has been involved in various areas of gaming and hospitality since 1976. He can be reached at wzender[at]lastresortconsulting.com.
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