I can’t stress enough the fact that every casino executive needs to have a good understanding of the mathematics behind casino table games and table game promotions. Many executives worry about losses due to card counting and cheating, but they totally drop the ball when it comes to understanding the numbers that drive promotional costs and theoretical table game win. I’m going to go out on a limb here and state that more money is lost every year in the gaming industry to losing promotions, bad marketing decisions and unnecessary operational costs than to all money lost to cheating, stealing and advantage play. Please take the following quiz and see which answer you would use to make these simple but crucial gaming operational decisions.
The Questions
Question #1
Your GM wants you to increase your play in craps. You look at a competitor and see they have instituted having the buy bet customer pay the “vigorish” on the 4/10 buy bet only if the bet wins for the player. How will paying the commission “late,” when the bet is paid instead of when the bet is made, change the bet’s house edge?
A) The mathematical edge drops from 4.76 percent to 1.67 percent due to the late payment.
B) The late commission payment won’t change the house edge. The mathematical advantage stays at 5 percent, the rate of the commission.
C) The house edge drops from 5 percent to 4.76 percent when the commission is paid late.
D) It doesn’t matter. Commission on buy bets is somewhat arbitrary, and as long as you charge the player something, it’s additional profit for the house.
Question #2
To be competitive in craps, marketing feels that you need to change the field bet from double on both the 2 and 12 to paying “triple” on the 12. How does this change the mathematical edge on the field bet?
A) The field bet is such a sucker’s bet that it really doesn’t matter if you give up a percent or two.
B) Paying “triple on the 12” in the field lowers the house advantage by 50 percent.
C) The change is very slight. It’s a wonder why more clubs don’t offer triple on both the 2 and the 12.
D) All “triple on the 12” accomplishes is to attract more dice scooters.
Question #3
In order to drive more craps play, management has decided to change the pass/come odds from 3-4-5X to 20X. As the table games manager, you are reluctant. Your argument is that the increase in odds will lower the pass/come house advantage, and your hold percentage will take a downward hit. The GM questions your statement. Are you correct in your thinking, and how do you explain your position on this matter? Which of the following statements is the most correct answer?
A) The pass/come house advantage drops because the additional money placed on the odds bet increases the player’s chance to win.
B) The increase in odds allows the player to wager more money that is not subject to a house advantage.
C) You realize you are wrong about the change to the house advantage, but that the player buying in for more money to bet the high odds multiple will decrease the hold percentage.
D) You realize your argument is baseless, and decline to comment.
Question #4
Your casino is located in a highly competitive market. The casino in your market relies heavily on “2 for 1 match play” coupons to market its table games. The coupon war is heating up, and your marketing department has decided to double the number of $10 match play coupons they distribute every month. The concern is with the other casinos’ increase in match play coupon distribution. After listening to their strategy at the weekly management meeting, you are asked to make a comment about this plan. What is your comment?
A) Since you have to be competitive with the other casinos in your market, you’re “on board” with the program.
B) You don’t understand why marketing only wants to increase the program by double. If they are so sure it will work, why not increase the match play promotion by triple?
C) You’re hesitant to back the increase, because you’re not sure of the cost or the effect the coupons have on your win and hold. After being chastened about not being a “team player,” you reluctantly give your approval.
D) You ask the director of marketing what each coupon costs the casino in expense and revenue, what method marketing has used to measure the promotion’s success in the past and how long it takes for the casino to win back the cost of each coupon through additional play.
Question #5
In order to improve table game play, marketing has decided to give away a bonus hand each month. They have decided to start the first month by paying a bonus to any player, regardless of their betting limit, of $100 on any three-card 6-7-8. As the casino manager, you ask what the bonus hit frequency would be. They show you a report from a mathematician at the local university that says the 6-7-8 hand would hit once every 363 player hands (based on the player always drawing the third card). Your casino is small and attracts only low limit players. They ask you for your input. What do you say?
A) The cost of $100 every 363 hands will be easily absorbed by any new players the promotion attracts.
B) You quickly divide $100 by 363 hands and discover the cost per hand is 28 cents. Since your average bet at blackjack is presently $10, a 28-cent cost per hand means nothing.
C) Since you only attract low limit players, the promotion will probably be a big success because the $100 bonus hand, though only hitting once every 363 player hands, will be a very attractive amount to win.
D) You quickly calculate the cost per hand at 28 cents. Then you calculate the theoretical win per hand per average bet player. You realize it’s a bad promotion, and show everyone your calculations.
Question #6
Six months ago, your casino contracted with a company to install a side bet on a large portion of your blackjack tables. The contract is coming up for renewal, and the CFO wants to know whether you want to keep paying a monthly fee for the use of the side bet. How can you measure the success of your side bet on blackjack, and do you keep it, look for another side bet option or get rid of side bets entirely?
A) You never have liked side bets. You’ve been in the business for more than 20 years, and most of that time blackjack did fine without offering time wasting and costly side wagering options. You vote to get rid of them.
B) You know that side bets are worthwhile. They provide the customer with an additional betting option and provide the casino with an additional revenue flow. You’re not sure how to measure the bet’s success, other than it appears to have increased blackjack revenue, but the last several months are always the casino’s busiest. You like side bets and figure any one is as good as another.
C) You contact surveillance and have them perform a survey of the side bet. You have them look at the betting frequency and the side bet average. You also look up the mathematical advantage of the side bet, and you determine how much money is won by the house per wager. You decide to keep the side bet, because it is increasing the win substantially and increasing your hold in blackjack by over 1 percent.
D) You contact the owner of the side bet, tell him his side bet is a piece of trash, and the only way you will keep it on the floor is if he gives you a huge discount for a long period of time. You get the discount and save the casino big bucks over the next two years.
Question #7
You’re approached by an Asian junketeer who tells you he can bring in millions of dollars of Asian play into your casino per month. All you have to do is offer a couple more baccarat games, put in a small noodle bar near the table and utilize a “dead chip” program for tracking the Asian customers. He explains that a dead chip program (also known as rolling chip) is used to record the amount of action the program players will provide for the casino. Since the special chips used for this program are non-negotiable and can only be played across the table, it guarantees his customers will buy in and gamble exclusively at your casino. For this opportunity, the junketeer is only interested in a small percentage of each dead chip buy-in. He asks you how much your baccarat games “hold” at this present time. You look at your daily game report and tell him it’s 12 percent. He smiles and says, “Splendid, let’s split it in half. For all my players buying in on the dead chip program, you give me only 6 percent in commission.” You ask him to give you a day to think about it. As the general manager, you are excited at the chance to increase your casino business by several million dollars in new business per month, but before you agree, you have to look at the situation from all sides. After thinking about this situation, you make the following decision:
Yes) I’ll do it. Six percent of several million dollars is nothing compared to what we have a chance of winning in the casino.
No) It doesn’t compute. When things sound too good to be true, they usually are.
The Answers
1) A
Because the casino does not collect the 5 percent commission up front, the casino wins less money when a 7 is rolled. For example: When paying commission up front, the player is actually making a $105 bet to wager $100. When the player wins, he receives a net win of $195. If the casino wins the bet, they gain $105. If the commission is paid only if the customer wins, the winning player bet still nets $195, but the casino will only win $100 because the commission isn’t part of the action.
The difference between the two situations illustrates how costly this “promotion” is for the casino. In order to attract players, the house is willing to sacrifice 3.1 percent of every buy bet on the 4 and 10. For every $100 wagered across your craps table on the buy bet of 4 and 10, late commission costs your casino $3.10. Calculate how many $100 wagers are made annually on the 4 and 10, and for each time you’re giving away $3.10. Do you think this “promotion” is worth it?
2) B
Paying triple on the 12 lowers the mathematical house advantage in the field by 50 percent. Paying double on both the 2 and 12 provides the casino with a mathematical edge of 5.56 percent. By paying triple on the 12, the house advantage drops to 2.28 percent. Some casinos have started going back to offering triple on the 12 because they believe it attracts more dice players. This is not true. Most players don’t know the difference, and don’t find this promotion attractive enough to seek it out when playing in a competitive market. In addition, higher limit players don’t wager in the field because of its reputation as a “sucker’s bet.” Again, the casino is offering an unattractive promotion that will cost them much more money than it will create in additional revenues. Note: If marketing decided to offer triple in the field on both the 2 and 12, the mathematical advantage of the field would drop to zero.
3) C
In a moment of haste to object to the pass/come odds increase, you wrongly stated that the pass/come odds will change. You quickly correct your position since you know that the mathematical edge on a bet is not influenced by another bet such as pass/come odd multiples. However, you do understand that any additional monies placed on the odds are not subject to a house advantage and will earn the casino “nada.” What it will do is increase the amount of customer buy-in without increasing the house’s revenue potential (unless the change attracts more players and increases pass/come play). Management needs to understand that an increase in drop (due to the higher odds) without a potential increase in win will cause the hold percentage to drop. Depending on the money wagered on the pass/come odds, it could drop several percentage points. Probably the most influenced metric to change due to the increased odds is game volatility. The boost in money on the dice layout without an improvement in win percentage increases the statistical win/loss swings known as fluctuation. The increase in odds could lead to more play and more win; however it will definitely increase the casino range of risk during short and mid-term periods of play. The right move in this spot is to argue for a lower odds limit that will accommodate new players but keep volatility at a more acceptable range.
4) D
After reading the sequence of answers, D is the obvious choice. But how many people would agree with answers A and B, and may have been “herded” into answer C? In the situation previously described regarding match play coupons, the use of coupons as game starters is almost always a big loser for the casino. The cost of a $10 match play (2 for 1) coupon is approximately $4.80, and it will take the average player another 38 hands (approximate), at $10 per hand, for the casino to break even with the single coupon played. If only one customer in five stays and plays after he/she has used the coupon, our lone “hooked” player would have to play for about three hours to reach the break-even mark. Does your casino make money with the coupon play, or is management increasing coupon distribution and putting your casino operation into a “death spiral” of coupon cost?
5) D
Once you read answer D, you should be asking yourself, “How much is the theoretical win on $10 at blackjack?” To calculate the theoretical win, you need to multiply the average bet ($10) by the estimated house mathematical advantage (estimated at 1.5 percent H/A). When multiplying the average bet by the H/A, you will discover that the theoretical win per hand is only 15 cents! That means that the average player will be costing the casino about 13 cents per hand ($0.15 – $0.28 = -$0.13). In order to break even with the promotion, a player would have to wager at least $19 per hand. One method for salvaging this promotion would be to lower the bonus payout or to set a minimum bet level to qualify for the bonus. Either method would greatly lower the target customer’s perceived value of the promotion, and render it worthless.
6) C
I wouldn’t be surprised if many casino executives have used the strategy described in answer D. Although answer B sounds good, the executive in that situation did not measure the performance of the side bet. What if it was underperforming? Why should the casino renew the contract? Wouldn’t it be time to look for another option? Answer C describes the reasoning of a smart casino executive. He/she looks to measure the utilization of the side bet, and then determines how much each wager is worth. The executive then compares the value of the side bet with what he or she believes it should earn. Once that is done, the executive will determine whether to keep the side bet or go shopping for another option that is more suited to their operation and customer market. Basing your decision on how much you can beat the vendor down on his pricing has appeal to the cost-based gaming corporation, but the money you save the company will probably be less than what it would make utilizing the best product for your casino.
7) No, don’t do it!
Many casino executives have fallen prey to this gaming form of bait and switch. The Asian junketeer knows that he can use the general manager’s desire for more players as a hook. Then he focuses on gaining commission based on the game’s hold percentage, not the game’s theoretical win. If 6 percent sounds low, it’s not. When calculating theoretical win based on multiple play chips, such as those used in a dead chip program, you use the non-negotiable chip buy-in times twice played on the average. This gives you total handle. Then multiply handle by house advantage. In baccarat, the house advantage is estimated at 1.15 percent (average between banker and player bet). If a customer bought into the program for $10,000, under the junketeer’s plan, the junketeer would receive $600. However, when calculating the theoretical win, we arrive at the number of $230 ($10,000 X 2 X 1.15% = $230). As you can see, the junketeer earns $370 more than the casino stands to win for every buy-in of $10,000. The loss is not transparent. The cost is absorbed by marketing as an expense while the pit games receive a marginal increase in win. Unless someone compares the two numbers, the dead chip program rolls along without being noticed by management until much later. Not all dead chip programs are bad. If the junketeer were to receive 1 percent of the buy-in, the program would return an acceptable profit to the casino operation.
Excel spread sheets available upon request at wzender[at]aol.com
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]billzender.com.
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