I would be willing to bet a good portion of my bankroll that the majority of Advantage Players’ got their start by playing Blackjack, specifically using a card counting strategy that moves the wager up and down with the count. Somewhere in the first year of training, the counter concludes that the deeper the penetration (where the cut card is placed), the better game is for the player. But what is often overlooked, especially by table game managers and gaming executives, is that the lower the cut card is placed, the more profitable the game is for the casinos. I know this seems counter intuitive, no pun intend; but I promise things will come into focus, by the end of the article.
The foundation of my assertion is that a dealer who isn’t dealing is not making any money for the casino. When you factor hourly wages, sick days and personal days, as well as benefits and vacation time I conclude that for every hour a single dealer is not dealing it cost a casino $22. This is a standard net loss. An even more staggering number is the opportunity cost associated with a stagnant dealer.
Opportunity cost in laymen’s terms is how many dollars one course of action is costs over another. For example, every year we hear about the high cost of raising a child to the age of 18. A recent article put the cost at just over $233,000. What is not clear is that the majority of the cost is associated with the opportunity cost of raising the child. More to the point, raising the child is one path and working is another. By choosing to raise a child or children over working, the parent loses the income that they would have otherwise earned by working.
Similarly, different casinos vary in their placement of the cut card in a blackjack shoe game. Some cut 2 decks and some cut only a single deck in a six deck shoe game. Consider two games where the difference between the cut cards placement is 1 deck, e.g. in deck A the cut card is placed 2 decks from the bottom and in deck B the cut card is placed 1 deck from the bottom. In order to derive the net gain for the casino for each additional round dealt, some reasonable assumptions have to be made. Those assumptions are defined in the following list, and have been verified by gaming experts such as Michael Shackelford, creator of the Wizard of Odds website.
- Average # of cards per hand of Blackjack is 2.3
- Average number of players per table is 4
- Players average bet $40 ( some bet more some bet minimum of $25)
- 84 rounds of blackjack are dealt per hour
- Average of 7 active tables per casino
- Average Player plays to a -1.3% expectation against the house
- Only 1 in 47,000 players can accurately count cards in a casino
- Only 10% of the 1 in 47,000 players have a sufficient bankroll and time to play full time.
*I am ignoring lower denominations because I don’t consider the $5 tables that pay 6:5 on naturals and have automatic shufflers to be Blackjack.
52 cards make up the deck difference between cut card placements. Dividing 52 by the 2.3 cards the result is approximately 22.6 additional hands being played (equation 1). Dividing by 4 players per table, it results in 5.65 more rounds being played in the shoe with the lower cut card (equation 2).
THE MATH
equation 1 – 52 cards / 2.3 cards per round = 22.6 additional hands
equation 2 – 22.6 hands / 4 people = 5.65 additional rounds dealt
Using these assertions we can derive the additional hold a casino can expect by additional rounds played.
To determine the additional action we apply the average wager:
5.65 rounds * 4 people * $40 = 904 dollars
Applying the average hold:
904 * 0.013 =$11.75 per shoe
Multiplying by 7 tables:
$11.75 * 7 = $82.26 dollars per shoe
Multiply by 26 shoes per day:
$82.26 * 26 = $2,138.86
Multiply by 365 days a year:
$2,138.86 * 365 = $780,685
Divide by 5.65 to determine how much each additional round makes:
$780,685/5.65 =$138,174.50
The opportunity cost for a higher cut card as opposed to a lower one is approximately $138,000.00 per round. The time per round on a 4 player table is 1.4 minutes, and using a shuffle time of 5-7 minutes (using the high side of 7 minutes makes the math work out clean so I will use that).
1.4 minute hands/7 minutes = 5 hands
Every time a casino shuffles they are losing money and when done consistently over the course of a year they lose $780,685 per shuffle. So it stands to reason that the casinos would want to play more and, shuffle less. But if we know anything for certain it is that most land based casino’s hire management personal that couldn’t think their way out of paper bag.
This derivation is a stripped down analysis. Things get more complicated when you consider the number rounds played and exact time it takes to shuffle for 6 and 8 deck shoes. Also, the average bet sizes on lower denomination games restructure the hold for the games; the 6:5 win on a natural blackjack also plays a part in the exact calculation for the hold in these more complex scenarios. The lower denomination games, even with the 6:5 payout still brings in less money on a direct player to player comparison. The last thing is to consider is how much additional money would be taken out of a casino with a lower cut card counters. I think it is fair to say that most high threat players have moved into advantage play techniques that are Beyond Counting, pun intended, so this impact would likely be minimal.
Casinos are seeing drastic drop offs in their player rates. The 80/20 rule; this is where 80% of companies revenue comes from 20% of their customers, is shifting to an 80/15 rule and in some jurisdictions the shift has migrated to where 80% of the casinos gaming revenue comes from only 10% of their players.
The casino doesn’t make any money when a dealer doesn’t deal. I can’t be the only person ever to run through this derivation. With this calculation in place why do some casinos choose to cut 2 and sometimes 2.5 decks?, especially when it leads to a dealer shuffling more and dealing less. We have shown how much a shuffle costs a casino in actual dollars, but still nothing changes. Why? In its simplest form and, in its most convenient definition the answer is a casino will not purposely do anything that will lead to a player winning. I think this is paradoxical, because just being in the gaming industry will result in some players winning. The key is that vast majority of players will ultimately give up money to the house; A concept that most casino executives have yet to grasp.
Nicholas G. Colon is the managing director of Alea Consulting Group, a casino gaming consulting firm with a player centric philosophy.
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Zender has been preaching this for years and it still falls on deaf ears.
Somehow casinos think they are smarter than basic economics …. but yet there revenues continue to tank…
Casinos would rather win less in the aggregate than allow one or two players the possibility of getting the best of them. I’ve been a professional AP for two decades and can guarantee the casinos that make the most money deal the games fast and deep, have virtually no 6/5 tables, and don’t sweat winners or low stakes players. (betting less than $200). Smart casinos know the best way to maximize profits is to increase the drop. Time and Motion is a science that impacts almost every business in terms of productivity. If you build cars you want that production line always moving. You don’t want to have to keep stopping production to reload the riveter. Excessive Shuffling = Downtime = Lost Profits.
Something about preaching and a choir comes to mind here BP. It’s high time someone invite casino management to the Sunday service.
I wrote an article about the very same issue about 10 years ago using similar calculations. Where did you get the number 1 of 47,000 for counters? Any source?
By the way the most interesting is “backwards” calculation: what is critical density of counters should be for the casino to make deep penetration unprofitable? Any intuition in advance?
Counter density 1 in 47k # was taken off from Henry Tamburins site. He got it from one of his seminar instructors. I asked about once but he never did get back to me on it. Feel free to contact him at smartgaming or bjinsider. If I had to guess I’d say there was some general ball park assumptions made about number of people who walk through a casino cross references with the griffin book on known counters. It gives a rough approximation. I’d take it one step further in saying that the only 10% of those folks have enough bank roll and time to implement the system.
The problem with the math is that the system is dynamic: if the casinos offer a better game, the counter ratio will go up — gradually at first, and then likely following an exponential curve as word gets out. Where along the “counter curve” any casino wants to be is a more meaningful way to model the whole game, and all the counter-advocates disregard this simple reality.
I say this as a professional counter who would be thrilled to have more of these good conditions!
When binion moved into tunica his pen on his blackjack games increased and rules were better than any other joint in town. Shortly there after he was pulling in more money on his tables than all other casino combined.
Similarly in AC during the great experiment when counters were allowed to play th AC tables made more money in that week than in any other week to date. All documented.
Both circumstance are well documented.
The reason is that everyone thinks they can be an AP but everyone does not have the patience and persistence, they simply don’t put the work in. Good games bring in more people who don’t have the skill set and ultimately lose to the house.
I am skeptical on your astertion as the two examples here show it not to be accurate. Also all the good games in LV do much better than the poor games.
On differnt sources I found the number 2.7 for the average number of cards in the hand. You’re using 2.3. Who’s wrong?
Some sources say as high as 2.8 however the 2.3 number was taken using the original 1 deck game using good rules. The 2.71 number is for a 6 deck shoe game h17 game. It’s understandable that as number of decks goes up number of average cards per hand goes up. I cover myself toward the end by adding a qualifier stating exact numbers for each game vary. Also cut card placement plays a part as well. Lots of factors
But the take away here more hands less shuffleing equals more money for casino.
I ran the calculation using 2.71 the cost per round is 138,118.95 as oppose to 138,174.50. The difference is not significant. They are merely estimates which is intended to set a trend line and not really define an exact solution.
Hope this helps.
Great article! I agree with everything. All of the really profitable casinos cut only a half deck. Most people cannot count cards and eventually they will detect the good counters and back them off before they win to much. I would say about 1 in 10000 people have a long term winning skill level.
Thanks ….things are going to get worse before they get better … just the nature of the beast.
I agree. As someone who works in the industry, and sees the direct effects of changing penetration, the less penetration, the less losses. The author here assumes that casinos make their money on tables, when in reality, nearly all successful casinos make the majority on slots. So mitigating the loss by minimizing penetration is the best way for casinos to ensure they don’t attract people who could turn a $500 loss into a $10k win. I think of this as a curve, at first, the profits would increase, and then as the counters increased, the losses would build up and the casino would then spend more money trying to figure out what is going wrong. Consultants like Bill Zender aren’t cheap and the advice they give is already known fact, so the idea that increasing penetration automatically turns into profits is not reality.
I and many people smarter than me do not agree with your evaluation. And history and presence conditions contradicts your assertions. Think Belagio vs Venetian . Thin tunica and jack binion think AC during the experiment. Gaming is the most poorly managed industry I’ve seen.
If any one knows it’s zender
See his response below after I asked him about counter density
Nick,
It’s extremely thin. I believe there are only about 100 to 125 professional
level card counters in all of North America. There are more advantage
players who attack hole-cards and location play than there are counters. I
believe Darren Hoke stated the percentage as 0.006% based on total BJ
players a compare to confirmed professional counters at his casino in
Louisiana.
Cheers.
Bill Zender