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The Cost to a Casino of High Cut Card
Introduction
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 their 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. This 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 $30. 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 costs over another.
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. In order to derive the net gain for the casinos for each additional round dealt, some reasonable assumptions have to be made. Those assumptions are defined in the following list.
- Average # of cards per hand of Blackjack is 2.71
- 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
*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 2.71 cards the result is approx 19.19 additional hands being played. Dividing by 4 players per table, it results in 4.8 more rounds being played in the shoe with the lower cut card.
52 cards /2.71 cards per hand = 19.19 additional hands
equation 1
19.19 hands / 4 players = 4.8 additional rounds dealt
equation 2
Using these assertions we can derive the additional revenue a casino can expect by additional rounds played.
To determine the additional action we apply the average wager:4.8 rounds * 4 people * $40 = 768 dollars
Applying the average hold: 768* 0.013 =$9.98 per hoe
Multiplying by 7 tables: $9.98 * 7 = $69.86 dollars per shoe
Multiply by 26 shoes per day: $69.86 * 26 = $1,816.36
Multiply by 365 days a year: $1,816.36* 365 = $662,971.4
Divide by 4.8 to determine how much each additional round makes: $662,971.4/4.8 =$138,118.95
The opportunity cost for a higher cut card as opposed to a lower one is approximately $138,000.00. 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 $662,971. So it stands to reason that the casinos would want to play more and, shuffle less. This is a benefit for online casino companies who use software as opposed to live dealers for their speed dependent games. 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 average number of cards for different variations of blackjack, the number rounds played and exact time it takes to shuffle a 6 or 8 decks of cards. 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.
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. According to the Wizard himself, Michael Shackleford, "The cost to casinos due to induced additional play from card counters as a result of deep penetration is hard to estimate but my professional opinion would be at most 3% of the additional gain via more hands per hour and more realistically about 1%. Every card counter I know, and I know many, have moved onto other more lucrative forms of advantage play. Still, some dabble at it as a sideline. As usual, casino management is least a decade behind the times when it comes to advantage play."
Some may assert that the card counter density will go up as the games become better. However, past history shows us that as rules improve and a cut card is placed lower the revenue increases. This is easily ascertained when during the experiment in Atlantic City when card counting was legal, the town as a whole had the best week they have ever had. Similarly, when Jack Binion opened the Horseshoe Casino in Tunica MS, his blackjack games were earning more than all other casinos combined. Why? Because his blackjack games were better than the other casinos blackjack games.
The casino doesn't make any money when a dealer doesn't deal. With the derivation in place why do some casinos choose to cut 2 and sometimes 2.5 decks, this leads to a dealer shuffling more and dealing less. We have shown how much a shuffle costs a casino in actual dollars. The calculation is not universal but is intended to establish a trend line of the cost incurred when a casino shuffles more and deals less. Despite this derivation nothing changes. Why? In its simplest form 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.