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#1




5, 7, or 9 Box Blackjack ?
Looked at wizardofodds website but can't find the answer to this teaser.
Anyone got any idea on the theoretical analysis of number of boxes on a BJ layout? When I first started in the business it was always 7 box BJ, then everyone got excited about adding an extra 2 boxes to squeeze in 9 box BJ midnineties. Now I've noticed some sites are running with 5 box BJ layouts, and I was wondering on what (if any) difference does it make? I appreciate the customer satisfaction side of it, less boxes mean they can be more comfortable at the table, but does the number of boxes (assuming all get played) affect odds greatly. And if so by how much? more hands per hour v less cash on the layout. Less hands per hour v more cash on the layout Which is the dominant force? 
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#2




Time and Motion
The math says that the more players at the game, the more money you make. Hands per hour is the key, but if you keep everything constant the results are as follows (I used a spreadsheet from Bill Zender's website which is a source I trust):
# of tables = 1 # of players= 5 Average Bet= 10 # of rounds= 50 House Edge = 1.5% Win per round = 0.75 Win per day = 900 Win per year = 328,500 ## of tables = 1 # of players= 7 Average Bet= 10 # of rounds= 50 House Edge = 1.5% Win per round = 1.05 Win per day = 1,260 Win per year = 459,900 # of tables = 1 # of players= 9 Average Bet= 10 # of rounds= 50 House Edge = 1.5% Win per round = 1.35 Win per day = 1,620 Win per year = 591,300 
#3




The only other thing I would add to the above is that you also need to take into account operating costs per unit.
Less boxes per game may mean more tables to accommodate the same number of players (dependent of course on demand and player preference). That of course leads to more employees (and all the associated costs), tables fees/taxes and higher expenses in general and also assumes you have the floor space to add tables if that's the way you wanted to go. Personally I never use nine boxes. I have seen one exception where it may be useful but would still be reluctant; that is a country where more tables are not allowed by legislation and a player preference for controlling their own box rather than playing behind. I've found that when you consider the available mass market floor space, operating costs and extra fees seven boxes for mass market is still usually the better compromise. High limit and VIP play less if your specific situation allows. This only really matters anyway if you have the volume of play to warrant change. In large US, Asian and Australian casinos with tables that often run to capacity it will be a consideration. If you are in the UK or Europe and your tables habitually run with 34 players it may not be an issue. You need to find a balance that's right for you. Last edited by 123; 17th December 2009 at 03:17 AM. 
#4




123
Very well stated and excellent advice.

#5




I should also have added that limits and typical bet size are a factor. $5 and $100 minimums are a world apart when determining if the extra revenues generated are worthwhile in relation to the increase in costs.

#6




Can't agree
SG  you indicate Zenders work showing a constant number of Decisions/Hour. Surely velocity of game has to diminish as number of players increase.
Kilby  Fix tackled this issue in their Casino Operations text and indicated that revenue declines with full tables and 45 players is optimum. As 123 indicates though, I am sure there are situations of compromise according to the particulars of the operation. My personal feelings were influenced somewhat when working for Harrahs. They employed a corporate table games division that had some pretty smart cookies in the mix. Their mandate to the table games leaders was to implement 5 spot layouts on all BJ games, I don't think that decision would have been made by the largest gaming company in a vacuum.
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#7




Moike
"SG  you indicate Zenders work showing a constant number of Decisions/Hour. Surely velocity of game has to diminish as number of players increase."
I agree Moike but I had no idea of what the difference would be from 5 to 7 to 9 spots. That info. would be nice to know. I just kept everything constant to show the effect of adding spots if all things remained equal. As far as Harrahs goes, they have the volume to make that kind of decision so that was a good solution for them but I think that if your floor space is limited you may have to go 7 spots. I have never come across 9 spots snd I can't imagine the size of the table. I guess that you could adjust the procedures to make the game pace quicker on a 9 spot game but it sounds like it would be really cramped. 
#8




I seem to remember a 9 box BJ as being the same size as a 7 but with an extra box turned sideways at each end. It was very squeezy, not comfortable for the players, and tough for the dealer to keep an eye on the outside boxes. I don't remember them lasting long.

#9




Maybe this answers your question
@ Dai
Here is a link to an article in The Catwalk in which Bill Zender explains the profitability of 5 and 7 box layouts. http://www.worldgameprotection.com/p...July2008.pdf 
#10




:)
Many thanks Guster  what a great article.
And interesting comments from one and all  much appreciated. I guess ultimately it depends on your overall gaming table allocation as well. Typical small uk casinos mean that these sorts of decisions can hold even more importance, and getting pit bosses/managers to be flexible and 'read' the situation on the floor at the time to ensure maximum 'yield management' is another area where we could probably improve. Many thanks Dai 
#11




Urbino  Casino 2000
Andrew MacDonald from Urbino has offered this link on the topic of BJ tables and their numbers. It doesn't refer to the individual box numbers and game profitability but instead at the number of tables provided at various times and how a management decision perhaps related to costs can over time effect game demand.
Casino 2000  The determination of table gaming spreads and matching table openings with variable demand levels. http://www.urbino.net/casino2000.cfm...tion&trigger=1 Andrew has also recently taken up the position of Executive Vice President of Gaming at Marina Bay Sands in Singapore so congratulations to him in what will obviously be a very interesting and challenging role. Ian 
#12




number of boxes played isnt directly related to number of players at the table, even when the table is full. im sure we have all seen 1 customer play 7 boxes, or the flipside 3 or more people trying to bet on only 1 box because they think it is "lucky"
having said that i understood the main question to relate more to the maths: "but does the number of boxes (assuming all get played) affect odds greatly. And if so by how much? more hands per hour v less cash on the layout. Less hands per hour v more cash on the layout Which is the dominant force? " i would think the house edge stays constant if the only rule change is maximum number of boxes allowed. therefore NO the odds are the same. with respect to the dominant force between HPH vs bet size i would argue that the product of these two (ie volume) is the main consideration with regards to theoretical win, which is what i assume you are interested in. now assume a £100 bet per hand and a constant HPH rate. with regards to win it doesnt matter if that £100 is on one box or spread over 5, 7 or 9 boxes because volume and house edge are the same. what will change however is variance. a single large bet will result in greater swings than several smaller bets. from a dealing point of view the most important thing for comfort is layout design. even 5 box layouts can be awkward if the first box is too near the shoe or float. im surprised no one has mentioned side bets as im sure they are a factor in layout design with regards to number of boxes and a factor with regards to house edge and therefore win. 
#13




Quote:
Ultimately on any BJ game you theoretically make more money with one player, one box. However once you to factor in operating expenses you will reach a point where one on one in not profitable. Add to that one on one is certainly not practical or even desirable as you would also need to consider the psychological aspect and take into account any social preferences of the players you work with. Didn't Ian mention the Empire in London also had five? Is this one of the operations controlled by Harrahs in the UK now; and that there were a lot of players. It may be the case that five spots have been proven best in terms of profit per game with 100% utilization but what happens when you have more players than spots? Do you lose players, and ultimately profit because they want to play their own hand rather than behind. I think the OP has what he needs to make a decision. Its only important that he remembers that you need to balance the math and what is theoretically best, practical considerations such as floor space and demand with the psychology of your player base to determine how they will react. So Daithestick, you had a lot of feedback, are you planning to do anything with the information? Last edited by 123; 6th January 2010 at 03:53 AM. 
#14




i agree the assumed scenario is unrealistic. it was more of an aside to illustate the fact that with everything constant except number of boxes win stays the same and only variance changes.
my main point, maybe not clearly stated, was that volume is and always has been king (for a given set of rules/house edge) i can see there are a number of nonmath elements that are more important when dealing with more than 1 table, but i had nothing more to add on them and the OP seemed to be (foolishly?) looking for a maths slant rather than a casino ops POV. with regards to the empire, i believe it is controlled by harrah's and at one point they removed all 7 box bj layouts and replaced them with 5 box layouts. (possibly soon after they bought LCI) what surprised me was the decision to forbid playing behind, especially as the tables were often full and had people waiting to join. i believe that would definately lose profit and cant see any justification other than a belief their dealers are incompetent enough to pay bets behind without mistakes or a belief volume could be increased by skyrocketing HPH enough to compensate for the lost bets. yeah i thought my posting was probably overkill (as is this one) but i do like "advanced?" discussions on the job. plus being out of work i have time on my hands! 
#15




5 is the optimal balance of increased HPH and reduction in total bet per round.

#16




5 boxes = increased hands per hour ?
Hello Single Zero,
Are you saying that by having 5 boxes on a table, instead of 7, that you get more hands per hour. Do you mean rounds of play ? I would say that 9 box BJ will always result in more HPH and decisions but obviously on a full table, less rounds. Increasing the boxes in play means less time wasted delivering and gathering up cards and therefore more HPH. Ian 
#17




Yes that is what i am saying whether you use the term hands per hour, rounds per hour or decisions per hour. The relationship between the number of squares and the rounds per hour is not linear. The rounds per hour lost by having 9 squares is not made up by the increase in total bet per round. For example:
Use a house edge of 1% 5 squares $10/square 80 hands or rounds per hour. $40 Theo win 9 squares $10/square 40 hands or rounds per hour. $36 Theo win Each property will be different on their game speed in relation with number of squares and will need to take their own data to determine where they stand. Procedures, rules of the game, side bets, equipment, dealer skill as well as the experience level of your guests will effect this relationship. 
#18




Math doesn't always tell the story
Unlike in Europe American players almost exclusively want their own box. Playing behind another person is something completely alien to them.
So if you have a scenario where there are two BJ tables available and a total of 10 boxes that's only 10 players max. But what if you have another 5 or 6 who wish to play ? They have no action and they may possibly be bigger players. If you're on a cruise ship with shows and dinner you may only have a couple of hours prime time each evening so it's important to give them an opportunity to play  especially if they're player club members. The last thing any casino manager wants to read on a comment sheet from a rated player is "couldn't get a game". I disagree that having 9 as opposed to 5 boxes will lead to a halving in game speed although with splits and doubles the layout can get extremely cluttered. Do you have any stat's available ? Ian 
#19




Not a big fan of 5 or 9
Just to add, I'm not a fan of 5 box BJ. Harrah's introduced them to split players up and then get more HPH on two games instead of one  with the second table perhaps being at double the minimum of the first.
Neither do I like 9 box as not all players (especially in the states) will be able to sit. 7 is the traditional number and 7 IMHO seems to be right. Ian 
#20




Quote:
The level of play in your operation will have a major impact. $100 minimums may well justify five boxes though $5 minimums would not. There are many variables and its not a case of 5 tables automatically being the most efficient design. I think the important thing to remember is that all casinos are not equal and what works in one is not always suitable in a different location. 
#21




Quote:
Taking this theoretical example a step further To accommodate 45 players 5 spots would require 9 tables, total win $360. 9 dealers at $10 p/h = $90. Net win $270 9 spots would require 5 tables, total win $324. 5 dealers at $10 p/h = $50. Net win $274 Adding a swing, supervision, insurance and benefits, tax or fees per table etc and the costs associated with the extra tables are considerable. The typical amounts wagered on a game will determine more than anything whether it is worthwhile to reduce seats in order to spread play. With $20 bets 5 spots would require 9 tables, total win $720. 9 dealers at $10 p/h = $90. Net win $630 9 spots would require 5 tables, total win $648. 5 dealers at $10 p/h = $50. Net win $598 You could go back and forward with this all day. You need to consider the variables in your own casino before making a decision, don't just follow any recommendations based on information from other locations. (PS hope the math is correct, I didn't give it too much thought but the principle is there) Last edited by 123; 28th November 2010 at 12:33 PM. 
#22




Quote:
Use a house edge of 1% Each player on both tables comes with $40 to spend 5 squares $10/square 80 hands or rounds per hour. $40 Theo win It will take 5 hours for each player to be theoretically out of money. 9 squares $10/square 40 hands or rounds per hour. $36 Theo win It will take 10 hours for each player to be theoretically out of money. In 10 hours 5 squares accommodates two groups of 5 players for 10 total. 9 squares accommodates 9 people total Might not be good if you are looking at accommodating large groups of people in a short time span but overall you are actually dealing with more people with 5 squares. 
#23




Quote:
In Macau there was a period that even on Blackjack rebates of up to as ridiculous as 1.4% were given (for all advantage players: none left that allow junket chips on blackjack) and with the anyhow very nice for the player blackjack rules it was just a matter of turning over as much as possible. Playing 7 boxes was clearly not optimal. You would always have to split some hands and playing the full 7 boxes it takes time to neatly make space for those splits. Also dealers seem to get confused easier with more boxes. They cannot memorise the total of the hands, so need to recalculate more often. Breaking up large denominated chips to smaller ones and the other way round happens more often. Playing 5 boxes was optimal. You may also want to take as an advice that the smartest operator out there (Steve Wynn) has 6 boxes on his tables, while all the others (less smart LOL) still have 7. 
#24




5 box BJ
MBS in Singapore has just converted all BJ tables to 5 box tables  clearly someone knows more than SW.
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#25




Maybe we need to look on Urbino
Andrew MacDonald the founder of Urbino.net is responsible for casino op's at Marina Bay Sands.
http://www.marinabaysands.com/Corpor...MacDonald.aspx http://www.urbino.net Searching for "Blackjack boxes" has revealed 198 results. Marina Bay Sands has circa 700 tables that have minimums considerably higher than western casinos and locals also have to pay $100 to get in. Players therefore deserve a degree of comfort and privacy so I'd be reluctant to place too much emphasis on such a decision. I'll see if I can get some feedback from Andrew on the topic. Ian 
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