I received permission from Dr. David G. Schwartz, today to link to the article (but not to reproduce the content of the article on our site), 'Understanding Casino Math', which I think is a very well written and effective article for many purposes.  Showing how casinos use math, a basic understanding of casino math and how the casino related writers refer to 'HAs', etc. 

I do think this is an important work and certainly has value to use as a base of understanding from many aspects and points of view.

The author, recently past away and I will include a link as to whom he was as well.  He has written numerous things relating to casinos and players. 

Permission granted through, Dr. David G. Schwartz, Director, UNLV, Center for Gaming Research, 4505 Maryland Parkway, Las Vegas, NV 89154-7010. 

"This guide, written by casino math professor Robert Hannum, contains a brief, non-technical discussion of the basic mathematics governing casino games and shows how casinos make money from these games. The article addresses a variety of topics, including house advantage, confusion about win rates, game volatility, player value and comp policies, casino pricing mistakes, and regulatory issues. Statistical advantages associated with the major games are also provided."

http://gaming.unlv.edu/casinomath.html

Reference the author:

He was affiliated with the University of Denver:  http://news.du.edu/remembering-professor-robert-hannum/

From the author's website:  http://mysite.du.edu/~rhannum/

Thanks for the reference to the article. Understanding casino math is important so that the math can be reversed to obtain player advantage.

Fantastic. This looks so official. I mean it passes peer review and it looks like it makes the case for what is generally believed. So for me it represents a baseline for what is to follow.


For the sake of discussion only:
"Earning Potential = Average Bet ´ Hours Played ´ Decisions per Hour ´ House AdvantageFor example, suppose ... A player who bets $500 per spin for 12 hours in double-zero roulette at 60 spins per hour would be worth about $19,000 (500 x 12 x 60 x .053)."


This equation is incomplete in my understanding of the math that is to come:
Casino's Earning Potential = (Average Bet) times (Hours Played) times (Decisions per Hour) times (House Advantage)
The missing component is the result of an algorithm that equates to a random awareness coincidence factor. This component would be added to the original equation as a signed number. Now it must be understood that the original equation represent all time played and not just a winning segment's duration of play by the coincidence function. So the coincidence algorithm must also factor in for a result or returned value of the portion of time that the awareness function is utilized with reference to the full time considered in the newly constructed equation. This is a known value, because all expectations are after the fact. So the implication is based on real values and not just potential values. So with the added component added to the existing equation you get a real debatable original idea, possibly confirmed.
And you guys want to play me off as some kind of math illiterate. All that is needed is my knowledge and a proper (awareness coincidence factor) algorithm that returns a signed number. You add it to the end of your existing equation as "times (awareness coincidence factor)."

The article and others like it are great 'base' research and informational basics for players that truly want the understanding how the risk in the gaming business depends on certain things and length of play. desire to research, read, understand and use something in their own defense, etc.

Here is a few words as to what I am referring about, "Risk in the gaming business depends on the house advantage, standard deviation, bet size, and length of play".

In my own play, at least since 2000 and after, I attempt to stay 100% fully consciousness of 'length of play'.  Good Lord, do I know the down side of 4 hours or more or anything close to that, but a $10k or $20k win in the first hour or even 30 minuets, is extremely hard to walk to the cashier, cash out and leave.  But, once you truly understand casino mathematics, you can use them to your own advantage. 

Casino mathematics in no way shape or form, translates to every player will lose 'XYZ'% religiously, etc.  It means, if you play what the casino sets as "average bet, bet size, and length of play with whatever hold percentage they use", that will generally translate to what you should lose if you play 4 hours or greater a day.  Not what you have to lose or are certainly going to lose.  Likewise, you might, and as well-you might not. 

That is why virtually every comp is based upon '4 hours' of play being inserted with the other parameters.  Unless a floor person or host hand writes the comp based upon your known play and history, etc., at the property.