Casino Theo
Theoretical win and the standard deviations of expected value have been widely covered in numerous articles. Unfortunately for me, the discussion on the topic has seldom been comprehensive enough to be understood by the layperson (meaning me).
We look at theo as our expected loss. It is really the theoretical win for the casino.their expected win, given your bet, time, house advantage, etc. The casino has a formula using all those variables to determine what they expect to win from you. Your available comps are based on a percentage of that amount.
Sep 24, 2013 MOST casinos focus on your 'THEO' and you should always know what your ACTUAL theo is, since their records reflect their impressions and estimates about your 'theo'. MOST casinos base comps on your theoretical value (ie, expected losses) and only adjust this figure for massive actual losses and less often for massive actual wins. Taken over by Bally's; Casino closed + sold (now a Radisson non-casino property) Golden Nugget Atlantic City: Atlantic City: Atlantic: New Jersey: Marina: Formerly Trump Castle, Trump Marina. Harrah's Atlantic City: Atlantic City: Atlantic: New Jersey: Marina: First casino to open in Marina District; Formerly Harrah's Marina Resorts Casino. Your theoretical loss to the casino (your casino theo or average daily theoretical – ADT) is the way the casino calculates what you are worth to them. It’s not a theoretical win because every game that the casino offers have a house advantage and the payoff for a bet is always less than the odds of winning that bet. Casino management system, primarily for meals at the casino's restaurants. Also included are discretionary comps that are issued by casino hosts for additional meals, hotel rooms, airfare, limousine service and other premium services. Other comps that fall into player reinvestment are complimentary room offers.
This post attempts to explain the issue in the simplest possible way.
Why is this important?
Theoretical win is derived from the probabilities built into any casino game. As all casino games are designed (in theory) to guarantee a return to the casino, the theoretical win (winnings for the player) is always negative while the expected value, also known as expectation (winnings for the casino) is always positive.
However, like with all probabilities, an element of randomness exists. The standard deviation of theoretical win thus provides a threshold for casino managers to decide if play has passed the limit where it becomes suspect.
Theoretical Win and Expected Value
The average of results is determined by the theoretical win formula. Hence, 50% of all results will achieve this result.
For example:
A split wager on single-zero roulette pays 17:1.
The probability of winning a split bet is 2/37 (2 numbers wagered on from a total of 37 numbers)
The probability of losing the bet is 37-2 / 37 = 35/37 (for all the other numbers not wagered on)
The theoretical win formula is:
(Probability of winning x payout in terms of units of wager) – (Probability of losing x wager)
(2/37 x 17) – (35/37 x 1) = -0.02703
This means that 50% of all play on split wagers in single-zero roulette will (in the long-term) achieve a loss of $0.02703 per dollar wagered by the player.
Standard Deviation
The majority of results will fall within 3 standard deviations from the average.
(Source: http://schools-wikipedia.org/)
In order to obtain the standard deviation, we turn to the binomial distribution, which is a distribution where only 1 of 2 outcomes is possible. In our case, the outcomes being a win or a loss.
Games with only 2 Outcomes
The formula for a binomial standard deviation is:
Square Root (number of games x probability of winning x probability of losing) x average wager x (unit of wager + payout in terms of units of wager)
Using our current split wager example, with an average wager of $2 over 3 games, the formula would be as follows:
Square Root(3 x 2/37 x 35/37) x $2 x (1+17)
=Square Root(3 x 2/37 x 35/37) x $2 x 18
= 0.391659 x $2 x 18
= $14.09972 (standard deviation of theoretical win)
Games with 3 or more Outcomes
How about games with more than 2 possible outcomes, perhaps a win, loss or tie? Baccarat fits this description and for this we turn to the multinomial distribution:
This table describes the possible outcomes for a Player wager. A win on Player would give +1 and a loss on Player would give -1. A tie pays 0.
For a Banker wager, a win would pay 0.95, a loss -1 and a tie, again 0.
Player Wager
| Wager | Probability | Outcome |
| Player | 0.446246609 | 1 |
| Banker | 0.458597423 | -1 |
| Tie | 0.095155968 | 0 |
The expectation of the Player wager is just the product of the probability of each result by the outcome, the sum of which is -0.012350813:
| Wager | Probability | Outcome | Expectation |
| Player | 0.446246609 | 1 | 0.446246609 |
| Banker | 0.458597423 | -1 | -0.458597423 |
| Tie | 0.095155968 | 0 | 0 |
| Total Probability = 1 | Total Exp. | -0.012350813 |
The standard deviation of expectation for this is worked out below.
First, you get the variance for each wager:
| Wager | Probability | Outcome | Expectation | Variance | |
| Player | 0.44625 | 1 | 0.44625 | 0.44625 x (1- -0.01235)^2 = | 0.45734 |
| Banker | 0.45860 | -1 | -0.45860 | 0.45860 x (-1- -0.01235)^2 = | 0.44734 |
| Tie | 0.09516 | 0 | 0.00000 | 0.09516 x (0- -0.01235)^2 = | 0.00001 |
Notice that the working is really:
Probability x (Outcome – Expectation)^2 = Variance
The standard deviation for this is then:
SQRT(Sum of all Variances) = Standard Deviation of Expectation
| SD. Of Exp. | SQRT( 0.45734+ 0.44734+ 0.00001 ) = 0.95115 |
This means that the standard deviation of expectation of a $1 Player wager for 1 coup is $0.95115. For a $5 wager over 10 coups, it would be $0.95115 x $5 x SQRT(10).
The Result
To find out if the win of a player is improbable, we use the Z-table and the following formula:
Win – Average Win (Theoretical Win)
Standard Deviation
Our example will yield the following result should the player have won $15. The player played 3 games with an average wager of $2, so the total wager would be $6.
15 – (-0.02703 x $6)
14.09972
=1.075352
The result is 1.075352, meaning that the result of the player’s gaming is 1.075352 standard deviations from the average. This means that the player’s gaming results are within the top 15% of all results. Cause for some concern.
There you have it. Good luck!
In the context of casinos, comps are complimentary items and services given out by casinos to encourage players to gamble.[1] The amount and quality of comps that a player is given usually depends on a combination of factors: what game(s) they play, how much they bet, and how long they play.
Most casinos have casino hosts who are responsible for giving out free items and contacting players to bring them back to the casino. Pit bosses can also award comps at table games. Most casinos now urge players to obtain a player's club or similar card, so that their play can be tracked and comps awarded.[1]
Levels[edit]
The lowest level of comp available at most casinos is free alcohol and other beverages. Many casinos provide free drinks to anyone who is gambling.[1]
The second level of comp that many players earn is free self-parking, lounge access, or free meals. Many casinos have several players lounges and restaurants, and may require more play to earn a comp to higher-end restaurants. Often the player is given a certain amount to spend, but sometimes, particularly with high rollers, the player may be given the right to order as much food as they want and to bring guests.[citation needed]
The next level of comps is usually free hotel rooms, free valet parking, and free access to more exclusive VIP or 'high roller' lounges. Many casinos have attached hotels, but those that do not may have the ability to comp rooms to a hotel nearby.[citation needed] Many casino hotels have higher quality rooms, such as suites, villas, presidential suites, and so on for bigger bettors or VIP guests. Many players who receive hotel rooms receive a package called 'RFB' (for 'room, food, and beverage') or 'RF' (for 'room and food') for smaller bettors, or in jurisdictions where casinos are not allowed to give free alcohol.[citation needed]
Many casinos also offer other comps, especially to high rollers. These may include airfare reimbursement, limo rides, tickets to shows, golf, free concierge services, cash back, money to show up in the casino, loss rebates, private gaming areas, and private jet service.[2]
Casinos also frequently offer players comps by mail or email, or in casino apps. These may be free bet offers, free meals, discounted or free rooms, or entries into tournaments or prize drawings.[3] These offers will often come with terms and conditions that establish the rollover and wagering requirements.[4] An aspect most users overlook and the main cause for winnings withdrawal rejection.
Some casinos contract with bus companies to bring players in. Riders often enjoy free slot play, dining coupons, and other benefits, often worth as much as the bus fare itself.[5]
Calculation[edit]
Technically, every player may be offered comps, but most casinos require players to have played for a given period of time and play at a certain level, i.e., the duration of play and amount wagered are directly proportional to the level of expected comps. What games are played are also factors.[6] Casinos award comps based on a player's Average Daily Theoretical loss, also known as ADT, theoretical loss, or 'theo' for short. The theoretical loss is the amount of money a player is expected to lose based on the long run statistical advantage the casino has on the particular game being played.[7][8]
Theoretical loss algorithms differ somewhat among casinos,[9][10] but in general, the logic behind the calculation is as follows:
Casino Theoretical Win
- Theoretical Loss = (Casino Advantage) × (Total Wager)[citation needed]
Hustling[edit]
Players known as 'comp counters', 'comp hustlers', or 'comp wizards'[11] attempt to maximize the amount of comps they receive while minimizing their expected gambling losses.[12][13] Comp hustlers play games with a low house advantage, such as blackjack or video poker, or games with small bet sizes, such as penny slots. Comp hustlers may use tactics such as placing large bets when a pit boss is checking their bet size to rate them for comps, and then moving to a smaller bet size when the boss is not watching. They may also take frequent breaks from playing, play at full tables to be dealt fewer hands per hour, and play more slowly.[12] Comp hustling is a type of advantage gambling if the player is able to hustle more in comps than their average cost of gambling.[14] And the author of 'How to Get a Dollar in Casino Comps for Every Dime You Lose Gambling', in their summary of key takeaways from Max Rubin's book, Comp City,[15] observes: 'The next step up from being a comp wizard is to become a comp counter. These players have specific knowledge and skills that enable them to combine a low house edge with comps in order to profit.' Another step up are practitioners of 'ACES (Advanced Comp Earning System). People practicing this kind of system earn a dollar's worth of comps for every dime they lose gambling.'[16]
Casino Theo Win
Online[edit]
Online casinos, poker rooms, and sportsbooks offer a variety of bonuses that are similar to brick and mortar casino comps. Also similarly, comp hustlers and advantage players can use these bonuses to turn a profit via bonus hunting, or can convert these comps to a guaranteed profit using the technique of matched betting.
Casino Theoretical Formula
Many online casino operators are aware of the potential for losing money while giving out bonuses. As such, there is often a minimum wagering requirement for cashing out.
Some casinos will limit the payout in case of a win. Also, they may restrict players from playing certain games, often those games with a low house advantage. And, they may require players to bet the bonus amount multiple times before being able to cash out. For example, a casino may require a player to bet the bonus amount 50 times before being able to cash out. So, for a $100 bonus, a player would have to bet $5,000 before being able to cash out. Therefore, it is advantageous for players to check the wagering requirements of a bonus.[17] All bonuses have a turnover requirement. This means that placing a certain number of wagers, such as turnover 5x, means wagering 5 times the bonus. Most online casinos distinguish two types of bonuses: a no deposit bonus and a deposit bonus. First one does not require from a user to make a deposit at a casino in order to start playing. A deposit bonus requires from a user to make a deposit of certain amount of funds to start playing at the casino. Both of these type bonuses apply to terms and conditions of turnover requirements.[18]
References[edit]
- ^ abc'Keeping Customers Happy in Casinos'. ABCNews. November 1, 2007.
- ^'Cashback Casino Bonuses'. Best Online Casino Offers.
- ^Grochowski, John (17 June 2003). 'Comps - The Basics'. Casino City Times.
- ^'Rollover and Wagering Requirements'. Onlineunitedstatescasinos.com. Retrieved 7 October 2020.
- ^Moro, Marianne (Leaf Group). 'Travel Tips: Atlantic City Casino Tours'. USA Today.
- ^'THE EXPERTS GUIDE TO COMPS'. www.smartgaming.com. Retrieved 2016-01-13.
- ^'CASINO COMPS & YOUR 'AVERAGE DAILY THEORETICAL''. N.E. Time Gambling. August 10, 2016. Archived from the original on October 28, 2018. Retrieved October 27, 2018.
- ^Coach Kitty. 'Gambling: Casino THEO: It's All About the Theo'. TravelZork.
- ^Scoblete, Frank. 'Getting the Most from Your Slot Play: Points, Bounceback, Mail Offers and Good Machines'. CasinoCenter.com. Retrieved October 30, 2018.
- ^Coach Kitty (April 19, 2017). 'Caesars Total Rewards Part 4: Generating Casino Offers (Marketing OFfers)'. TravelZork.
- ^Stevens, Michael (June 10, 2018). 'How Comps Work In Gambling (And How to Make Them Work for You)'. GamblingSites.org.
- ^ abRubin, Max (June 2001). Comp City. Huntington Press. ISBN978-0-929712-36-9.
- ^Scott, Jean (July 2005). The Frugal Gambler. Huntington Press. ISBN978-0-929712-40-6.
- ^'Comp Hustling'. Casinopedia. Retrieved October 27, 2018.
- ^Rubin, Max. Comp City.
- ^Rubin, Max. 'How to Get a Dollar in Casino Comps for Every Dime You Lose Gambling'. Gamblingsitesonline.org.
- ^'Casino bonuses'. Retrieved 2014-03-07.
- ^'No Deposit Bonus'. Retrieved 2019-05-24.