How often is it you meet a 3rd party service provider or even an agency that doesn't know your lingo? ADT, theo win, slot occupancy – these are just few terms that are tossed around daily by casino executives, marketing teams and database marketing departments. We get it, we know your language, and we're here to help.

Casino Theo Wins
Casino Theo Win Free
Casino Theo Win Loss
Casino Theo Windsor

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. The casino industry’s methods of analyzing gaming devices are based on metrics, such as win per unit per day or theoretical win per unit per day. In this article we dig into two types of metrics, optimization and outcome, and we show why traditional outcome metrics, such as theo win. The “theo” or “theoretical” is the actual dollar amount the casino expects to win from the player. The “return to player” measures the fraction of the player’s total wagers the player is paid back in live casino play. Coin-in and coin-out is the raw data needed to calculate win/loss data. If you placed $100 in wagers and got $95 back, your loss is $5. So to you it might look like you put in a $20 bill and cashed out with $15, but to the casino it looks like $100 and $95 because the total wagers is an important part of the casino math.

If you're new to gaming or training new employees, please refer to the below glossary of casino marketing terms. This list should help make meetings and casual conversations with casino industry veterans less stressful.

A
Acquisition
The process of acquiring new guests. In gaming this refers to gathering new player’s club members.
Active
Player’s club members that have played within a certain time period, usually in the last 12 months.
Actual Win
The monetary amount the casino actually wins from a player. There can be a large discrepancy from theoretical win (Twin) if someone hits a jackpot or if there is a savvy table games player. Also known as 'casino win.'
ADT
Average Daily Theoretical win (See Theoretical win).
B
Bonus Points
Points that are not earned but rather awarded based on a promotion or event.
C
Carded Play
The portion of total gaming revenue that was tracked using player’s club cards.
Casino Win
The monetary amount the casino actually wins from a player. There can be a large discrepancy from theoretical win (Twin) if someone hits a jackpot or if there is a savvy table games player. Also known as 'actual win.'
Coin-in
Total bets cycled through a machine that includes both cash-in and credits played. Also referred to as ‘bet,’ ‘handle’ or ‘wager.’ Total coin-in reflects both carded and non-carded coin-in. Carded coin-in reflects only coin-in generated using a players club card.
Core Program
Regular monthly life-cycle program. (Acquisition, Loyalty, Downtrender, Recapture, Birthday, etc.)
Criteria
The selected parameters that need to be met to receive an offer or enter a tier or segment.
D
Database
All player data collected through the player's club, including gaming data, demographics,preferences, etc.
Demographics
Characteristics such as annual income, age, sex, distance to the casino, etc., which can be used to project or influence behavior.
Direct Mail
Mail programs in which offers are targeted to guests based on specific, pre-selected criteria with a specific marketing goal (acquisition, retention, reactivation, etc.). Can include email as well.
Downtrender
A player’s club member whose current play is lower based on Twin per month or quarter than it has been in the past. This can be attributed to a loss in frequency or spend.
F
Frequency
How frequently (often) a player visits and has activity. Trips in a distinct time period can also define this.
G
Goal
The purpose toward which an endeavor is directed. The state of affairs that a plan is intended to achieve and that (when achieved) terminates behavior intended to achieve it; “the ends justify the means.” Most gaming program goals involve Acquisition, Retention/Loyalty, Stretch, Recapture.
H
Hold
The amount the game or group of games made for the organization. This is based on game type, skill level, odds and system settings.
Hotel Occupancy
The amount of rooms occupied/sold expressed in a percentage of those available.
I
Incremental Win
The difference between win that normally would have occurred based on a guest’s RFM score (see RFM definition below) and win when provided with a stimulus (i.e.: a coupon).
K
Key Metrics
Identified areas of measurement that are considered high priority in analyzing operational performance.
L
Layering
Creating offers and promotions in such a way as to allow players to redeem multiple things in one trip/day.
M
Marketing
Everything involved in the movement or sale of goods.
Marketing Mix
The percentages and dollars budgeted to each sub department in the overall marketing department.
Market Share
The amount of Guests that patronize our casino vs. visiting other casinos in the area.
Member File
The entire database of player’s club members; all enrolled members including active and non-active.
Modeling
Identifying particular demographics that model a particular behavior such as gaming characteristics. Used primarily in determining acquisition efforts.
N
New Members
New patrons joining the player's club database.
Non-Active/Inactive
Player’s club members on our member file who have not played within a specified time period.
O
Offer Redemption Percentage
The quantity of players that redeem a specific offer expressed against the total number of offers distributed. (total offers redeemed / total offers issued = offer redemption percentage)
P
Player Development
This definition varies widely; it is used to describe the internal department and functionality of casino hosts. In actuality, it is everything involved in increasing loyalty and therefore the RFM of each player. This includes one-to-one service, personalized benefits, direct mail offers and copy, etc.
Player Type
Usually used as a stratification tool based on distance of residence or by arrival type. Examples include local, junket (bus), group (convention), destination, etc.
Postforma
A document that measures the profitability of a specific program. This includes all program-specific expenses and revenue. Preforma is a similar document that is used for forecasting a program's profitability.
Preforma
A document that projects the profitability of a specific program. This includes all program-specific expenses and forecasted revenue. Postforma is a similar document that is used for measuring acutal profitability of a program.
Profit Margin
The percentage of expense compared to revenue. Net Revenue / Gross Revenue = X%
R
Reactivation
The process of attracting guests who have not played for an extended period of time, but at one point were active.
Recency
A method of measurement that identifies how recently a wager or purchase has been made.
Response Rate
The quantity of players who responded to an offer expressed against the total group of players issued offer(s). (total player responders / total number of players who received offer(s) = response rate)
Retention
The process of retaining current guests on the member file. The period of time used depends on the overall RFM of the member file. This sometimes means re-activating members from the member file that have become inactive. Reactivating members is 1/3 of the cost of Acquisition.
RFM
Recency, Frequency, Spend. A common method of assessing value of customers through recency, frequency and spend. Spend refers not only to the wager amount but also the items/services purchased.
S
Script or Point Redemption
The financial term for the cost of the cash back redemption. It is generally one of the larger expense items.
Segments
Defined groups within the database based on recent play and used to determine the offers the patron will qualify for.
Share
The portion of the spending that occurs at our facility vs. other entertainment organizations.
Slot Occupancy
A plan of action intended to accomplish a specific goal, using all the forces to execute approved plans as effectively as possible.
Stratification
To divide guests into a series of graded statuses or classes; i.e. dividing the database into tiered segments based on player type, etc.
T
Tactical (Tactical Execution)
An expedient for achieving a goal; a maneuver of less long-term significance than strategic operations or strategy.
Theoretical Win (or Theo Win or Twin)
The amount that the casino should win in theory, based on hold percentage and the random number generator or game type/odds. (coin-in x hold = theoretical win)
Tiers
Most often used to describe the defined groups within the player's club structure based on play and used to determine player's club benefits.
Trip(s)/Days
The frequency measure used in gaming. A defined period of time that starts when the player’s club card has been inserted and there has been play. The length of a trip and associated parameters vary widely.

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).

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

Casino Theo Wins

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

Casino Theo Win Free

=1.075352

Casino Theo Win Loss

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.

Casino Theo Windsor

There you have it. Good luck!