Authors’ Note: On this fifth article of our 12 part series on customer centric gaming floors, we will be able to examine the price of availability and queueing mathematics, and the way they are often applied to the slot floor. Please note these articles are supposed to stimulate thought and that we're using some deliberately provocative metaphors and examples which have to be all in favour of a grain of salt.

It’s no secret that slot players are sometimes willing to attend to play their favorite game. What's more of an unknown is how long will they wait before they walk clear of the slot?

In the fashionable casino, determining the typical wait time for specific games is a vital factor for operators trying to optimize slot floor performance. At the surface, this will likely seem an effortless equation to resolve; in actuality, it requires availability and queuing theory—a level of mathematics well past standard optimization metrics.

The availability theory we explore below relies on well-proven manufacturing models adapted to the gaming world. This approach will develop the intuition and mathematical formulas required to drive this significant analysis.  Finally we introduce preference filters into the combo to come back up with a real determination of ways long the most efficient customers must wait to play their favorite games.

OPTIMIZATION METRICS PRIMER

In part two of this series, we described the significance of the player perspective. To have a look at the gaming machine from the player perspective, we wanted to seem into metrics which can be felt by the player. Players don't sit at their game and look at the hold percentage or the theoretical win per day of the sport. Instead players live within the gaming experience—feeling how much they win or lose, they alter their betting behavior in line with the result of the games; they usually feel the impact of a game they would like to play being occupied by another player or players. To optimize the games, we want data that may see into the gaming experience and optimize it. This approach may be very different to optimizing the result of the game—to clarify this, we describe two other forms of metric: optimization and outcome.

Optimization metrics: These are metrics that measure effects the players can observe. In our previous articles, now we have explored how occupancy and the price of the sport play including game speed are the important thing optimization metrics. The following article we dig deeper right into a new and more predictive roughly math—the math around queueing theory. In short, we wish to optimize the provision of games to players; for example, we wish to make certain that high-value players can generally find the sport they want, within the location they might wish to play it. While the maths is complex, the consequences are remarkable in that it allows us to drive the yield of the sport. In summary, we now have a brand new class of metrics called availability, and this class of metrics tells us if a game is out there at any point in time.

Outcome metrics: These are metrics that the players don't observe. For example, the theoretical win per unit per day at the gaming machine, that is a typical from various different players. Quite simply, players don't experience the spending of alternative players. Another outcome metric is the slot floor hold percentage, or what's often incorrectly termed the “price” of our games.

AVAILABILITY ACTIONS

Game availability is central to the user experience and optimization of that have. Imagine a floor where we relate customer preference for a particular game and the chance of that game being available once they want to play it. To know the facility of availability modeling, let’s consider the next eight optimization questions:

Should I'VE a ten pack or a 12 pack of games on this area? The form and selection of games is obviously important, but something as fine grained because the value of a ten pack of slots versus a 12 pack of slots is tricky to look analytically. When checked out using availability, the direct value of availability to players can also be calculated.

In a mixed bank should I run two of any game? As we can show below, the probability of finding a game you prefer is massively increased while you move from one game to 2. Armed with this knowledge, the gaming floor can now be optimized to supply high preference games where needed. Furthermore, we will be able to back into the provision models using hypothesis testing; in other words, change the ground and measure the modeled versus actual outcome of the gaming optimization decisions.

Are there any games which can be substitutes for a well-liked game?One solution for a game availability issue is to usher in substitutes, which gives a low-cost way of finding games that act as “drawcards” for other games.

How many games should I'VE at the floor? Optimization may also help operators determine the perfect choice of games there have to be at the slot floor. For example, a floor can have 1,000 games, but operates optimally with 950. These small changes balance the selection of games with the capital/depreciation and running costs of these games.

Can I close off areas of the gaming floor at certain times of the day?This is a critical question on the subject of reducing staff, power and other operating costs. The trick is to do that in some way that also ensures availability of the suitable gaming experience in a unique area of the ground. Consider the instance of a room where there exist players who've a robust preference for that room—closing that room will directly impact this player group.

How does a jackpot impact the provision of a game? On a contemporary gaming floor, there are levers that may be pulled to regulate the supply. For example, adjusting the jackpot behavior changes the occupancy and so it may be modified to maximise yield.

Are players waiting in line to play this game?Oftentimes customers will play a game with a lineof sight to the slot they would like to play. The provision of a game gives a view into the chance that players are waiting.

How does the provision invert to foretell demand? The inverse of availability combined with game presence gives us a metric that may be representative of demand. Game demand is a measure of its attractiveness and offers critical insight into the need of adding or removing games from the floor.

PICK YOUR POISSON

These eight optimization questions illustrate how the provision metrics of a game opens the door to a brand new approach for customer centric gaming floor management. There are various mathematical approaches to calculate availability, starting from simulation models to numerous statistical techniques. One powerful method is predicated at the Poisson distribution.  This technique is advantageous since a small amount of key metrics may give accurate predictions.

The Poisson distribution is called after by Siméon Denis Poisson and gives a remarkably simple mathematical model that determines the probability of a variety of events occurring in a selected time frame. This straightforward distribution have been applied in powerful how one can understand wait times in queues. For our purposes, we can explore the chance that a customer’s preferred game is unavailable once they wish to play it. On this example, there are two separate calculations to consider—customer play a selected machine and the possibility that this machine is available.

Example question: Given a machine is occupied, what's the likelihood that a player desirous to play this machine finds the machine occupied between the hour of 5:00 pm to 6:00 pm on Friday over a six month period?

Example assumptions: The Poisson distribution requires a suite of assumptions; the next is an outline of ways these assumptions are met within the context of the instance question:

• The development of finding the occupied machine can occur greater than once within the hour.

• Each player finding the occupied machine is independent of different players finding the similar machine.

• For the duration of time between 5:00 pm to 6:00 pm on Friday, the speed of the development is the same.

• Two events cannot occur at the exact same instant.

• The probability of an event in an interval is proportional to the length of the time we're examining.

• The standard with which that if these conditions are true determines the applicability of the Poisson distribution.

IN ALL PROBABILITY

Given players can find the occupied game within the time between 5:00 pm to 6:00 pm and that this will occur quite a lot of times, the common selection of events in an interval is designated λ(lambda). Lambda is the speed at which individuals find the occupied game, also referred to as the velocity parameter. The development of finding the sport occupied has a percentage chance of happening, and the formula for determining this percentage is shown in Figure 1: Poisson Distribution.

To explore the facility of this formula, let’s consider the instance of the individual finding the occupied game 2.5 times per hour (λ = 2.5). This situation is simplified to turn how the mathematics can also be applied and, like several models, the standard of the input data and the way it meets the assumptions determines the accuracy of the consequences. That being said, we will see that the Poisson distribution gives fascinating insight into the player experience, and it might probably show the impact that an occupied game will have at the player gaming experience. What's remarkable is that the knowledge to calculate that is available, and that it opens the door to optimization of the gaming floor according to the supply of games.

However, to take these calculations to the following level, a unique more or less math called queuing theory is wanted. Indeed, given this illustration of the way the maths of availability can also be calculated, we have to dig into way more sophisticated models to make this idea directly applicable to gaming and to plan gaming specific models that operators can apply to their casino floor. Queuing theory is usual in lots of business areas, retail checkout models are an example, and it's been proven in all kinds of applications. Using these calculations, critical questions reminiscent of the impact of adding an extra game or the chance of finding a customer’s game occupied can also be explored. These models are extremely powerful and in future parts to this series we will be able to cover how you can create and apply them. sM&M

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