The mechanics of RC popularity is poorly understood. But simply put, popularity is a measure of efficiency. Because different restaurants have complex mechanics, we will picture a simplified ideal restaurant for a simpler understanding of the matter.
Popularity achieves a state of equilibrium depending on the efficiency of the restaurant. For every satisfied paying customer, 0.1 popularity is gained. On the other hand, every unsatisfied customer decreases popularity by 0.1. For every restaurant, there is a maximum capacity determined by the layout. That is, all restaurants have only a certain number of customers it can serve over a fixed amount of time. The ideal scenario is the case where whenever a customer orders a meal, the waiters can serve it instantly, consuming only 15 seconds preparation time to serve each customer. With 6 chefs cooking 1 meal each every 15 seconds, this gives us 24 customers served per minute. This is equivalent to 24 thumbs up per minute, which then gives our restaurant a 2.4 popularity gain per minute. Thus, if there were no unsatisfied customers, the popularity would increase until it reaches the 50.0 popularity cap.
However, unsatisfied customers are inevitable. Popularity increases the number of people going inside the restaurant, and there will come a time that more than 24 people per minute will go inside the restaurant. First, 25 people per minute will enter. No matter what we do, that extra customer cannot be served. Thus he will leave, and give a negative point. This will give us a net gain of 2.3 popularity per minute, but this is still a positive value and will still increase our popularity. As popularity increases, there will come a time that the popularity is high enough so that 48 people will enter the restaurant per minute. 24 of them can never be served, and thus will leave giving us -2.4 popularity per minute. At this time, the number of thumbs up and thumbs downs are equal and thus the net popularity gain is 0. The popularity rating will remain steady, and this will be our equilibrium point. The popularity rating at which this occurs is the equilibrium popularity, which is the popularity at which satisfied and unsatisfied customers per minute are equal.
(This is where I state the logic for letting us have more employees! We do deserve them.
)More efficient restaurants can serve more customers per minute so their equilibrium popularity is higher. Sometimes the restaurant is efficient enough to be worth more than 50.0 popularity, meaning at 50.0 popularity, more customers get served than leave unsatisfied. This leaves the net popularity gain per minute a positive value, but because there is a cap, no gain in popularity occurs and no extra customers enter per minute. This is why I think the 50.0 cap is pointless, as there is still a maximum number of customers 8 employees can serve. Only when the number of employees are unlimited will a popularity cap make sense. This can also serve as a reason as why we should be free to hire as many employees as we want: the maximum amount of customers we can serve is determined by how many customers enter the restaurant anyway and so it shouldn’t matter if we use 20 employees serving them or if we use only 8. Nevertheless, this is a separate issue which isn’t directly related to the issue at hand.
More often than not, for low-level restaurants and inefficient restaurants, the equilibrium point is achieved before the 50.0 popularity rating is reached. But people want to achieve 50.0 popularity no matter what, and so resort to using arcades.
Solnaga's level 5 restaurant. You can see that with the addition of arcades, the popularity rating of his level 5 restaurant has increased and reached the 50.0 popularity rating cap. Although he has lots of customers inside, he can still serve at most 4 customers per minute, and has not improved his GP or EXP earning capacity. http://forum.playfish.com/showthread.php?p=20447718
Arcades raise the equilibrium point by preventing customers who cannot be served from giving a thumbs down. In a restaurant which is already at equilibrium, each arcade added will decrease the number of thumb-downs per minute. Let us say that an arcade takes 15 seconds as well for a customer to finish before leaving. This gives us up to 4 unsatisfied customers per minute per arcade who are prevented from giving a negative rating. At our current popularity if we add 1 arcade, that means that 24 customers will get served, giving 2.4 popularity per minute, 20 people will leave while giving -2.0 popularity and 4 people will use the arcade and leave without a rating. This gives us a net of 0.4 popularity gain per minute, and thus will increase the popularity. This will go on until such a time that the popularity is high enough so that 52 customers enter the restaurant per minute, with 24 being served and giving 2.4 popularity per minute, 24 people leave and give -2.4 popularity per minute and 4 people leave after using the arcade. At this time, a new equilibrium popularity is reached. As seen from this example, arcades increase the number of customers coming to the restaurant, but do not affect the rate at which they are successfully served. In our example restaurant, only 24 people per minute can be served, no matter how many arcades we have. It is therefore evident that even though arcades can increase the popularity of a restaurant, it does nothing to increase the rate at which the restaurant earns money and GP, which is solely determined by the number of customers served by minute, and not the total number of customers going inside the restaurant per minute.
In summary, even though arcades can make a restaurant’s popularity go up, it does not increase the rate at which customers get served, which is the sole thing that determines the rate of Exp or GP gain. It is worthy to note that popularity can only be seen by you, and not by any visitor, and so it is pointless to have 50.0 pop with the use of arcades if your concern is to make your restaurant ‘efficient’ or to earn money and exp faster. If you are new to the game and would like to level or gain money faster, arcades are not a solution. But if you like the way it looks in your restaurant or if you like seeing the number 50.0, then by all means use it.
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