Morning Maths - or - Finding the nerdy side of Covet Fashion

My friend D spent the week-end with me and we had a wonderful time having the most girliest week-end ever with baking Nutella-bread, watching "Gift vid första ögon kastet" (Married at first sight) and playing Mortal Kombat X

During the week-end D had also introduced me to a game called Covet Fashion and on Monday morning she came to the breakfast table with a thoughtful look on her face and asked the question

"How many votes on average does my look get per event?"




Asking this type of question with mathematicians around the table is of course a dangerous matter and soon enough, Matte had found some pen and paper and the calculations had started (We were both late for work that day)

Some background first before I get to the calculations.
Covet Fashion is a game where you create "looks" that you enter in to events. These looks are then voted on by everyone in the game and you get a score based on how well your look was ranked vs the other looks.

It costs tickets to enter events and to get tickets you need to vote on other looks. Voting works as such that two looks in that event are randomly picked out and presented to the player. The player chooses which one s/he likes and by choosing that look the other look gets a negative vote. So for every click the player does, 2 votes are made, one positive and one negative.

What my friend wanted to know was how often just her look for that event got shown to other people. In other words, how many times was her look voted on.

As I mentioned before, it costs tickets to enter events. There is always one event that cost 15 tickets and the other events costs 25 tickets. You get 20 tickets free as a daily gift and by voting, you get 2 tickets for every five choices you do. As each choice is in fact 2 votes, we will say that 10 votes = 2 tickets, and simlpified, 5 votes = 1 ticket

So let us say that the average player will enter x events per day where x ranges from 1 - 6.
The reason the maximum is 6, is because that is the maximum number of events possible to enter in one day.

We also assume that everyone who is playing the game enters at least 1 event - otherwise, why play the game? There could be players who just play Covet Fashion to vote on other looks be we deemed them not a large enough group to take in to consideration.

So our assumptions so far:
1. A player will only vote to get enough tickets to enter the average number of events s/he wants.
2. A player will always enter at least 1 event.

3. A player will always enter the event that costs only 15 tickets because there are other factors that motivates this (more ingame money and such)

We start with setting up the initial formula for T(x) as the total number of tickets a person needs to enter x events:

Each event costs 25 tickets, except the first event which costs 15 tickets. So the above formula will give us the number of tickets required for entering 1-6 events.

But the individual player gets 20 free tickets every day and we are more interested in how many tickets the individual player needs to gather so we set up a new formula P(x) = T(x) - 20. P(x) is therefore saying how many tickets a player needs to get to enter x events. When we simplify this formula we get the following:

We have a nice formula saying how many tickets a player needs. Now what? We are interested in how many votes a look gets on average so how is this formula going to help? Well. We have a nice connection with tickets and votes. For a player to get 1 ticket they need to vote 5 times.

We therefore set up the relationship "Vote needed for x events" V(x) as 5 times the number of tickets needed for x events:

And V(x) in x:

So we now have a formula for the number of votes a player needs to do to enter x events.

As we had also assumed that each player will only vote to get enough tickets to enter the events they want, we can therefore say that the total number of votes in the system will be p*V(x) where p is the number of players. So the only thing left to do to answer the question is divide by the number of players and the average number of events the player will enter per day:

This gives us the following formula for average number of votes per look:

So all that's left to find out is what is the average number of events a player at Covet Fashion. This is usually company secrets.. so I sent them a twitter message. Let's see if they answer :-)