Winggy Wing reloaded

A small message wrote with a crooked finger on the dust of my monitor awared me this morning:
I’m back!

That moment I knew that Winggy Wing did return. Because is hard to hide or to move to another apartment in such a short time, I decided to face her and to teach her a lesson of dignity.

Therefore I came back from my job and I screamed, as usual:
Fuck! Fuck! Fuck! Fuck! Fuck! Fuck!

Then, with a smile in the corner of my virile mouth, I said:
Come out, Winggy! Repair that!
And I added about 84 more Fuck!s.

This wasn’t fair at all!, said a voice and Winggy suddenly appeared through the walls. I don’t care, it’s your job to protect me, so do it, bitch!, I said laughing a lot in my inner forum. But why, honey, why?, asked her. Because of Prizee, this is why! And all is your fault. Of course, she said, let me see what is all this about. Tell me everything, we’ll get a solution.

Ok, remember our last discussion? I have more news related to this damn game.

First of all, let see a more actual graphic of bubz, got between the dark age between Silver 4 and Gold 2 ranks.

You discovered the “ultimate formula” of the game
Bubz = 0,0274 * DayNo + 25,562

..and I was happy a while. A short moment.
Then I started to think about relations and rules that acts between the classes of bubz.

I said: Let study a little bit the main classes of bubz, 0-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, 81-80, 91-100 & over 101. If I consider my daily earned bubz as an instance of one of these classes, maybe I’ll be more closer to the mastermind behind Prizee.
And this is what I done.
For instance, if in day #414 I got 33 bubz, then day #414 will be labeled with class 31-40. This way we get a sequence of classes instead of a sequence with numbers.
This is pretty funny, because the next step is to represent in terms of graphs the relations between these classes.

Interesting, this is a connected graph having the incident matrix

Ok, it’s a small step for man, but a huge one for… dolphins. Because mankind has different stuff to do.
Now, we get the background for detecting the behaviour of each class. Because the graph built is a very common random graph, let generate random paths on it and see what kind of distribution we get for each node/class. It would be like 1000 users would play based on the statistics hidden in the early displayed bubz per day data.

Good plan. But how?

Simulating plays under the control of statistics bubz per day produces our first nice result:

		Result #1  Each class of bubz is instantiated based on a normal repartition.

These are pretty good news related to the honestity of the people who give us our daily bubz.
Of course, it matters a lot the average and the standard deviation of the repartition, but what the hell!, in a way or another, if we play enough, we will get “for sure” any instance of the classes. I mean all! For sure you will get a day when you will get less than 10 bubz, and this – doesn’t matter if you are Platinum 4 ranked! Of course, the probability is small, but it still exists.

In my case, the probability of getting less than 10 bubz is about 4%, and to be honest, in about 150 days it happened once, in the darked day #526. On the other hand, in the early days of of Bronze rank, it happened many, so painfull many times…

You can see beside an example of a beautifull Gaussian bell for the class 61-70. See the rest of distributions bellow.

This is the behaviour of each class of bubz, ok.
What about the relationsships between them? If, let say, if today I make 42 bubz (therefore an instance of class 41-50), what should I expect from the day of tomorrow? Ok, I have an formula which estimates me a certain amount of bubz, but I want more!

Actually, it would be nice to have what could be called the genealogy tree of the bubz.
Obviously, some classes of bubz are more appropiated by another ones, more often it happens that after a day when you get something between 21-30 bubz the next day or the previous one you got something from 41-50 or 11-20. Basically, it is the ancient say that “a trouble never comes alone” – or something like that. If there is no such a say, it should be created.
Well…

Ok, here it comes the nicier part of applying the great neighbour-joining algorithms.
I will come back later with some small details on this and also on the metric used. If you want to get an idea about what this metric is and how it is related to the the neighbour-joining algorithm see

An Eficient Approach for the Rank Aggregation Problem

A low-complexity distance for DNA strings

written by an interesting math guy called Liviu P. Dinu.
Anyway, I used his metric – which actually is one of a common-sense with some really astonishing results in genetics.

Ok, here we go. Bellow you get the data processed in a very primitive way.
On the first hand, the table of neighbour occurrences:

On the second hand, the rankings of each class based on its neighbours:

I was a little bit forced to work with characters (A,B,…,K) instead of ordinary numbers (1,2,…,11) for fetching data with my app. Anyway, A stays for 1, B for 2,…, K for 11 and the meaning of the row 41-50 DECBFGAHIJK, for instance, related to class 41-50 is this one: class 0-10 is the 4th/D ranked from occuring as a neighbour for class 41-50, class 11-20 is 5th/E ranked, class 21-30 is 3rd/C ranked and so on up to class over 100 which is 11th/K ranked from the same neighbour point of view.

Pretty exciting.
Now we can run our small .NET app and get this genealogy/philogenetic tree of classes of bubz.

		Result #2  The genealogy tree of classes of bubz is:

It can see the “balancing” way of acting of the bubz generator. As a famous Prizee player, Mr. Fazikowi, said in a certain moment of his life, if you get something poor in bubz today, let say 8 bubz, it’s pretty probable that yesterday/tomorrow you got/will get about 60-70 bubz.
Of course, the general formula published in the previous post acts very ok, but in a statistical way. Concretelly, today or tomorrow there are good chances to get bubz in the most appropiated “relative” class to the one I instanciated today.
Got it?

Winggy!
What the fuck are you doing while I’m speaking here…..?

(c) marius09.wordpress.com

		Thanx! Pics above were collected from: http://www.imagehousing.com/image.php?file_thumb=http://img396.imageshack.us/ img396/7388/cce730aa16309b2c4dfc3ecqw0.th.gif&cat=angel http://www.imagehousing.com/image.php?file_thumb=http://img152.imageshack.us/img152/6056/ 3e6b90a86a43e51015521dczy7.gif&cat=funny

		Normal distribution for each class of bubz

		Info for next generation of prizeefobia     Prizee is a nice French site hosting a set of Flash games. As everywhere in this part of universe, you create an account and start to play. What to play? Well, there is a standard set of different games and you get only one of each per day, for free. If you want more, then you pay and get more. It is about you, I am too parsimonious. Winning a game will put some bubz in your bag. When you get a certain amount of bubz, you can order various gifts. Try it, if you really need to lose some time…

		More info about Kolmogorov test & the other algorithms    …I’ll be back on these. Anyway, the net is full of examples and discussions around these topics

		Evolution of population of Winggy Wing’s fans

(c) 2009 marius09.wordpress.com