Mission DOG TAG, fair or fake? Let's do the math!

Hi ppl.
The dogtag system fails me every time. I always get 8 of 9 dogtags, and then, after getting those 8 dogtags 3 times AGAIN, i get the last one.
So I'm gonna do the math here to prove the developpers that they need to find a new random generator for the game, OR , at least let them admit that it's programmed to NOT give you the dogtag for a number of days.


Let's assume:
1) the dogtag does not depend on the time of day when you finish your mission. ( meaning that whether i finish mission at 3 p.m, or at 4 p.m, has no influence on the tag.)
2) the dogtag does not depend on the mission. ( meaning that if - in an alternate reality - I were to finish mission 3 instead of mission 1 , i'd still get the same tag )
3) the chance of getting each dogtag is the same: 9 different tags, so chance of 1/9 to get each tag.

I will start from the fact that a player ( say myself ) already has 8 out of 9 dogtags. *(1)(see note at bottom of text about this assumption)
The chance of getting that last dogtag is 1/9. I will refer to this event as a 'POSITIVE'. The chance of getting a different one is 8/9. I will refer to this event as a 'NEGATIVE'.
From that day, the probability that I get the correct dogtag on the X-th day ( with X>1) is described by the geometric distribution function *(2)(see reference at bottom of text ).


For example: The probability (= the chance that this would happen to me) of getting a NEGATIVE for 20 days, and getting the POSITIVE on the 21th day is:


Pr(X=21)= POSITIVE * (NEGATIVE)^X-1
Pr(x=21)= (1/9) * (8/9)^20
Pr(x=21)=0.01053%


MEANING: there is a chance of 1.1 percent that this should happen to me.
Okay, you can say, 1.1%, if you have 9000 players, then this would happen to 99 of them. Okay, I can live with that.
But this calculation method applies to anything with fair odds. So using the same rule, let's calculate the probability of this happening to me ( or you )... about 5 times?

( with NEGATIVE = chance that it happens to me , and POSITIVE = chance that i doesnt happen to me )

Pr(Y=6)= (NEGATIVE)^Y-1 * POSITIVE
Pr(Y=6)= (0.01053)^5 * 0.98947
Pr(Y=6)= 1.2809E-10 ( = 0.00000012809 PERCENT chance, - don't count zero's, give or take XD )

Concluding: the chance that 5 times in a row, you get 20 NEGATIVES and then a POSITIVE is astronomically small.
Either I am the unluckiest ******* in the world, or the dogtag-system is programmed to give you anything but the right tag ( for number of days ). Or, the third option: The random generator used by the game is about as good a random generator as the following code:
for(int i=0;i<20;i++){
dogtag = Player.get_List_of_owned_Dogtag().get(i%8);
}

NOTES: ( for the educated ppl among u )
(1) If I start calculating from the very start (0 dogtags->8 different dogtags->then calculating odds for 9th tag), then the math gets to complicated to explain in a foreign language, but those calculations would conclude the same thing.
(2) geometric distribution : this is a function that describes the chances of event with succes rate 'p' occurring after 'k-1' fails. See wikipedia if u are not familiar with basic statistics http://en.wikipedia.org/wiki/Geometric_distribution