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Forum > Tuber's secrets > thread

Letter Appearance Hypothesis

Le Panthéon ! 1
Tuesday 21 Apr 2009 07:58
Yeah, I had a bright idea the other day - instead of trying for the big crystals EVER I go entirely for letters (with the exception of levels like 31 or 52 where you can only kill one at a time, or levels like 53 or 41 where it's fairly easy to kill three at a time and get the crystal. Or levels that are pretty hard). As you may or may not know, depending on how many enemies you knock off with one bomb, you will see up to that number of different letters on the next run.

What I've discovered, however, is that it is a better strategy to only knock out two or three at a time instead of as many as possible. This is because of the probability a letter will appear is different for each letter and I've observed fairly frequently that it makes a difference not only based on how often the letter appears throughout the levels but also how often it will appear in that particular level. Thus, if you knock of three enemies the probability pool is drawing from three letters (say I, L and A) but if you knock off 5 you'll be drawing from a pool of five letters (say I, L, A, R, C)

Never mind the fact that the fireball usually will come around about the time of say, the 5th or 6th letter, in the first case you are more likely to draw the L than in the second case because of the smaller probability it must have. Lets say the probability of letters being chosen for a level is:

C: 1/5 R: 1/5 I: 1/10 S: 1/10 T: 1/20 A: 3/10 L: 1/20

As Decimals:
C: .20
R: .20
I: .10
S: .10
T: .05
A: .30
L: .05

In the first case (I + L + A) the total of these decimals is .1 + .05 + .3 = .45 and the probability then of an L being selected is .05/.45 or 1/9. In the second case (I + L + A + R + C) the total is .1 + .05 + .3 + .2 + .2 = .85 and now the probability of drawing an L is .05/.85 or 1/17. Out of 5 letters there is less than a 1 in 3 chance of you actually seeing an L, and that's if you don't kill all the enemies in that time.

Now, this is only a personal observation over about 200 games, but I'm going to start gathering actual data for use. Though I will ask, is there a list or even better a data table of the most common/least common letters already available? The general frequency seems FAIRLY obvious with T and L being the rarest and A and... probably R being the most common, with C, I and S being mixed in there somewhere, but if a pretty reliable table of this data already exists that would be rather convenient.

Am I over-thinking this? The fact that I get an average of 8-10 CRISTAL's per game (usually one in the first 10 levels) tells me no, but I could just be blowing my own horn before knowing the full story.
Le Panthéon ! 1
Tuesday 21 Apr 2009 09:01
Well, at the very least, the decimals seem about right; just one edit i'd like to make:

C: .20
R: .25
I: .10
S: .05
T: .05
A: .30
L: .05


S seems just as rare as T or L to me, while R appears almost as often as A. ;)
Le Panthéon ! 1
Tuesday 21 Apr 2009 09:02
According to a sticky on the french forums, the chances of each letter appearing are exactly this:
C: 16%
R: 16%
I: 16%
S: 10%
T: 16%
A: 16%
L: 10%
Le Panthéon ! 1
Tuesday 21 Apr 2009 12:11
I have noticed that many times I get the C-R-I or C-R-A combinations. Almost every time if I have got two of that letters and I expect 3, I know which one the third will be.
Le Panthéon ! 1
Tuesday 21 Apr 2009 13:28
C: 16%
R: 16%
I: 16%
S: 10%
T: 16%
A: 16%
L: 10%
??? Never. S and L, okay, but A and R appear more frequently, don't they???

ColdFrog: you forgot one thing - when you kill three enemies, your chances of the L being in the pool decrease. So you have an increased chance of finding the L if it is in the pool, but a decreased chance of actually having it in the pool...

electriczax: I think this is just depending on luck - I think that R and A are more common, so C-R-A is nothing special. I could also say that I have often had exactly C-I-A (it is true!) and C-S-A, but I think there is no special thing about that
Le Panthéon ! 1
Tuesday 21 Apr 2009 19:20
C: 16%
R: 16%
I: 16%
S: 10%
T: 16%
A: 16%
L: 10%
??? Never. S and L, okay, but A and R appear more frequently, don't they???

If it's posted by an admin I GUESS it's true, but I still don't believe it. I'd want to compile some data just for that .


ColdFrog: you forgot one thing - when you kill three enemies, your chances of the L being in the pool decrease. So you have an increased chance of finding the L if it is in the pool, but a decreased chance of actually having it in the pool...


Hmm, good point. Well, I've still found my way to work well for me, but I wonder if I can take this into account... I'll think about it.
Le Panthéon ! 1
Tuesday 21 Apr 2009 19:24
If it's posted by an admin I GUESS it's true, but I still don't believe it. I'd want to compile some data just for that .

It wasn't posted by an admin, but it was posted by a moderator, which is almost as good.
Le Panthéon ! 1
Wednesday 22 Apr 2009 11:09
I don't know why you bother with this so much. This is a % chance. So this % chance can change every game. You have 10% chance of getting L, but I've played games where I don't get L in 30-40 levels! There were games that I have waited for each letter for many levels. So I don't care if I have 10 or 99% chance of getting it. What I care is if I get the letters in the game I play at the moment.