Hero to Zero: How to transition to Folrart from Crest

[InigoMontoya]

From http://www.alteil.com/forum/index.php?f ... ic&start=0:

There is some transparency in the boxes, but we don't know the distribution of the card lottery. So in the interest of science, I just now purchased the maximum of 99 cards at once through the card lottery and here’s what I got:
2 three-stars
6 two-stars
91 one-stars

Note that I am notoriously unlucky and once again get screwed.

[hanul]

let say the distribution of the card lottery is in proportion to the card recycle value.

5 star: 300 4 star: 150 3 star: 30 2 star: 10 1 star: 5

Let G = Gran you get from lottery ; Let y be 5 star card.

therefore 4 star = 2y 3star = 10y 2 star = 30y
and 1 star = 1 - [ y+2y+10y+30y]

G = 300 x y + 150 x 2y + 30 x 10y + 10 x 30y + 5 x {1 - [ y+2y+10y+30y]}
G = 1200y + 5[1-43y]
G = 985y + 5

10g per lottery
If G = 10 it is a no gran lose distribution, therefore G < 10
G = 985y + 5 < 10
985y + 5 < 10
y < 0.5

5 star < 0.5% 4 star < 1% 3 star < 5% 2 star < 15% 1 star < 78.5%
If y > 0.5 you gain gran per lottery.

I might be off and there is condition needed.

[InigoMontoya]

let say the distribution of the card lottery is in proportion to the card recycle value.

5 star: 300 4 star: 150 3 star: 30 2 star: 10 1 star: 5

Let G = Gran you get from lottery ; Let y be 5 star card.

therefore 4 star = 2y 3star = 10y 2 star = 30y
and 1 star = 1 - [ y+2y+10y+30y]

G = 300 x y + 150 x 2y + 30 x 10y + 10 x 30y + 5 x {1 - [ y+2y+10y+30y]}
G = 1200y + 5[1-43y]
G = 985y + 5

10g per lottery
If G = 10 it is a no gran lose distribution, therefore G < 10
G = 985y + 5 < 10
985y + 5 < 10
y < 0.5

5 star < 0.5% 4 star < 1% 3 star < 5% 2 star < 15% 1 star < 78.5%
If y > 0.5 you gain gran per lottery.

I might be off and there is condition needed.

Your math looks good except for the 1 star probability. That should be > than 78.5%, not less than 78.5%.

[Peralisc2]

Could be worse. Its not something you can test.

[InigoMontoya]

Could be worse. Its not something you can test.

When you say "could be worse," I'm assuming you mean the percentage chance of getting a one-star could be worse than 78.5%, whereas I said the chance of getting a one-star was greater than 78.5%. You then said it was not something you can test.

I beg to differ. Mathematically, the chance of getting a one-star isn't worse than 78.5% and you can test it. In fact, if you look through the thread you will see I did test it.

"... in the interest of science, I just now purchased the maximum of 99 cards at once through the card lottery and here’s what I got:
2 three-stars
6 two-stars
91 one-stars"

So from the test, you can see the chance of getting a one-star with an N of 99 was 92%, which is not worse than 78.5%.

All of Hanul's predictions worked out actually. He predicted less than 0.5% chance of getting a five-star, less than 1% four-star, less than 5% should be three-stars, and less than 15% should be two-stars. The only error he made was he forgot the one-stars are calculated by {1 - [ y+2y+10y+30y]} so if the two to five-stars are *less* than certain percentages, that makes the one-star frequency *more* than the remainder.

I certainly welcome more testing, but the key to the experiment would be prospective data gathering rather than retrospective data gathering. In other words, someone would make a commitment to purchase 99 cards and post the results no matter the outcome. This is exactly what I did in my experiment. Retrospective data is what we see on threads like "Luckiest Lotto Draw!" Someone says they spent 10 gran and got a five-star, but they make the decision to post that information after the fact. That's biased data. It's interesting and fun information to read about, but it can't be relied upon for understanding the probabilities of the lotto.

[hanul]

yes 1 star >78.5% and total equal 100%

[Xuande]

let say the distribution of the card lottery is in proportion to the card recycle value.

5 star: 300 4 star: 150 3 star: 30 2 star: 10 1 star: 5

Let G = Gran you get from lottery ; Let y be 5 star card.

therefore 4 star = 2y 3star = 10y 2 star = 30y
and 1 star = 1 - [ y+2y+10y+30y]

G = 300 x y + 150 x 2y + 30 x 10y + 10 x 30y + 5 x {1 - [ y+2y+10y+30y]}
G = 1200y + 5[1-43y]
G = 985y + 5

10g per lottery
If G = 10 it is a no gran lose distribution, therefore G < 10
G = 985y + 5 < 10
985y + 5 < 10
y < 0.5

5 star < 0.5% 4 star < 1% 3 star < 5% 2 star < 15% 1 star < 78.5%
If y > 0.5 you gain gran per lottery.

I might be off and there is condition needed.

I have done at least 2000 lottery pulls at the 10 gran level, never having done them at 30 gran since I started after that went away.

Based on my experience, 0.5% is pretty close to the actual ***** rate (I would estimate 0.333%), and 1% is pretty close to the actual **** rate (I would estimate 0.666% myself). I would put *** around 4% as well, but I would drop ** a lot - perhaps only 10%. My estimated numbers would leave * at 85% - 17 cards per 20.

This is of course based off personal experience and memory, however, and thus subject to error.

85% to be a *
If not a *, 66.666% to be a **
If neither, 80% to be a ***
None of those? 66.666% to be a ****
Dodge all that, and you got a *****

[Peralisc2]

When you say "could be worse," I'm assuming you mean the percentage chance of getting a one-star could be worse than 78.5%, whereas I said the chance of getting a one-star was greater than 78.5%. You then said it was not something you can test.

I mean the chance to get something better than a 1 star could be worse.

"... in the interest of science, I just now purchased the maximum of 99 cards at once through the card lottery and here’s what I got:
2 three-stars
6 two-stars
91 one-stars"

So from the test, you can see the chance of getting a one-star with an N of 99 was 92%, which is not worse than 78.5%.

I expected a bad result like that.

[InigoMontoya]

I mean the chance to get something better than a 1 star could be worse.

Ah! I understand. That completely makes sense.

[InigoMontoya]

85% to be a *
If not a *, 66.666% to be a **
If neither, 80% to be a ***
None of those? 66.666% to be a ****
Dodge all that, and you got a *****

Very clever!