[Inaccurate]Chart for alchemist ranker wannabes.

[Jake]

EDIT: I tested some of this experimentally. It seems my math is wrong.

Here is the situation:
You know your chance of success with creating condensed potion.
You want to find out how many creation attempts you must do in order to gain 1000 points.

I made a chart for that.

The chart:

Spoiler

Chance (%)               No. of attempts needed
60                              5294
61                              4833
62                              4411
63                              4026
64                              3673
65                              3350
66                              3055
67                              2786
68                              2539
69                              2315
70                              2109
71                              1922
72                              1751
73                              1596
74                              1453
75                              1324
76                              1206
77                              1099
78                              1001
79                              912
80                              831
81                              757
82                              690
83                              629
84                              573
85                              523
86                              477
87                              435
88                              397
89                              362
90                              331
91                              302
92                              276
93                              252
94                              231
95                              211
96                              193
97                              177
98                              162
99                              148
100                            136

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Corresponding graph:

Spoiler

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Applications:

Spoiler

Kindly find it on your own!
However, I will tell you what was my main motivation in making this chart. I wanted to know how much effort is involved to become rank 1 alchemist. (since it is directly related to how many bathories I have to hunt)

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Theory behind chart: (would be nice if someone verifies)

Spoiler

Lets suppose that the success chance of creating condensed potion is 60%

Rank Point +1: 3 Condensed Potions created without failure in a row.
Probability of making 3 condensed potions in a row = 0.6*0.6*0.6 = 0.6^3
Reward gained = 1 point.
Mathematical expectation = Probability*Reward.
                                          = (0.6^3)*1 points
This is for 3 attempts.
Expectation per attempt = {(0.6^3)*1}/3 points

Rank Point +3: 5 Condensed Potions created without failure in a row.
Probability of making 5 condensed potions in a row = 0.6*0.6*0.6*0.6*0.6 = 0.6^5
Reward gained = 3 points.
Expectation = (0.6^5)*3 points
This is for 5 attempts.
Expectation per attempt = {(0.6^5)*3}/5 points

Rank Point +10: 7 Condensed Potions created without failure in a row.
Proceeding in the same way as above,
Expectation per attempt = {(0.6^7)*10}/7 points

Rank Point +50: 10 Condensed Potions created without failure in a row.
Proceeding in the same way as above,
Expectation per attempt = {(0.6^10)*50}/10 points

Total expectation per attempt = Sum of individual expectation per attempt
                                                 = [{(0.6^3)*1}/3] + [{(0.6^5)*3}/5] + [{(0.6^7)*10}/7] + [{(0.6^10)*50}/10] points

Number of attempts needed to gain 1 point = 1/(Total expectation per attempt)
Number of attempts needed to gain 1000 point = 1000/(Total expectation per attempt)
                                                                            = 1000/[[{(0.6^3)*1}/3] + [{(0.6^5)*3}/5] + [{(0.6^7)*10}/7] + [{(0.6^10)*50}/10]]
                                                                            = 5294 attempts

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Credits:

Spoiler

Microsoft Excel
(For number crunching and getting graph)

http://irowiki.org/wiki/Potion_Creation#Fame_System
(For information about the game mechanics)

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[Scribbles]

Now, I would never reach that goal in ... ever. But I know a lot of people who would create that much just because they have the drive to do so.

Also bots; bots have the drive to do that too.

[Triper]

This only applies to renewal.
Pservers and official iro classic[at least I think this applies to it too] have a variation as seen in here and here

[Jake]

This only applies to renewal.

This applies for both renewal and non-renewal. The fame system mechanics is same for both.
It is evident from the following links:
http://irowiki.org/oldwiki/Alchemist#Fame_System
http://irowiki.org/wiki/Potion_Creation#Fame_System

The following link that you gave does not say anything about fame system mechanics at all.
http://ratemyserver.net/brew_calc.php

[Triper]

You're talking about fame system while I'm talking about variation on the chances when making them and the values used to make the chart.

In your examples and chart you based in on fixed values which is wrong for slims since the creation rate isn't fixed at all, it has a variation as you can see on the 2 links I posted. Aside for pservers and for red slims, the entire math fails because you've to work with min, avg and max values and each one for each type of condensed.

The formula used by you is also the formula for renewal which has no variation and that's why I said that it's only for renewal.

[Jake]

You're talking about fame system while I'm talking about variation on the chances when making them and the values used to make the chart.

In your examples and chart you based in on fixed values which is wrong for slims since the creation rate isn't fixed at all, it has a variation as you can see on the 2 links I posted. Aside for pservers and for red slims, the entire math fails because you've to work with min, avg and max values and each one for each type of condensed.

The formula used by you is also the formula for renewal which has no variation and that's why I said that it's only for renewal.

Triper, please think this (imaginary situation) yourself and answer me:
You want to get into the rank list. You want to find out approximately how many bathories etc.. you have to hunt.
When looking at the chart, will you use your Min. success chance, Max. success chance or Average success chance?

EDIT: I thought it would be pretty obvious that this chart deals with averages.

[Triper]

I actually use the min values as reference instead of avg at pservers.

If you've 95% to make pots and the avg is 100%, the difference is something when making slim whites.

95% of 20000 is 19000, that's something.

And the 3 websites[iro pre-renewal, iro renewal and pre-renewal pservers] have 3 different values for those variations.

[Jake]

I actually use the min values as reference instead of avg at pservers.

What exactly can you compute using the minimum? You certainly can't compute the maximum number of attempts needed in order to gain a minimum of 1000 points.

If you've 95% to make pots and the avg is 100%, the difference is something when making slim whites.

95% of 20000 is 19000, that's something.

I didn't fully understand you. Please explain in more detail.

The chart is to be used for average values.
In the rare case that Max. success chance is supposed to be greater than 100%, you can't directly use the average success chance.
For example, if your Min. success chance = 95%, your Max. success chance =105% and your Avg. success chance = 100%, then your true average success chance is not equal to 100%. But instead, it is a number between 95 and 100. It is equal to 98.75% if my guess is right.

[Triper]

The chance to make a potion in pservers for white slims[using it as an example] have a variation of -5 and +5% making it a variation of 10%.
For renewal there is no variation on them.
For pre-renewal officials there is even a different variation.

So you can't just make a chart for generic avg values for 1 generic type of pots, you've to do more or specify for what type of server is it made or show some calculation made between all of them so people can see that is a plain average value.

And yes, you can use min as reference. In my case I use it as what I should expect at least from the pots I make so I don't have to be like "Crap, not enough pots to get that points and steal the 2nd place!" or "Crap, not enough pots to use now near the end of woe" and if you're selling your services on a server you should do it based on that and not avg because is a more realistic value to what people can expect. If I make more then good but if not at least I won't make less then that or if it goes off it shouldn't be for much since the fluctuation value is near 0 because I'm using the minimum value predicted.

If you want to do this easier just say people that this is the avg value for XYZ servers but has an error value that is equal to the variation.

[Jake]

The chance to make a potion in pservers for white slims[using it as an example] have a variation of -5 and +5% making it a variation of 10%.
For renewal there is no variation on them.
For pre-renewal officials there is even a different variation.

So you can't just make a chart for generic avg values for 1 generic type of pots, you've to do more or specify for what type of server is it made or show some calculation made between all of them so people can see that is a plain average value.

And yes, you can use min as reference. In my case I use it as what I should expect at least from the pots I make so I don't have to be like "Crap, not enough pots to get that points and steal the 2nd place!" or "Crap, not enough pots to use now near the end of woe" and if you're selling your services on a server you should do it based on that and not avg because is a more realistic value to what people can expect. If I make more then good but if not at least I won't make less then that or if it goes off it shouldn't be for much since the fluctuation value is near 0 because I'm using the minimum value predicted.

If you want to do this easier just say people that this is the avg value for XYZ servers but has an error value that is equal to the variation.

In my chart, the 'Chance (%)' is your true average success chance of creating a condensed potion. And the 'No. of attempts needed' is the corresponding average number of attempts needed to gain 1000 points.

These are not affected whether or not there is a variation in each attempt. So this chart is applicable in any server.

The 'No. of attempts needed' involves a standard deviation whether or not there is a variation in success chance in each attempt.

If there is a variation in success chance in each attempt, then, what this means is that, the standard deviation will be a bit higher than that in the case where there is no variation in success chance in each attempt. The average number of attempts needed to gain 1000 points will not change.

Let me give a fresh example to illustrate how the averages won't change when there is a variation:

Lets suppose that poring drops jellopy at 50% chance.
After you kill 1000 porings and pick the jellopies, you can expect to have around 500 jellopies (this is the expected value A.K.A. average).
When you look in your inventory, you may not see exactly 500, it may be less or more. It may be 400, 650, 23, 900 etc... In fact, it can be any number beween 0 and 1000. Now, if this experiment is repeated many times, and you find the average, you will see that the average becomes closer and closer to 500 jellopies. (see Law of large numbers).

Lets suppose that poring drops jellopy at 45% to 55% chance.
After you kill 1000 porings and pick the jellopies, you can expect to have around 500 jellopies.
When you look in your inventory, you may not see exactly 500, it may be less or more. It may be 400, 650, 23, 900 etc... In fact, it can be any number beween 0 and 1000. Now, if this experiment is repeated many times, and you find the average, you will see that the average becomes closer and closer to 500 jellopies.
Meaning that the average is same.

[Creme]

I think he's trying to tell you that there's three different formulas for potion brewing.  The Pre-Renewal official formula is not the same as the Renewal formula, is not the same as the Private Server formula. 

The Pre-Renewal Official formula used on iRO and other servers is NOT the same as the forumla used on pre-renewal private servers.  I think that's what Triper's trying to say lol.

Compare the Private server formula here:  http://ratemyserver.net/brew_calc.php
vs. the Official Pre-Renewal formula here:  http://irowiki.org/oldwiki/Alchemist#Potion_Creation

Note specifically where it says "(10 to 1000 at random) -- 10% variation from max to min " on the Private Server formula.

[Jake]

I think he's trying to tell you that there's three different formulas for potion brewing.  The Pre-Renewal official formula is not the same as the Renewal formula, is not the same as the Private Server formula. 

The Pre-Renewal Official formula used on iRO and other servers is NOT the same as the forumla used on pre-renewal private servers.  I think that's what Triper's trying to say lol.

Compare the Private server formula here:  http://ratemyserver.net/brew_calc.php
vs. the Official Pre-Renewal formula here:  http://irowiki.org/oldwiki/Alchemist#Potion_Creation

Note specifically where it says "(10 to 1000 at random) -- 10% variation from max to min " on the Private Server formula.

Dude, I understand what Triper is saying.

I'm trying to explain that the chart holds true whether or not there is a "10% variation from max to min"

The chart holds true irrespective of what the brewing success chance formula is.