Ok I have explained this in game for the lost count time now.
So I am just going to put this topic up so those of you still not understanding it can review it at your leisure.

This is how drops work. in this example we will use the standard drop rate for most rares

1
----
317

To win the rare both events must be won.

1st event the coin toss.
(Commonly referred to as DAR or Drop Anything Rate.)

Upon each enemies death a coin is tossed

If it lands on heads event 2 will happen a die roll and something will drop.

If it lands on tails it will drop nothing. As landing on tails = no die will be rolled and event 2 will not take place

All the prizes are on the die the coin toss is to determine weather or not the die will be rolled.

A coin has 2 sides so it is a 50% chance of landing on heads or tails.
However in DAR case the varying %'s of DAR = the amount of times the coin will land on heads out of 100 attempts (on average).

2nd event the die roll.

If the coin toss was a success and landed on heads event 2 takes place a die will be rolled.

Using our example rate lets break down what that means

1 = The number of wins or rare will drop sides of the die
----
317 = The number of sides on the die

So basically when the die is rolled you are rolling a 317 sided die with only 1 side of the die that says drop the rare. All the other sides of the die will contain various other items such as tool drops weapon drops armor drops pd drops ect. Whatever side the die lands on is what will drop.


Special rules exclusive to eden.
Drop rate penalties and boosts.

If playing by yourself you may notice less rares dropping that is because here on eden we have a little system in place to encourage you to team up and play together.

If playing alone the number of sides on the die for every drop rate are increased by 20%

so if we take our example of

Example

1 = The number of wins or rare will drop sides of the die
----
317 = The number of sides on the die


It will now look like this for solo play.

1 = The number of wins or rare will drop sides of the die
----
380 = The number of sides on the die

If playing with 2 the number of sides on the die for every drop rate are increased by 10%

1 = The number of wins or rare will drop sides of the die
----
348 = The number of sides on the die

If playing with 3 the number of sides on the die remain what is listed.

1 = The number of wins or rare will drop sides of the die
----
317 = The number of sides on the die

If playing with 4 the number of sides on the die for every drop rate are decreased by 10%

1 = The number of wins or rare will drop sides of the die
----
286 = The number of sides on the die


In the case of 4 or less people on line then the rates are as if for 3 people are in your game.

1 = The number of wins or rare will drop sides of the die
----
317 = The number of sides on the die

Unless all 4 of you who are the only ones on are playing together

1 = The number of wins or rare will drop sides of the die
----
286 = The number of sides on the die

After the 5th or more person is on line in game drop penalties will be applied as listed above.


Now for a little info about which id is the active one.

Are you implying that the DAR are 50% for ALL enemies? Unless I'm reading you uncorrectly (and if I did, my mistake), you are wrong. The DAR is different for every enemy and every difficulty.

You will find on PSO-World the DARs for each enemy and each difficulty that applied to the GameCube version of PSO :

http://www.pso-world.com/sections.php?op=viewarticle&artid=2277
http://www.pso-world.com/sections.php?op=viewarticle&artid=2278

Now, there is a possibility that the DARs are different on Blue Burst compared to GameCube, but somehow, knowing Sega, I doubt they bothered changing it... As for epIV enemies, Sodaboy programmed it to link them to specific epI and epII enemies. (you can easily verify this by looking at the source code)


Also, I think you got some of your numbers wrong. If I take your example of the 1/317 drop rate, you shouldn't be multiplying 317 by 1.2, but rather multiply 1/317 by 0.80. As, the way I understood it, drop rates are reduced to 80% for a 1 person game, 90% for a 2 person game, 100% for a 3 person game and 110% for a 4 person game. This means, your drop rate would be modified this way :

1/396 for a 1 person game
1/352 for a 2 person game
1/317 for a 3 person game
1/288 for a 4 person game

The coin flip still happens 1st.

But to explain what those DAR number represent on pso-world's are
the % of number of sides on the die that say anything at all.
The other remaining %'s on the die will say loose and still nothing will drop.

Booma utl at 30%, and lets use the 1/317 rate as an example

30% of the sides on the die will have drop able items listed on their sides.

95 sides of the die will say something will drop.
With 1 side being the rare

70% of the die will say loose and still nothing will drop.

222 sides would say loose and nothing will drop regardless of wining the coin toss, as the die came up loose.

The DAR is different per enemy/difficulty/section id.

Dark Falz's DAR is modified by the server after the ItemPT.gsl (it's 0 in there) file is loaded.
Also, there's some "enemies" that are capable of dropping items, but have a DAR of 0. For instance the 2 crystals next to a gran sorcerer are actually capable of dropping items I think, just have a DAR of 0, and don't have a rare assigned to them.

Japanaman2 pretty much has it right though.

DAR, check. Then if the rare will drop.
If the rare doesn't then a common item in the common table will drop (I think if that fails, then meseta drops, haven't looked at it for a bit).

As pointed out by Rika, the DAR is checked first, then if it is decided than an item will drop, the drop rate is checked.

That means that if I take your example of the 1/317 drop rate and the booma that has a 30% DAR, I guess if you wanted to formulate it as a "dice with several sides", it would go like this :

The dice has 1057 sides.

On 740 of them, there is nothing at all.

Out of the 317 sides with something on them :
1 of them has the rare.
The 316 left have either an armor, tool, weapon, etc.


The drop rates shown in this drop chart :

http://chokoserv.sylvanet.net/drops/

They do NOT take into account DAR, just the "drop rate" itself which is checked after the DAR.

Okay teachers let's see if this formula explains it all, even with event based variables.

X = A * P * R * Y

X = The cumulative probability of obtaining the desired rare item listed on the drop tables at edenserv.net/drops

A = The probability of finding the desired rare item listed on the drop tables at edenserv.net/drops only considering the two events described by japanman2 such that it is 0.5 * T. Ergo, A = 0.5 * T

T = The basic probability of finding the desired rare item listed on the drop tables at edenserv.net/drops

P = The fraction of A where P is 0.8 in solo mode, 0.9 if 2 players are in one party, 1 if 3 players are in one party or if there are less than 4 players online in the server, and 1.1 if there are 4 players in one party. (Fun Fact: P is labeled a percentage when it is multiplied by 100%.)

R = The probability of a rare monster appearing where it is 1 when no such rare monster is a factor in solving for X. (R is some unknown value that I cannot provide to you readers now; please consult a reliable source for this "random variable".)

Y = The event rate where it is dependent on what GMs say because there must be some "random variable" left to explain any other effects on X. For instance, if you are the Chosen One, then Y = 2.

With this formula in mind, let's describe two similar events with the exact same probability: Finding a Red Ring (=RR) when Whitill is the leading section ID, and finding a Parasitic Gene "Flow" (=PGF) when Viridia is the leading section ID (assuming the leading section IDs are hunting in Ragol). Let's add that there are parties of four and that the drop rates are doubled under a certain event; ergo, Y = 2 and P = 1.1

What is T in both situations? I see 1/36, or 0.02777 with 7 repeating indefinitely, for both cases.
What then is A? A = 0.5 * T = 0.5 * (1/36) = 1/64 or 0. 013888 with eight repeating indefinitely
So what is X? X = A * P * Y = 0.013888 * 1.1 * 2 = 0.030555 with 5 repeating indefinitely.

As a percentatage, 100% * X = 3.0555% with 5 repeating indefinitely.

Homework: Find X and it's percentage (= 100% * X) for Nei's Claw and Sealed J-Sword.

Bonus Problem: Find X and it's percentage (= 100% * X) for a Heaven Punisher from a Hildetorr, a Psycho Wand from a Mil Lily, and a Siren Glass Hammer from a Kondrieu, provided that the random variable R is given in each case.

Are you surprised about how lucky you need to be?