Probability of getting that drop

This particular discussion first appeared in another thread, but I will thank you if you don't start on that subject again, and instead keep to this one. Because it's a good topic and very good points have been made.

It's been said that, the longer you farm, the better your chances are of getting drops, and the better of getting one particular drop.

Is it true or false? I've been arguing pro and con with a couple of other users. Links to the relevant posts, so you can catch up with the original arguments if you want: [1], [2], [3].

To save you some time, here's the gist of it:

Xeno put it in cold hard math:

I stand corrected, you are both right (and that's a very useful formula). The probability does increase as the number of attempts goes up. (I haven't taken Xeno on his word, btw, in case anybody's wondering, I ran the numbers myself, using a couple of different methods. Plus I wrote a program and ran some simulations. It checks out.)

But I'd like to point out that we still have two problems:

1) The smaller X is, the bigger N has to be to get decent probabilities. The formula for the attempts (N) needed to raise an item's original probability (x) to probability (p) is: N = log 1-x (1-p). See the table below for several items. It's a lot of attempts for many of them. And you never get 100%, only come very close to it.

2) Probabilities are theoretical. Even if the theory tells you that if you open 7800 gifts you have 99% chances of getting Yakkington, in practice it's perfectly possible to try 10,000 times and not get a single one, just as it's perfectly possible to try 5 times and get 5 of them.

Without further ado, here's a table with the number of attempts needed for certain probabilities of success and certain items. "Chance" column taken from wiki "rate of drop" tables.

How to use: you want 90% chances of getting Gwen, who has 0.033% chances of dropping, you have to open 6,976 Gifts.

But: it does NOT mean that if you open 54 Coffers you get 50% of them to wield Armbraces. You get 50% chances of getting ONE Armbrace.

Item	From	Chance	50%	90%	99%	99.99%
Gwen	Gift of Traveler	0.033%	2,100	6,976	13,952	27,905
Brown Rabbit	Gift of Traveler	0.047%	1,474	4,897	9,795	19,591
Yakkington	Gift of Traveler	0.060%	1,154	3,836	7,672	15,345
Armbrace	Coffer of Whispers	1.26%	54	181	363	726
Mallyx	Coffer of Whispers	0.76%	90	301	603	1,207
Medal of Honor	Royal Gift	12.006%	5	18	36	72
Elite tome	Zaishen Chest	2.21%	31	103	206	412
Regular tome	Zaishen Chest	9.83%	6	22	44	89
Celestial Rabbit	Lunar Fortune	0.61%	113	376	752	1,505

Take all values with a grain of salt, for probability's sake. And even those probabilities have a margin of error to begin with. Bottom line: you're nuts if you use this table for anything serious.

Isn't this just common sense?

^^ agree with the above

Ofc over the course of time your chances will increase across all instances...but each instance's chance will remain the same.

RNG loot is RNG

say it with me, repeat it a few times, and let it sink in if you didn't know allready! :
"Previous results DO NOT influence future outcome."

Perhaps it is common sense, but before I did the math myself I wasn't so sure.

And if people see some actual numbers maybe it will give them some perspective and cause them to re-evaluate their options. Randomness and probability are tough things to get your head around. See the Monty Hall problem.

So, if you've been opening gifts like crazy hoping for a mini Yakkington -- how far along are you? Just kidding, but seriously, see point (2) above.

This is why it is incorrect to say you chance to get something increases. It never increases. It is always the same X% chance to drop every time. The math is just to remind you that if you opened 27,905 gifts and didn't get a mini Gwen that you are really unlucky, possibly cursed.

I never heard of the Monty Hall problem so thank you for the link. I love statistics and think (thought) that I was pretty good at it. But I can't for the life of me follow the reasoning behind the explanation. Maybe I should have a few drinks and then try again...

In fact, if you have a lot of money to invest, it's a good thing to make a lot of coffers to get ambrace that gives more money that what you had invest at the beginning?

No. You would need to get an armbrace in under 15 coffer openings. The above table suggests that to even get a 50/50 shot you need to open 54.

i dont think so, because 15 coffers is equal in value to 1 ambrace, and the probability of getting an ambrace from opening 15 coffers is only around 15.825%, according to my math.

however, this doesnt take in account the other rewards from coffers. in order to incorporate those i would need a list of them and their values, but i still think your better off selling the coffers

it helps to think of it with more than 3 doors. imagine if there were 1 million doors, and only one had a car, with the rest containing goats. you stand in front of the doors and pick one, hoping for the car. the host then goes down the row of doors, and all the other doors except one, leaving two doors closed. the ones he opens all have goats. logically, which door do you think would be more likely to contain the prize? the door you chose when their were a million doors to chose from, or the door you choose when there are only two to pick from

thats how my ninth grade statistics teacher explained it to me (although he was more eloquent) and it made alot more sense.

its pure chance....I have tried on one account to get a boss to drop their green, tried and tried.....never got it. my 2nd account was in that area (quest or something)...happened to kill the boss ONCE and got the green .....
(nic gifts--opened well over 3 stacks-not all at the same time...last time opened ONE stack, on number 150 I got a mini bunny--first mini from the gifts, I have seen others get it on the first try....chance pure chance).
You can do the statistics all you want, but it just says that you might possibly get a drop. (or it can say that you will maybe not get a drop--)

Setup:
There are three doors, two have goats behind them, one has a car behind it. You pick a door and if there's a car behind it, you win the car. The twist is that after making your choice, one door that has a goat behind it is removed and you are asked if you want to swap to the remaining door.
Is it better to swap, stay with your current door, or does it not matter?
Note that the removed door always has a goat behind it.

So:
The probability of picking a door with a car behind it at the start is 1/3 and the probability of getting a goat is 2/3.
Let's assume I pick a door with a goat. Then when one door is removed, the remaining door has the car I want behind it. So swapping doors makes me win, sticking with my current door means I lose.
If I pick the door with the car behind it at the start then clearly swapping is detrimental. This happens 1/3 of the time.

2/3 > 1/3 so you should swap doors.

By swapping you bet that your initial choice was wrong. By not swapping you bet that you were correct.

Edit:
Another way of thinking about it:
If you choose not to swap, the chances of you winning are exactly the same as they were at the start. You picked a door that had a 1/3 chance of having a car behind it and that does not change until you see what is behind it. However, after one door is removed from the problem, you know that whatever is not behind your door is behind that one and so the probability of the car being behind that door is 1-1/3 = 2/3.

Technically it does, since all random number generators are actually pseudo random number generators. The important point is that predicting what the future outcome would be is nigh-impossible.

Easiest way is to just enumerate the options.

If you pick the right one in the first place, and switch, you get the wrong one. This happens 33% of the time.

If you pick the wrong one in the first place and switch, you get the right one (because the OTHER wrong one is always ruled out as it was revealed already). This happens 66% of the time.

So if you don't switch you always have a 33% chance, if you switch you have 66% chance

It's always just about luck.
The human brain is rigged to look for patterns, even if there are none. So many people will think that there's a way to increase the chances to have something drop instead something else when there's none.

I've head lots of silly stories about timing with server time to prompt a certain drop and whatnot, but such things will never work.

I have never scored anything nice from gifts. It's luck or bad luck.

2 stacks of royal gifts and no mini.

Red rocks are the best nic can do for me.

Dozen characters worth of minis and since yr 1 and no greens. 1 gold 2 years later on a 2nd account. 6th year gift = tahlkora. I have 3 more and I am considering selling all. But I'm due right?

Nothing from zchest at r3 and that's not counting more than that before the update.

I have scored from other chests and drops, but if you farm long enough...

not everyone is as smart as you, most people haven't even won a cape trim like you have so that just about sums it up.

You don't have to be good at the game, or smart to see that the more times you play a random number generator the higher the probability that the number you want comes out. And that just because an item has an x% chance of dropped doesn't mean if you try get it 100/x times you're certain to get it.

correct, for real life odds such as dice rolling, or coin flips etc.

this is code. computers cant generate 'random' when a computer is asked to give a random number there's certain code applied to some preprogrammed seeds, and it spits back what it's coded to do. certain types of rng code are pretty simple to understand... and predict! computers are incapable of random. everything is coded and happens for a reason, some exceptions would be when circuits start breaking down or overheating. the rng just gets really complex



The point is... that RNG for computers is coded. the game developers can alter that code to suit things however they want.

This was publicly acknowledged by a game developer when it came to light that a bug with player ids at char creation altered the loot rate for those specific players. I dont remember the game name but i remember seeing the acknowledgement coming directly from the devs of that game. a very simple random generator was used in some fps to generate where bullets would go on a 'spray n pray' hackers figured it out, built some code to automatically aim their gun where the bullet would 'randomly' go and they would get headshots everytime if they wanted.

Now whats to prevent a game dev from trying to keep the market unsaturated while keeping players hooked by specifically coding in loot rate changes? the best way is to have high odds to drop high value loot, but then as time progresses and the player is fully hooked into 'farming' severely decrease the loot rate, but not so much that its obvious.

Im not saying guild wars does this, nor is it realistically provable. it's also not realistically unprovable. your assertion that previous results dont influence future outcomes is without proof. did you write the code? have you seen the code?

All im doing is showing you that not only is it possible, its happened in the past by accident. Logically is something has happened once, that proves that the situation is in the realm of possibility. furthermore there is a motive for game devs to purposefully code it in to manipulate the gamer's addiction without over saturating the market.

random is random is correct. but guild wars isnt flipping coins or rolling dice. therefore its quite correct to say that RNG is not necessarily random. most of the time perhaps, but not always.

rng is coded. coded by people who can alter the code.

Pray they don't alter it any further.

The synch experiments have shown that GW's PRNG for loot generation is not very well armored at all. It's seeded with zone-in time, and seems to be used exclusively for loot generation. If you really wanted to, it would not be hard to create a bunch of instances with duplicate (potential) loot, farm one instance to see if the loot was worthwhile, then cash in all the duplicates when you finally got lucky. This is largely prevented by the fact that no single piece of loot (excluding old school things with incredibly unlikely mods) in GW is worth enough to justify the trouble. In short: it's not that you can't game the system; it's that the system isn't worth gaming.

Been solo farming ectos in the first chamber of UW for a few days now. So far I have come up with:

4% or 1 in 25 chance of any ecto dropper to drop an ecto
70% chance of getting one ecto from a run
Cost per run after selling drops but not ectos about 300 gold.

Only on 40 runs right now but the numbers have stayed surprisingly steady from 20 to 40.

GW and other similar games are the babies of what us old folks like to call MUD's, and MUD's are the babies of what some (like me) might remember as Dungeons & Dragons (et other table top dicers). GW is the same thing, with graphics (ooo), and much larger servers. At the heart, and very basic game mechanics, the games remain the same. It IS flipping coins/rolling dice.

If x item has a 40% drop rate assigned to it, then every time there's a chance for it to drop the code essentially rolls a 60 sided die, and every time that roll goes you have a 1 in 60 chance of getting it. No 60? No item! Grab 6x 10 sided dice (if you're like me and still have some) and toss them 60 times. How many times did you roll 60?

I don't know for certain sure how GW works 100% when it comes to assigning priority over other items that can drop from said mob, but I do know when I worked on a MUD way back when we coded it to give priority to more common items. If mob X has a chance to drop 5 items (a/b/c/d/e) with respective drop rates of 80% / 70% / 60% / 40% / 10% then the code rolled for each item, and if more than 1 item rolled gold it would only drop the one with the highest % to drop. Ex: It rolls 15/30/4/1/90 the code would plop out item b as opposed to item e, even though they both rolled the magic numbers.

It does the same thing for your weapon damage. 15-22 for your sword, every time you swing it the code rolls a 7 sided die and generates your damage.

Are there other factors that effect your chances? Sure are! Some you know about, some you don't, and that's why threads like this pop up every once in a while.

And now I return to chasing hoodlums off my lawn with a cane ....

Wiki used to have under each ecto dropping foe their %.
Aatxes/mindblades/dryders ( forget the others ) are 4% and smites are 2% chance to drop an ecto.

Way i read things - you enter a zone and you have set % chances or each foe - say run ended and you got no special drops now if you retry farm then you have % chance from start again .Say you did 50 runs that 50 chances you have and again thats the same % reset each run.
It may seem that more runs you do the better chance but actually its the same chance and same odds but that run may be the winning run.

Ages ago i used to farm the avatar of dwayna for either elite derv tomes or the scythe , did about 20 runs consec and i only got 1 elite tome an 1 scythe.few days later did another 20 runs and nothing.I was lucky on the runs that gave the scythe an elite tome and the 38 other runs i was unlucky on.

Exactly, I have noticed that in just the 40 runs it averaged out amazingly well. It is like a coin flip though. No matter how many times you flip a coin EACH flip is still 50/50.

One trend that seems to be manifesting is that the single Aatxe that roams up the stairs to the right (when facing north) drops more often than any other Aatxe. Same with the Skellie up the stairs to the center. Not enough data points to call it a significant trend but even before collecting data I noticed the trend.

What is the point of this thread?

Sorry but how obvious is that? How could someone possibly think the chance of getting a particular drop over a period of time doesn't increase the longer the period is? The fact that chance doesn't have memory (chance of getting the drop you want from a chest is the same each time you open it)... is also obvious?

It's not "obvious" for everybody. And even if it's "obvious" for some people, it's nice to have actual math proof and numbers.

Look at it this way: the next time somebody disputes that claim you can say "go read this thread", instead of "it's obvious".

I think he meant it in the physical sense. The code is not physically throwing dice, which would be "real" random generation. Instead it's doing all sorts of gimmicks that make the numbers seem random enough. But it uses the same way of doing that (the same algorithm), and so the first number picked to start the sequence will produce a fixed sequence. Now, consider that usually that first number is taken from the system clock, and you'll see why it's technically possible for people to sync their entry into an instance and basically share the same "random" sequence.

It doesn't mean it will be a particularly lucky or unlucky one, but, as Chthon described, if it is it can be exploited.

I wonder why nobody invented a purely physical device for this. Feed cabbage to a bunny and have a sensor go off whenever it farts or something like that. ^_^

OR!! i got a good analogy... !! ask someone...

If you stand on a road for 5 minutes and for 5 days... At which of those two instance is the possibility of u getting hit by a car higher...

Ask him to conduct a empirical test... and if comes back in 5 days tell him hes lucky....

While this may be true for some MUDs (yes, I played one for years too!) I highly doubt it in GW. You either beat the odds and get lucky with the drop out of their present items, or you don't. I don't believe for a second that, for example, Lucky Aura or putting on particular titles gives you any advantage outside of pure coincidence. Same deal for having a lucky or unlucky character as some seem to believe.

Re: The drops being pre-planned on entry into the zone and sync entering...They never did this with dungeon chests or with present type items which both are most likely generated separately from monster/locked chest loot. If you could prove that sync entering altered those contents to match then you'd be onto something but I doubt it. A few tried to game the system already in Strength of Snow watching for small updates indicating the Polar Bear model loaded and we see how well that worked out...

Exactly this, lol. How's it even worth putting on a forum? Even if you don't know any math at all, it's just logical.

This mechanic opens up a lot more questions that have never really been answered. A quick listing of relevant theories on item generation:

- The drop seeds get worse and worse (on average) as you repeatedly farm an instance. The game always claimed that it worked that way in the help messages, and the data I had from Prot Bond farming back in 2005 strongly suggested that this was the case. If you went and played a mission or two then returned to UW, the frequency of ecto drops more or less doubled, and I did enough runs under both conditions that it was extremely unlikely that random chance was the explanation.

Anecdotally, there is additional evidence that tends to confirm the theory. Most UW/FoW groups seem to subscribe to the theory that the noob always gets the good drop from the end chest. Repeatedly farming the instance fits the theory; the players that have farmed the instance the most are likely to be the most skilled, and incompetent players very likely haven't done as many runs. The result would be that the incompetent player is more likely to get a good drop from the end chest on any given run, leading to players noticing a pattern.

Finally, I've also noticed that non-max items such as Bone Dragon Staves only drop from end chests for players that have been repeatedly farming the instance for some time, which also fits the theory.

- The number of players farming an instance affects the seed. I got a very nice controlled experiment during HM Urgoz farming, because I was down there for three weeks before some nitwit posted to Guru. The drop rates on Gold items per hour halved once the instance became crowded, and that sort of change was extremely unlikely to be caused by random chance given the number of runs involved.

- The time of day affects the seed and interacts with the number of players. Gold item drops tended to cluster around the top of the hour once everyone showed up in HM Urgoz. The pre-crowd drop rate prevailed for about fifteen minutes, and then Gold drops would dry up until the beginning of the next hour. No such pattern was observed prior to the large increase in players after the Guru post.

That data isn't exactly current, of course. I don't have anything available from more recent events such as Elemental Sword farming, Chaos Plains, or keg/raptor farming that suddenly exploded in popularity after a Guru post, so some or all of the above explanations may no longer be true. There is countervailing evidence that current UW ecto drop rates seem to be consistently replicated by players even after numerous runs, which suggests that at least some aspects of the drop code have changed since 2005-2007.

More accurately: you get 50% chance of getting 0, and 50% chance of getting at least one (could be more of course). Because you are actually calculating the odds of never getting one and then subtracting that from 100% to get odds of getting at least one.

I agree with both of these observations and can say CoF took a massive hit once 600 became widespread and popular. Unless you farmed it at off peak hours it was not unusual to see runs without a single gold drop in it's prime. How do you convince people to stop farming an area to improve the overall volume of drops...you can't. It's a perfect system to keep popular areas in check.

There was a post from Gaile at the time loot scale was implemented admitting that this was how the "anti-farm code" had worked, and claiming with vehemence that it was removed and replaced by loot scale.

In any event, the synch tests show without a doubt that entry time alone controls the PRNG, and the PRNG controls what drops and what mods it has. Loot scale (possibly along with other anti-farm measures) is layered over the top of the basic loot generation system and causes non-materialization of certain generated drops in certain situations. I've got no data on how loot division works.

thats not correct. at its heart a computer is 1s and 0s.

did you open your computer case and see a tiny gnome in there flipping coins and rolling dice?

no?

then rng is CODE.

Ive shown you examples of other games where rng can be, and has been manipulated.... because its code, and humans make code.

Ive shown you how devs might have a motivation to manipulate rng.


im not saying that guild wars does this purposefully. for guild wars 2 i have a strong feeling the devs have at least looked at the possibility of having loot limits or timers put in place.


but in general, for all computer games and code.... RNG is essentially random, but not necessarily random.

Right, but do you believe Gaile, or your own lying eyes?

The way it looks to me, based on the evidence, is that the repeated instancing code was replaced when loot scaling was introduced for items that drop from monsters. (Otherwise, it's hard to explain players' ecto drop tests, or my own HM Urgoz drop results.) However, it seems as though repeated instancing causes a decline in the quality of drops from end chests.

That proposition is impossible to support without a lot more runs than I'm willing to do given the extremely low drop rates involved, but there is more evidence to support the proposition than there is that contradicts it.

The best way to describe it is pseudo-random: a computer's RNG mimics a random number generator in certain essential ways, but if you can figure out the code underlying the seed you can cause non-random behavior.

I made sure to farm UW no more than 10 times in a single set of runs without either logging off for a day or doing something else. I don't know when the anti-farming code kicks in but I bet it takes more than 10 runs.

Previously it was less than a dozen before you got a window that warned you the quality of drops would diminish due to repeated zoning or something similar to that wording. Used to set that thing off constantly farming greens back in the good old days. Whether or not this is still the case....?

I don't know that any of those things in particular would affect your drop chances, but there are definitely factors beyond the rng code. Of this I am certain sure. My husband and I have both logged quite a few thousand hours on our main accounts since 2005. He has had a few hundred black dye drops over the years & I have had a sum total of 4. It doesn't matter which computers we play from, or which ISP we use, the ratio remains the same. While there may not be a drop choke on every account I am positive there's one associated to black dye on mine.

I'm not standing in a road at any point because the odds are greater during the night, but less probable because of lower traffic, it is the opposite during the day. I get what you're saying though it doesn't relate to the drop rate of ectoplasm much, it is completely coincidental.