## The math behind random drops and rolls

Reader Sekhar P. sent us an interesting story of a strange roll seen in Naxx recently: Haunting Call dropped, and four people needed. The rolls came up, in order: 1, 2, 3, 4. The raid boggled at how unlikely that must be. Sekhar's tip set off a round of discussion among our WoW Insider staff: while it seems unlikely that four numbers would come up in sequence, the math on it isn't any more likely than any other four numbers (3, 69, 82, and 95, for example, or even 4, 8, 15, and 16). The odds come out to 24/100^4, about 0.00000024%, or about two chances out of 10 million. Of course, probability is tricky, so the chances that any one of those rolls would come up is still one out of 100 -- just like coin flips, previous die rolls won't affect the current die rolls (mistaking that is often called the gambler's fallacy) But the chances that any specific four numbers would come up are the astronomical chances above.

Of course, math aside, that still doesn't keep us from trying to predict how random rolls might work. We also recieved word from reader Emily about a site she and some friends are working on that is trying to predict just how much you'll have to run a certain instance to pick up some of the rarest items in the game, like Baron Rivendare's mount. Unfortunately, it's not a relevant indicator -- it looks like all they're doing is "simulating" runs on the item, and then tracking when it drops in their simulator. They're putting the math behind the chance into practical numbers.

But of course, while it comes up with a lot of interesting numbers, it means nothing at all in the game -- if you make a run on the Deathcharger, you've got just as much chance to get it as you did on the run before. Quest items are subject to progressive rates, but these random items are just that -- random. A high string of "hits" on a simulator (or even in the game -- it's possible to do five Strat runs in a row and see the charger drop each time) doesn't have any effect on any given run in the game. Emily says the site is entertaining, and it is -- at the very least, it shows you that the item

Of course, math aside, that still doesn't keep us from trying to predict how random rolls might work. We also recieved word from reader Emily about a site she and some friends are working on that is trying to predict just how much you'll have to run a certain instance to pick up some of the rarest items in the game, like Baron Rivendare's mount. Unfortunately, it's not a relevant indicator -- it looks like all they're doing is "simulating" runs on the item, and then tracking when it drops in their simulator. They're putting the math behind the chance into practical numbers.

But of course, while it comes up with a lot of interesting numbers, it means nothing at all in the game -- if you make a run on the Deathcharger, you've got just as much chance to get it as you did on the run before. Quest items are subject to progressive rates, but these random items are just that -- random. A high string of "hits" on a simulator (or even in the game -- it's possible to do five Strat runs in a row and see the charger drop each time) doesn't have any effect on any given run in the game. Emily says the site is entertaining, and it is -- at the very least, it shows you that the item

*is*dropping, while 99 runs without a drop in the game might have you convinced otherwise. But the math doesn't work that way -- either the Baron has the mount when he spawns, or he doesn't.Filed under: Analysis / Opinion, Odds and ends, Blizzard, Raiding, NPCs

## Reader Comments (Page 1 of 5)

## msingletary Apr 7th 2009 11:08AM

The odds are definitely against you. Not only do you have to rely on RNG to determine whether the item you want will spawn on the boss, you may have to deal with RNG again when you have to roll to get that item if someone else wants it, too! Ugh!

## Damntheman Apr 7th 2009 12:52PM

Stick to blogging.... wow, the chance of [1,2,3,4] is 1/100^4 but something tells me they would have been equally amazed by [2,3,4,5] or [4,3,2,1]. Of course your comment section is a much richer source of math-gasms. I like how "a little knowledge is a dangerous thing" never seems to apply, where the rule is "numbers are scary so just make it up because U R so SMRT, your high school math teacher said so!".

## Imbasaur Apr 7th 2009 11:10AM

RNG can be extremely crazy. we all know how it is.

In tonight's sarth 3D, me and a hunter rolled for the melee dps trink. He rolled a 45, and i followed with a 45.

The next item up for rolls was the twilight drake. Somebody rolled an 100, and vent exploded in congratulations , yelling, etc. The next roll? another 100. The two 100's had to reroll, and u guessed it. The original person that rolled 100 lost the mount ; )

## Jay in Oregon Apr 7th 2009 11:27AM

On a timed CoS run for the Bronze Drake, I rolled a 99 and the next person to roll got a 100.

I have the screenshot to prove it:

http://www.flickr.com/photos/25514859@N08/3313611553/in/set-72157614510933244/

## Elmo Apr 7th 2009 12:22PM

Back in SSC 2 people did an offspec roll (not for DKP but for RNG)

33 vs 33

82 vs 82

10 vs 10

35 vs 76

Really they rolled the same number 3 times in a row.

thats a chance of 1 in 1.000.000 (100x100x100)

although I made the numbers up it really happened

## barth Apr 7th 2009 11:10AM

Exactly.. the site would be useless since you have just as much a chance of getting the mount on run #1, or you could run it everyday, 100x per day for 10 years and never see it drop.

## mord Apr 7th 2009 6:18PM

Not quite. I think Baron's mount has a 0.1% to drop so there is a 99.9% chance it will NOT drop. Therefore, the chance of it not dropping in 100 runs is 0.999^100 = 90.48%. So you have a 9.52% chance to get a mount in your first 100 runs.

How many times must one run strat to give oneself a 99.9% chance of getting a mount? Well, 0.999^6904 = 0.1%, so theres a 99.9% chance of getting Baron's mount after 6904 runs. So if a player decides to run strat 100 times per day, then he/she has the same chance of getting the mount on the first run as he/she has to not see the mount at all in 3 months (or 69 days).

(this is just an example for an ultra-rare drop, Baron's mount might have a droprate slightly higher than 0.1%)

## Socordia Apr 7th 2009 11:14AM

The chance to roll in a certain _sequence_, e.g., (1,2,3,4) in that (and only that) order, is only 1/(100^4).

## musicjunkie300 Apr 7th 2009 12:02PM

close but not entirely right.

the first number can be any number from 1-97 (if 98 or higher than u can't get 4 in a row) therefore for the first roll you have 97/100 chance

2nd roll you have a 1/100

3rd roll you have a 1/100

4th roll you have a 1/100

so therefore

it's .97 * .01 *.01 * .01 =.00000097

## Penguirrel Apr 7th 2009 3:11PM

I believe what he means is a callinga certain sequence to come up is 1/100^4. Say calling 45, 46, 47, 48 to come up is a 1/100^4. Whereas calling ANY progressively growing number sequence to come up without wraparounds at the ends (like 99, 100, 1, 2) has a 1/(.97*100^3) chance.

## McRaider Apr 7th 2009 3:36PM

Cool. Math rules!

## capitalism Apr 7th 2009 11:15AM

23, 42

## Talmar Apr 7th 2009 11:15AM

Just a couple weeks ago I did a pug 25 OS. 2 of the warrior T7 glove turn ins dropped. I thought I was a shoe in for the 2nd one as I rolled 95, then I saw... 96, 97 and 98.

I've been in a few heroic runs where 3 or 4 people all rolled the exact same greed number.

Sometime RNG doesn't seem so RNG. Either that or I'm just one unlucky sob.

## Rihlsul Apr 7th 2009 11:18AM

We had something like that last night. 97, 98 and 99.... call went out for 'last rolls' - blam, 100.

Lotta groaning/cheering on vent. =P

## Amrytale Apr 7th 2009 11:48AM

Statistically speaking, the lack of patterns in (mostly) random numbers would be unlikely. If the RNG consistently output what seemed like random numbers, that would be evidence that it was being directed.

## Karilyn Apr 7th 2009 4:08PM

To expand on what Amrytale said...

Patterns are a normal part of true random.

This is easy to see with coin flips.

HHTTHTHTTT

THHTTHHTTT

THHHTHTTHH

TTHHHHTTTH

THHTHTTTTT

That's 50 coin flips. Genuine coin flips. Go figure, I was bored.

Notice some of the chains...

5 tails x 1

4 tails x 2

3 tails x 8

4 heads x 1

3 heads x 1

That's true random. A fake random, would likely never have had more than 2 of any coin in a row. In reality, it is statistically LIKELY to have at least one chain of 5 coins in a row.

## gwarharhar Apr 7th 2009 11:21AM

I think you mean 1/100^4 ... not sure how you got 24... To get any number out of 100, your chance is 1/100. To get any set of 2 numbers in two rolls is ( 1/100 ) X ( 1/100 )... etc...

## Avrus Apr 7th 2009 11:24AM

The random numbers generated by computers are only 'pseudo' random. They typically use the real time clock or some other predictable number as their seed.

While it's more than sufficient for an online game, it's not truly an RNG.

## Braundo Apr 7th 2009 11:28AM

Now that that obligatory post is out of the way, let's not bring it up again.

Yes, yes, we know.

## Kakistocracy Apr 7th 2009 12:32PM

Well, this is where we have to wish out language used more parenthesis, perhaps, it is the generator, and not the number that is random. So a "Random (Number Generator)" rather than the assumed "(Random Number) Generator". In which case, the number can be as determined as possible while while name maintains accuracy.

1| 2 | 3 | 4 | 5 | Most Recent | Next 20 Comments