
Originally Posted by
CYoung187
If 8 people are rolling then the chance of winning is 12.5%, 5 people rolling is 20% chance of winning.
Thanks for playing, but I decided to do the math myself, since it looks like nobody else cares.
If everybody drew lots based on how many people could roll, the chances would definitely be 20% chance to win between 5 people and 12.5% chance to win between 8 characters. However, since everybody's rolling out of 100, the chances are not so simple.
Please keep in mind that I'm not dealing with ties, since I'm not sure how those are handled in the game (I don't think I've ever seen one either and it would be pretty rare anyway). I've been crossreferencing statistics sites that deal with dice rolls and chance, but I ultimately had to do the work myself, since the loot system is pretty unique (read as: nobody actually uses it in the real world).
Disclaimer: I don't do statistics and welcome any critique/corrections.
Hello and welcome to a crazy thing I decided to do using spreadsheets and too much time at work. Essentially, the question that arose earlier in this thread is whether or not your chances of lotting on the the Oil of Time, should it drop, is significantly affected by other people dropping out earlier in the raid. This is assuming that the only reason people would drop is if they already rolled successfully on another piece of loot, since it wouldn't affect your chances if somebody drops without getting their loot
What we do know about the loot system is that for need tier and greed tier, is that the winner is determined by the person who rolls highest in the group with a roll out of one hundred. I do not know whether a person can roll 100 (I've never seen it), but I do know people can roll as low as 1. A pass or inability to roll in the tier counts as a roll of 0. Since everybody can roll need on an Oil of Time, things are simplified somewhat: we only need worry about need tier chances.
Since we are essentially finding the chances of winning a die roll on a die with an extreme number of sides, there is no easy formula (that I know of) that we can just use and plug in values for an answer. So we'll do it the long way. We'll find out every possible way to win the roll.
Say we roll a 1. We know we won't be winning the OoT because everybody else will roll higher than us. So we can discount that roll.
Code:
Us Them
1 1 1 1 1 1 1 1
In the event we roll a 2, there's only one possible way we could win the roll: If everybody else rolls a 2 (I know I assumed no ties, but bear with me).
Code:
Us Them
2 1 1 1 1 1 1 1
When we roll a 3, things start to get more interesting: now there are 128 different ways we can win with 8 rolls, and 32 different ways we can win with 5.
Code:
Us Them
3 1 1 1 1 1 1 1
3 1 1 1 1 1 1 2
3 1 1 1 1 1 2 1
3 1 1 1 1 1 2 2
...
3 2 2 2 2 2 2 1
3 2 2 2 2 2 2 2
Things are beginning to take a pattern. For every roll, there are a number of winning combinations equal to (r -1)^n-1, where r is the roll value and n is the number of rolls. If we sum this up among all rolls, We can find out the number of winning combinations for the die roll.
Essentially:
This comes out to about 1.107*10^15 for 8 people rolling and 1.854*10^9 for 5 people rolling.
In order to find out the percent chance of a winning combination, we need to find out the number of total combination possible. Since we're rolling a 100 sided die 8 times for 8 people and 5 times for 5 people, the total number of combinations for scenario is 100^n.
So our formula for calculating the chance of winning an Oil of Time can be calculated as follows:
Code:
100
100^n / ∑ (r -1)^n
r=2
tl;dr
The chances of winning a loot where everybody needs is as follows
8 people: 11.07%
5 people: 18.54%
You're squabbling over 7% chance. Go do hunts if you want an oil that badly.
(I did this because I was bored at work, hope this entertains somebody out there.)