10 raiders kill a raid boss. Some of those raiders will use a bonus roll, and of those that use a bonus roll some will also win an item from it. In how many different ways can this happen?
10 raiders kill a raid boss. Some of those raiders will use a bonus roll, and of those that use a bonus roll some will also win an item from it. In how many different ways can this happen?
This is harder than I thought.
Do you consider the raiders different people or not? If raider 1 takes a bonus roll and nobody else does, is this the same as raider 2 doing it and nobody else?
Last edited by reckoner04; 2013-02-13 at 03:49 PM.
59049 ways.
There are 10 raiders, and each has 3 possibilities (no charm, charm with no loot, charm and loot).
3^10 = 59049
Naw, because the question simply asks how many different ways are possible. For example, let D = person doesn't use bonus roll, B = person uses bonus roll but doesn't win an item, I = person uses bonus roll and wins an item.
Then for 10 people one possibility is:
{D,D,D,D,D,D,D,D,B,I}
another is
{D,D,D,D,D,B,B,B,B,B}
yet another is:
{I,D,B,B,B,D,D,D,D,D}
and so on...
This should make the problem a lot easier to understand/solve!
*edit* Static Transit got it correct before I posted this tip!
If you used a bonus roll, either you won it or not. Those are the two possibilities. The probability of winning an item doesn't change the fact that there are two possibilities.
But the game won't tell you that. We're not enumerating each individual possible roll, but rather if you won, if you didn't win, or if you didn't roll at all. In your scenario, the game won't tell you "Welp, you were ALMOST there! Just one higher and you would've gotten it. Oh well! Better luck next time!"
Also, the concept of "almost" winning in a pass/fail roll system is an illusion. The pRNG system doesn't work like one of those hammer games at the carnival, where if you just put in a little extra effort you would've won.
Why only D? Why aren't we considering the win / no-win for not using a bonus roll? If we do, then the outcome space has 4 discrete possibilities, and we're looking at 4^10.
In this hypothetical scenario, since each raider is an individual, I suppose we'd consider the order unique - and so, 4^10 is accurate.
LPing For The Future: http://www.youtube.com/user/MrSayier
In my problem statement I intend for each raider to have three possible states: used bonus roll and won no item, used bonus roll and won item, didn't use bonus roll.
I suppose I could rewrite it to:
10 raiders kill a raid boss. Some of those raiders will use a bonus roll. Of those that use a bonus roll, some will either almost win an item, or win an item. In how many different ways can this happen?
This makes four possible states for each raider: used bonus roll and won no item, used bonus roll and won item, used bonus roll and almost won an item, didn't use bonus roll.
Hopefully this rewrite will help you to understand how silly that seems.