Thread: Combinatorics Question of the Day

1. Combinatorics Question of the Day

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?

2. given a lack of paramaters such as drop rates, it'll happen in an infinite number of ways

3. Originally Posted by mistuhbull
given a lack of paramaters such as drop rates, it'll happen in an infinite number of ways
This is incorrect. You do not need to know the probability of bonus roll success to be able to enumerate how many different ways the above can happen.

4. Originally Posted by Laurabelle
This is incorrect. You do not need to know the probability of bonus roll success to be able to enumerate how many different ways the above can happen.
sure I do.

If the bonus roll has 25% drop chance as opposed to a 50% drop chance, then they will have drastically different results. Not to mention that with the sample size and how odds works, really anything can happen

5. 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?

6. 59049 ways.

There are 10 raiders, and each has 3 possibilities (no charm, charm with no loot, charm and loot).

3^10 = 59049

7. 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!

8. Originally Posted by mistuhbull
sure I do.

If the bonus roll has 25% drop chance as opposed to a 50% drop chance, then they will have drastically different results. Not to mention that with the sample size and how odds works, really anything can happen
You don't need to know. Either they won or they didn't, you're not calculating odds here, but rather different possibilities (note: not PROBABILITIES).

9. Originally Posted by Static Transit
You don't need to know. Either they won or they didn't, you're not calculating odds here, but rather different possibilities (note: not PROBABILITIES).
isn't almost winning and completely not winning different possibilities? 2nd place is a different possibility than 3rd place, yet both are in the category of "not winning"

10. 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.

11. Originally Posted by mistuhbull
isn't almost winning and completely not winning different possibilities? 2nd place is a different possibility than 3rd place, yet both are in the category of "not winning"
You don't seem to understand how the bonus roll system works. You can't "almost win" or anything like that. If you roll certain numbers, you win. If you don't, you don't win. Think of it as a pass/fail check. You either pass or fail, there is no "almost."

12. Originally Posted by Static Transit
You don't seem to understand how the bonus roll system works. You can't "almost win" or anything like that. If you roll certain numbers, you win. If you don't, you don't win. Think of it as a pass/fail check. You either pass or fail, there is no "almost."
but there is an almost. If I rolled a 49 but the win roll was 50, then I almost won. I didn't win, but I almost did

13. Originally Posted by mistuhbull
but there is an almost. If I rolled a 49 but the win roll was 50, then I almost won. I didn't win, but I almost did
And? What has this to do with the possibility of getting an item? You either get it, or you don't. There is no "almost", since "almost" means you didn't get it.

14. Originally Posted by reckoner04
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?
They are treated as different possibilities, and different people. You could subscript or index each raider with a number (e.g. 1 through 10) if you prefer.

15. Originally Posted by mistuhbull
but there is an almost. If I rolled a 49 but the win roll was 50, then I almost won. I didn't win, but I almost did
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.

16. Originally Posted by Puri
And? What has this to do with the possibility of getting an item? You either get it, or you don't. There is no "almost", since "almost" means you didn't get it.
but I almost got it, which is a different possibility than getting it, or not being close to getting it.

---------- Post added 2013-02-13 at 08:00 AM ----------

Originally Posted by Static Transit
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.
Game doesn't tell you a lot of things, doesn't mean it's not there

17. Originally Posted by Laurabelle
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!
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.

18. Originally Posted by Stede
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..
You can't win or lose a game you don't play, my friend.

19. Originally Posted by mistuhbull
but I almost got it, which is a different possibility than getting it, or not being close to getting it.
There is so almost, there is a winner and a loser. If you are one under what it takes to be a winner you are a loser, simple as that.

20. Originally Posted by mistuhbull
but I almost got it, which is a different possibility than getting it, or not being close to getting it.

---------- Post added 2013-02-13 at 08:00 AM ----------

Game doesn't tell you a lot of things, doesn't mean it's not there
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.

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