View Full Version : Keys runs. A small calculation.
I don't know if this small calculation was posted before so I'm sorry if I'm repeating something.
I've calculated how many runs you need to do in avarage, to get 9 keys, assuming you kill all the 3 unique bosses in a single run.
I based my calculation on the chances that are given in Atma 1.11 Drop Calculator which are:
1/14 for Terror key drop
1/11 for Hate key drop
1/12 for Destruction key drop
The calculation:
In a single run (3 unique bosses kills) you have:
a. A chance of 1/1848 to get 3 keys
b. A chance of 34/1848 to get 2 keys
c. A chance of 383/1848 to get 1 key
d. A chance of 1430/1848 to get no keys at all.
The avarage number of keys you get in a single run is:
(3*1+2*34+1*383+0*1430)/1848 = (3+68+383+0)/1848 = 454/1848 = 0.245671
The avarage number of runs you need do to get 9 keys is:
9/0.245671 = 36.6
Conclusion:
In avarage, for each 36.6 runs you make, you'll get 9 keys.
Notes:
1. The calculation only gives the chance to get 9 keys, without seperating them to 3 of each type.
The avarage number of runs you need to do to get at least 3 of each type is 42 since Countess has a 1/14 chance of droping terror key and you want 3 of this.
2. The calculation is not 100% accurate because I've based the calculation on the assumption that the chances given in Atma are for getting exactly 1 key in a single kill although they are the chances of getting at least 1 key in a single kill.
The effect of it is very small so if you want you can just round the number 36.6 down to 36 and it should be pretty accurate.
strikeamatch
07-06-2006, 23:35
have u taken statistics?
your 36 number is crazy wrong... first of all they are all independant drops so you must treat them independantly... therefor 42 is the correct expected number of runs because it is the highest number of runs to get 3 of any one key.
36.6 runs is how long you should run to get 27 keys of any type. not 3 of each type...
moreover when running you can't perform partial runs or if you do, they're still a whole run, just not all 3 mobs, so 37 would be at least a more reasonable assessment of this math which as i said is invalid.
sorry :(
if u wanted to include trade values so your extra random keys dont go to waste...
apply your local value to get a generic variable X
X=1 tkey
1dkey = 2tkey = 2hkey (useast)
tkey drop value = X/14
hkey = X/11
dkey = X/6
then run your odds and get:
the average value = 0.245671 * 2 = .491342X (assuming your original number is correct and that your values correspond to useast last tiem i traded keys.)
the value of one keyset is 4X, 3 keysets is 12X
12X/.49132X = 24.4229 runs... a much better number that should still be rounded up to 25... hope this helps :)
Sorry but although you were harsh about my calculation, I still don't agree with you.
1. "therefor 42 is the correct expected number of runs because it is the highest number of runs to get 3 of any one key."
You sure you've read the notes I wrote?
2. I have clearly stated that 36.6 is the number of runs for 9 keys of any type (and not 3 of each) and I've based the calculation on this.
3. I have clearly stated that a run is all 3 bosses so if you decide not to kill all 3 in your runs, then abviously the calculation won't be accurate for you and yes, you would have to round it up not just to 37 but to more than 37.
4. Yes, I know the drops are independant and there's no problem with that. That's why you may get one time 2 keys in 2 runs and another time 0 key in 100 runs but in average, you'll get 9 keys in 36.6 runs.
5. "36.6 runs is how long you should run to get 27 keys of any type."
Eh?
6. What extra random key are you referring to? I've calculate the number of runs you need to get 9 keys so you may argue about the number of runs but how can you argue about the number of keys? 9 keys is the number.
About your calculation:
I understand why you valued a full keyset as 12X but I don't understand why you took the odds to get 1 key in 1 game (0.245671) and doubled it. Maybe you can explain it better.
strikeamatch
08-06-2006, 00:24
Sorry but although you were harsh about my calculation, I still don't agree with you.
you are correct in retrospect, you have roughly the right idea to get 9 keys of unknown type... i read some intent into the number 9 as seen below
1. "therefor 42 is the correct expected number of runs because it is the highest number of runs to get 3 of any one key."
You sure you've read the notes I wrote?
again working with the assumption you wanted 3 of each
2. I have clearly stated that 36.6 is the number of runs for 9 keys of any type (and not 3 of each) and I've based the calculation on this.
true... and why 9 of any type, this makes no sense since you clearly chose the number 9 which is the number of keys in 3 keysets... the number of keysets to get one organ set... the needed supplies for a torch... a random choice?
3. I have clearly stated that a run is all 3 bosses so if you decide not to kill all 3 in your runs, then abviously the calculation won't be accurate for you and yes, you would have to round it up not just to 37 but to more than 37.
yeah rounding always goes up, a side point.
4. Yes, I know the drops are independant and there's no problem with that. That's why you may get one time 2 keys in 2 runs and another time 0 key in 100 runs but in average, you'll get 9 keys in 36.6 runs.
i meant the drops for each key in a given game... again thinking u were aiming at keysets... which i'm not convinced you're not, just that if you're not, 9 was an odd number to choose.
5. "36.6 runs is how long you should run to get 27 keys of any type."
Eh?
replace 27 with 9.... mental blip.
6. What extra random key are you referring to? I've calculate the number of runs you need to get 9 keys so you may argue about the number of runs but how can you argue about the number of keys? 9 keys is the number.
assuming u wanted 3 of each key you would invariably wind up with extra random keys at some point, especially if this process was repeated...
About your calculation:
I understand why you valued a full keyset as 12X but I don't understand why you took the odds to get 1 key in 1 game (0.245671) and doubled it. Maybe you can explain it better.
you had 1/14, 1/11, 1/12
i had X/14, X/11, X/6 (which made sense, right?)
X/6 = 2x/12
1/(14*11*12) = some number
2X/(14*11*12) = 2X * (some number)
you use that number to calculate the rest so instead of writing all the numbers out again i just multiplied by 2 at the end. i'm pretty sure this works since i came out with the same number of runs i expected to based on my previous calculations.
Calculating exactly 3 of each (42) was too simple :smiley:
The calculation is just for the theory because in actual running, when you find 3 of one key type, you usually stop running for that key and make runs only for the other 2.
So why I calculated it?
I was just curious because I like math. thats all.
strikeamatch
08-06-2006, 00:36
Calculating exactly 3 of each (42) was too simple :smiley:
The calculation is just for the theory because in actual running, when you find 3 of one key type, you usually stop running for that key and make runs only for the other 2.
So why I calculated it?
I was just curious because I like math. thats all.
i suppose i'd have liked taking it to a generic value system to figure runs per torch value... (not including the uber runs of course, just the raw materials)
We can say that a 20/20 sorc torch is droped for each 121 sorc torches and sorc torch is droped for every 7 torches.
So the number of runs you need to do to get a 20/20 sorc torch is: 121*7*36.6=31000 (not much, is it? :wink3: )
Edit: I think I'm trying to understand why your number (24.4229) is lower than mine (36.6). Is it because the chances to get for example 9 DKeys are higher than to get 9 TKeys? and by your formula, you value DKeys more than Tkeys?
strikeamatch
09-06-2006, 20:46
We can say that a 20/20 sorc torch is droped for each 121 sorc torches and sorc torch is droped for every 7 torches.
So the number of runs you need to do to get a 20/20 sorc torch is: 121*7*36.6=31000 (not much, is it? :wink3: )
Edit: I think I'm trying to understand why your number (24.4229) is lower than mine (36.6). Is it because the chances to get for example 9 DKeys are higher than to get 9 TKeys? and by your formula, you value DKeys more than Tkeys?
yes, i value them higher because in trading i can get 2 tkeys or 2 hkeys for 1dkey... actually some people will pay 3, but those are somewhat few and far between these days. basically its lower because the most valuable (tradewise) is more likely to drop than the less valuable. my values there are based on my trading experience and kind of the standard for useast, although all values fluxuate pretty rapidly...
and your 31000 runs is wrong again because u need specific keys, not any random assortment of 9 keys... which is the direction i thought you were gonna take which is why i assumed u wanted 3 keysets, not just any 9 keys... if u know people who will swap one key for another of any type, then you're correct, you could get enough keys and then swap your extra (for example) hkeys for tkeys... lemme see what the odds of u getting a 20/20 storch in 847 torches... 63.23% so yikes.
On Europe it's even better; normal trade ratio is 1 Dkey for 2 Hkeys or 3-4 Tkeys. I've gotten considerably better bargains on b.net from time to time.
strikeamatch
09-06-2006, 21:52
On Europe it's even better; normal trade ratio is 1 Dkey for 2 Hkeys or 3-4 Tkeys. I've gotten considerably better bargains on b.net from time to time.
1:2:3 was the ratio that we had on east when i started... then 1:3:3, then declining slowly til it became 1:2:2
That's interesting.
Based on a ratio of 1:2:3, you can choose to only do Nihlathak runs so that after:
12 runs you have first D key
12 more runs and you have second D key
12 more runs and you have third D key
12 more runs and you have a D key that you trade for 3 T keys
24 more runs and you have 2 D keys that you trade for 3 H keys
In total, this is 72 Nihlathak runs to get full keyset.
With nature's peace ring it's really not big deal to run him.
strikeamatch
09-06-2006, 22:15
That's interesting.
Based on a ratio of 1:2:3, you can choose to only do Nihlathak runs so that after:
12 runs you have first D key
12 more runs and you have second D key
12 more runs and you have third D key
12 more runs and you have a D key that you trade for 3 T keys
24 more runs and you have 2 D keys that you trade for 3 H keys
In total, this is 72 Nihlathak runs to get full keyset.
With nature's peace ring it's really not big deal to run him.
pretty much exactly the reason why i ran nihli for about 4 weeks straight...
by the way do your calculations take into account double and triple drops? i could never figure out if atma did this already or not, but my first 3x dkey drop i about did a dance on the spot.
pretty much exactly the reason why i ran nihli for about 4 weeks straight...
by the way do your calculations take into account double and triple drops? i could never figure out if atma did this already or not, but my first 3x dkey drop i about did a dance on the spot.
ATMA looks at the chances of a key (or any item) dropping per kill, not per item that falls on the ground. So you could get two keys in a drop but you could also go 24 runs without a key. The 1/12 is the chance of a key dropping per kill.
Read note number 2 in my first post.
I'm almost certain that atma shows the chances for at least 1 key drop and not for exactly 1 drop.
I don't know the exact chances for 2-5 keys drop so I couldn't take it into account.
Anyway, about keys running in general:
Nihlathak runs have the advantage of finding the stairway down fast because there are only 3 options for the level so you remember where it is when you see the wp location.
Countess runs have the advantage of getting runes but tower runs take the longest time.
For those you use map hack, summoner runs are the fastest though.
strikeamatch
09-06-2006, 22:45
yep... basically. people still use maphack? what ever happened to playing the game?
sigh
usbserial
10-06-2006, 03:15
I think the reason dkeys are worth 2x other keys is the supposed difficulty of nithalak (mainly his corpse explosion). As long as you have rest in peace, he is just as easy as any of the others.
Jibblets
10-06-2006, 07:39
lets compromise... 39 runs for 9 keys of any type
strikeamatch
11-06-2006, 02:11
lets compromise... 39 runs for 9 keys of any type
what? that makes no sense... 36.6 was right for the expected runs to get any 9 keys, 42 for the expected runs to get 3 of each, 25 for the runs to get the value of an organset (at prices i normally get), 39 is just the avg of 36 and 42...
moo
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