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• posted a message on Magic Find and its efficiency: A statistical insight
So... that bonus drop that has a chance of occurring when a monster is killed in MP>1... think it's like one of the earlier slots? Or something new?
Posted in: Theorycrafting and Analysis
• posted a message on "Adds X% to Y damage" Stat, 1.0.4 vs 1.0.5
I just have to interject that it is completely asinine that "Adds 10% to fire damage" does not take the fire damage you and amplify it by 10%. Clearly it should be reading 10% as fire damage.
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5
Confirmed:
For players in Inferno participating in the Infernal Machine event (we’ll provide more info on this event soon), Monster Power will also increase the drop chance for Keywarden Keys and Demonic Organ Pieces by 10% for each MP level, all the way up to 100% at MP 10.

http://us.battle.net/d3/en/blog/7540457/Monster_Power_More_Guts_More_Glory-10_11_2012
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5
Quote from thundersteele

By "Key" you mean "Key run", right?

Once you stop putting a limit on the number of rings to craft, the calculation simplifies a lot. It's already clear that you need 30/MP key runs on average to craft one machine. On average you need 30/MP machines to gather three ring mats. Now they might not be the correct three mats, but over time they should average out. So it's just

30/MP * 30/MP = 900/MP^2 runs for one ring

Yes, key runs. Will edit to fix.

That formula is nearly right but I feel like it's a bit too disconnected from reality because no one is going to want infinite keys, and the difference between infinite and 10 and 1 is pretty large.
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5

Quote from Loroese

Do you basically start with gathering 9 keys, 3 of each, then opening 3 portals?
Eh, not exactly. Basically, I had it determine how many machines you would need, and then it simulates finding a set of keys for each machine. The result is the same except for the case where you showed up with 3 machines on your last run and only ended up needing 1 or 2 of them (so small effect, but I could probably refine code to correct that).
I changed to code to do this properly. OP updated.
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5
Quote from Lexikon

I think it could be useful to add the expected numbers of keys per ring, for many rings. That is simply 3*10/MP machines per ring, and 3*10/MP runs per machine.
Divide the first number by 4 for a full party.

After some runs at MP 1, the 10%/MP-level assumption looks more reasonable again. However, the size of the dataset is poor, just 33 key runs, 7 plan runs plus 19 organ runs.

For multiple rings, the key runs per ring is diminished. The reason is that... well, say you try to get a ring and you get the organs from portal 1 and 2 but not from 3. Next time, let's say your first portal is 1 again. It's not wasted if you wanted 2 rings instead of 1, because you wanted that portal again anyway. The difference not huge. If you wanted, say, 10 rings, here are the results:

Monster Power: 1
Rings Wanted: 10
Average Machines: 343.3471
Average Machines per Ring: 34.33471
Median Machines: 339
Median Machines per Ring: 33.9
Average Keys: 10307.5062
Average Keys per Ring: 1030.75062
Median Keys: 10163
Median Keys per Ring: 1016.3

Monster Power: 2
Rings Wanted: 10
Average Machines: 170.022
Average Machines per Ring: 17.0022
Median Machines: 167
Median Machines per Ring: 16.7
Average Keys: 2550.5963
Average Keys per Ring: 255.05963000000003
Median Keys: 2513
Median Keys per Ring: 251.3

Monster Power: 3
Rings Wanted: 10
Average Machines: 112.7076
Average Machines per Ring: 11.27076
Median Machines: 112
Median Machines per Ring: 11.2
Average Keys: 1127.5897
Average Keys per Ring: 112.75897
Median Keys: 1114
Median Keys per Ring: 111.4

Monster Power: 4
Rings Wanted: 10
Average Machines: 83.9712
Average Machines per Ring: 8.39712
Median Machines: 83
Median Machines per Ring: 8.3
Average Keys: 629.7703
Average Keys per Ring: 62.97703
Median Keys: 620
Median Keys per Ring: 62.0

Monster Power: 5
Rings Wanted: 10
Average Machines: 66.3255
Average Machines per Ring: 6.63255
Median Machines: 65
Median Machines per Ring: 6.5
Average Keys: 398.0607
Average Keys per Ring: 39.80607
Median Keys: 393
Median Keys per Ring: 39.3

Monster Power: 6
Rings Wanted: 10
Average Machines: 54.7384
Average Machines per Ring: 5.47384
Median Machines: 54
Median Machines per Ring: 5.4
Average Keys: 273.6837
Average Keys per Ring: 27.36837
Median Keys: 271
Median Keys per Ring: 27.1

Monster Power: 7
Rings Wanted: 10
Average Machines: 46.3121
Average Machines per Ring: 4.63121
Median Machines: 46
Median Machines per Ring: 4.6
Average Keys: 198.4168
Average Keys per Ring: 19.84168
Median Keys: 196
Median Keys per Ring: 19.6

Monster Power: 8
Rings Wanted: 10
Average Machines: 39.9846
Average Machines per Ring: 3.99846
Median Machines: 39
Median Machines per Ring: 3.9
Average Keys: 149.9349
Average Keys per Ring: 14.99349
Median Keys: 148
Median Keys per Ring: 14.8

Monster Power: 9
Rings Wanted: 10
Average Machines: 34.8634
Average Machines per Ring: 3.4863399999999998
Median Machines: 35
Median Machines per Ring: 3.5
Average Keys: 116.1321
Average Keys per Ring: 11.613209999999999
Median Keys: 115
Median Keys per Ring: 11.5

Monster Power: 10
Rings Wanted: 10
Average Machines: 30.0
Average Machines per Ring: 3.0
Median Machines: 30
Median Machines per Ring: 3.0
Average Keys: 90.0
Average Keys per Ring: 9.0
Median Keys: 90
Median Keys per Ring: 9.0

Quote from Loroese

Yeah, that's a monte carlo simulation, which is what I expected. I'm far too rusty with my probability theory to try outright calculating any final probabilities, so this method should work fine.

Ok, cool. Have not heard that term before.

Quote from Loroese

Do you basically start with gathering 9 keys, 3 of each, then opening 3 portals?
Eh, not exactly. Basically, I had it determine how many machines you would need, and then it simulates finding a set of keys for each machine. The result is the same except for the case where you showed up with 3 machines on your last run and only ended up needing 1 or 2 of them (so small effect, but I could probably refine code to correct that).

Quote from Loroese

After that if you're still missing 3 organs, repeat until missing 2 or less, then open portals 1, 2, or 3 at a time? Also, do you track excess organs obtained while hunting for the last one?
Yeah, it will open 3 portals in one game but only open portals after the first if the organ from that portal is needed for the targeted number of rings. I do not track excess organs, but you can get a sense of their benefit by telling the program you want to find 10 rings instead of just 1.
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5
I originally intended to use a formula to compute this. That can be easily done if you only open one portal per game. It makes more sense to make decisions along the way based on how many of the unopened portals in your game are still valuable to you, though, and that made the math more complicated than I could tackle.

Basically, what the program does is say two things.

In a subfunction, it says goes and finds three keys for a machine. For each key, it creates a random decimal number (0-1). If that number less than the chance to find a key, then the key is successfully gathered. If it's not less, then you add one to the attempt count and try again. For example, if your MP is 3, you'd have to roll 0.3 or less to be a success.

The main function basically does the same thing with organs. The difference is that it also assigns an order for each game for the portals to open. (Portal 1, then 2, then 3; or portal 3, then 1, then 2, etc). The player will only bother opening the second and third portals if he needs organs from them. That reduces the total number of machines needed... and also make the math more involved. Simulation was pretty simple.

It basically runs this "ring hunt" for 10,000 players at each MP, logging how many keys and organs it took to get the ring. Then it just summarizes.
Posted in: Theorycrafting and Analysis
• posted a message on Expected Runs for Keys and Organs in 1.0.5
I am NOT a programmer, but I took a stab at writing a bit of code to simulate the key and organ hunt based on MP level. The current theory is that the chance of finding a key or organ is MP*0.1. That is, 10% at MP1, 20% at MP2... up to 100% at MP10. We don't know that this is exactly true yet. All that has been stated by blues is that MP1 is >0% and MP10=100%. Seems logical but may possible be incorrect.

The other thing to note is that you can open three portals in a single game and they are guaranteed to be different. So, if you need portal 2 and 3 and you open portal 1, you have a 100% chance of getting a portal you need by opening a second portal in that same game. The optimal strategy, then, is to always have 3 machines with you in case the portal you need is not the first one to open (since subsequent portals have a better chance of matching your need than the first).

Code is at the bottom (python 3.3)

1 Ring Wanted:

Rings Wanted: 1

Monster Power: 1
Average Machines: 42.6
Average Machines per Ring: 42.6
Median Machines: 38
Median Machines per Ring: 38.0
Average Key Runs: 1307.1
Average Key Runs per Machine: 30.7
Average Key Runs per Ring: 1307.1
Median Key Runs: 1158
Median Key Runs per Machine: 30.5
Median Key Runs per Ring: 1158.0

Monster Power: 2
Average Machines: 20.9
Average Machines per Ring: 20.9
Median Machines: 19
Median Machines per Ring: 19.0
Average Key Runs: 327.7
Average Key Runs per Machine: 15.7
Average Key Runs per Ring: 327.7
Median Key Runs: 293
Median Key Runs per Machine: 15.4
Median Key Runs per Ring: 293.0

Monster Power: 3
Average Machines: 13.7
Average Machines per Ring: 13.7
Median Machines: 12
Median Machines per Ring: 12.0
Average Key Runs: 145.7
Average Key Runs per Machine: 10.6
Average Key Runs per Ring: 145.7
Median Key Runs: 131
Median Key Runs per Machine: 10.9
Median Key Runs per Ring: 131.0

Monster Power: 4
Average Machines: 10.0
Average Machines per Ring: 10.0
Median Machines: 9
Median Machines per Ring: 9.0
Average Key Runs: 81.5
Average Key Runs per Machine: 8.1
Average Key Runs per Ring: 81.5
Median Key Runs: 74
Median Key Runs per Machine: 8.2
Median Key Runs per Ring: 74.0

Monster Power: 5
Average Machines: 7.8
Average Machines per Ring: 7.8
Median Machines: 7
Median Machines per Ring: 7.0
Average Key Runs: 51.4
Average Key Runs per Machine: 6.6
Average Key Runs per Ring: 51.4
Median Key Runs: 47
Median Key Runs per Machine: 6.7
Median Key Runs per Ring: 47.0

Monster Power: 6
Average Machines: 6.3
Average Machines per Ring: 6.3
Median Machines: 6
Median Machines per Ring: 6.0
Average Key Runs: 34.9
Average Key Runs per Machine: 5.5
Average Key Runs per Ring: 34.9
Median Key Runs: 32
Median Key Runs per Machine: 5.3
Median Key Runs per Ring: 32.0

Monster Power: 7
Average Machines: 5.2
Average Machines per Ring: 5.2
Median Machines: 5
Median Machines per Ring: 5.0
Average Key Runs: 24.8
Average Key Runs per Machine: 4.8
Average Key Runs per Ring: 24.8
Median Key Runs: 24
Median Key Runs per Machine: 4.8
Median Key Runs per Ring: 24.0

Monster Power: 8
Average Machines: 4.3
Average Machines per Ring: 4.3
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 17.9
Average Key Runs per Machine: 4.1
Average Key Runs per Ring: 17.9
Median Key Runs: 15
Median Key Runs per Machine: 5.0
Median Key Runs per Ring: 15.0

Monster Power: 9
Average Machines: 3.6
Average Machines per Ring: 3.6
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 13.0
Average Key Runs per Machine: 3.6
Average Key Runs per Ring: 13.0
Median Key Runs: 10
Median Key Runs per Machine: 3.3
Median Key Runs per Ring: 10.0

Monster Power: 10
Average Machines: 3.0
Average Machines per Ring: 3.0
Median Machines: 3
Median Machines per Ring: 3.0
Average Key Runs: 9.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 9
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0

10 Rings Wanted:
Rings Wanted: 10

Monster Power: 1
Average Machines: 342.8
Average Machines per Ring: 34.3
Median Machines: 338
Median Machines per Ring: 33.8
Average Key Runs: 10312.9
Average Key Runs per Machine: 30.1
Average Key Runs per Ring: 1031.3
Median Key Runs: 10164
Median Key Runs per Machine: 30.1
Median Key Runs per Ring: 1016.4

Monster Power: 2
Average Machines: 170.2
Average Machines per Ring: 17.0
Median Machines: 168
Median Machines per Ring: 16.8
Average Key Runs: 2567.1
Average Key Runs per Machine: 15.1
Average Key Runs per Ring: 256.7
Median Key Runs: 2532
Median Key Runs per Machine: 15.1
Median Key Runs per Ring: 253.2

Monster Power: 3
Average Machines: 112.6
Average Machines per Ring: 11.3
Median Machines: 111
Median Machines per Ring: 11.1
Average Key Runs: 1135.8
Average Key Runs per Machine: 10.1
Average Key Runs per Ring: 113.6
Median Key Runs: 1120
Median Key Runs per Machine: 10.1
Median Key Runs per Ring: 112.0

Monster Power: 4
Average Machines: 83.8
Average Machines per Ring: 8.4
Median Machines: 83
Median Machines per Ring: 8.3
Average Key Runs: 635.5
Average Key Runs per Machine: 7.6
Average Key Runs per Ring: 63.6
Median Key Runs: 627
Median Key Runs per Machine: 7.6
Median Key Runs per Ring: 62.7

Monster Power: 5
Average Machines: 66.4
Average Machines per Ring: 6.6
Median Machines: 66
Median Machines per Ring: 6.6
Average Key Runs: 403.8
Average Key Runs per Machine: 6.1
Average Key Runs per Ring: 40.4
Median Key Runs: 399
Median Key Runs per Machine: 6.0
Median Key Runs per Ring: 39.9

Monster Power: 6
Average Machines: 54.7
Average Machines per Ring: 5.5
Median Machines: 54
Median Machines per Ring: 5.4
Average Key Runs: 278.3
Average Key Runs per Machine: 5.1
Average Key Runs per Ring: 27.8
Median Key Runs: 275
Median Key Runs per Machine: 5.1
Median Key Runs per Ring: 27.5

Monster Power: 7
Average Machines: 46.4
Average Machines per Ring: 4.6
Median Machines: 46
Median Machines per Ring: 4.6
Average Key Runs: 202.6
Average Key Runs per Machine: 4.4
Average Key Runs per Ring: 20.3
Median Key Runs: 201
Median Key Runs per Machine: 4.4
Median Key Runs per Ring: 20.1

Monster Power: 8
Average Machines: 40.0
Average Machines per Ring: 4.0
Median Machines: 39
Median Machines per Ring: 3.9
Average Key Runs: 153.1
Average Key Runs per Machine: 3.8
Average Key Runs per Ring: 15.3
Median Key Runs: 152
Median Key Runs per Machine: 3.9
Median Key Runs per Ring: 15.2

Monster Power: 9
Average Machines: 34.9
Average Machines per Ring: 3.5
Median Machines: 35
Median Machines per Ring: 3.5
Average Key Runs: 118.7
Average Key Runs per Machine: 3.4
Average Key Runs per Ring: 11.9
Median Key Runs: 118
Median Key Runs per Machine: 3.4
Median Key Runs per Ring: 11.8

Monster Power: 10
Average Machines: 30.0
Average Machines per Ring: 3.0
Median Machines: 30
Median Machines per Ring: 3.0
Average Key Runs: 90.0
Average Key Runs per Machine: 3.0
Average Key Runs per Ring: 9.0
Median Key Runs: 90
Median Key Runs per Machine: 3.0
Median Key Runs per Ring: 9.0

Note that this is solo. If there are 3 of you, each can build up the mats for one machine and you can each open a portal and use each others', so the actual number of runs needed is the result above divided by cooperating players.

Code:

```import random[/size]

portals = [0,1,2]
Iterations = 100000
rings_wanted = 1

def Keys_for_machine(MonsterPower):

keys = [0,0,0]
keytrials = 0

while keys[0] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[0] = 1
while keys[1] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[1] = 1
while keys[2] == 0:
keytrials = keytrials + 1
trial = random.random()
if trial <= MonsterPower*0.1:
keys[2] = 1
return keytrials

print("Rings Wanted:",rings_wanted)

for MonsterPower in [1,2,3,4,5,6,7,8,9,10]:
Results_keys=[]
Results_machines=[]
while len(Results_keys)<Iterations:
machines_used = 0
keys_used = 0
organ = [0,0,0]
while organ[0]<rings_wanted or organ[1]<rings_wanted or organ[2]<rings_wanted:
skipped = 2
keys_used = keys_used + Keys_for_machine(MonsterPower)
random.shuffle(portals)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[0]] = organ[portals[0]]+1
if organ[portals[1]]<rings_wanted or organ[portals[2]]<rings_wanted:
skipped = 1
keys_used = keys_used + Keys_for_machine(MonsterPower)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[1]] = organ[portals[1]]+1
if organ[portals[2]] < rings_wanted:
skipped = 0
keys_used = keys_used + Keys_for_machine(MonsterPower)
machines_used = machines_used + 1
trial = random.random()
if trial <= MonsterPower*0.1:
organ[portals[2]] = organ[portals[2]]+1
Results_keys.append(keys_used+skipped*Keys_for_machine(MonsterPower))
Results_machines.append(machines_used)
print("\n")
print("Monster Power:",MonsterPower)

average_machines = 0
for i in Results_machines:
average_machines = average_machines + i
average_machines = average_machines / Iterations

print("Average Machines:", round(average_machines,1))
print("Average Machines per Ring:",round(average_machines/rings_wanted,1))
Results_machines.sort()
print("Median Machines:",Results_machines[int(Iterations/2)])
print("Median Machines per Ring:",round(Results_machines[int(Iterations/2)]/rings_wanted,1))

average_keys = 0
for i in Results_keys:
average_keys = average_keys + i
average_keys = average_keys / Iterations

print("Average Key Runs:", round(average_keys,1))
print("Average Key Runs per Machine:",round(average_keys/average_machines,1))
print("Average Key Runs per Ring:",round(average_keys/rings_wanted,1))
Results_keys.sort()
print("Median Keys:",Results_keys[int(Iterations/2)])
print("Median Keys per Machine:",round(Results_keys[int(Iterations/2)]/Results_machines[int(Iterations/2)],1))
print("Median Keys per Ring:",round(Results_keys[int(Iterations/2)]/rings_wanted,1))```

Posted in: Theorycrafting and Analysis
• posted a message on [PROJECT] PTR Opportunity - Affix Research
Thanks! I still need to aggregate what info we have. I got side tracked and haven't had a chance to do this yet. I was hoping for several thousand data points and it looks like we'll end up with just a few hundred, so the results won't be as robust as I was hoping.
Posted in: Theorycrafting and Analysis
• posted a message on Magic Find and its efficiency: A statistical insight
The chance for Legendary and set items to drop has been doubled

http://us.battle.net/d3/en/blog/7390518/Public_Test_Realm_Patch_105_Notes-9_27_2012
Posted in: Theorycrafting and Analysis