Dragon Tower and more Pop Rates

Over the last couple of weeks the main project I've been working on is finishing off levelling my newest thief. I chose to make this thief a dwarf as I wanted a good aligned thief and I had a couple of pieces of equipment sitting around on storage doing not much that would be perfect for a good thief - an iron hand of kargoth and a cloak of the eternal wanderer. Before hitting level 50 I chose to stock up on a pair of ring of the dragons from Dragon Tower.

My earliest memories of Dragon Tower was as a level 20 being sent for a guild quest to get a pair of leggings of dark dragonscale. Very nice leggings for a level 20 character but difficult to get on your own without any avatar characters to help. From memory it took me seven attempts and my first ever run in with a death trap. Since then it has been modified to include the rings. These rings are not that hard to make but rather time consuming to get all of the parts. I tried killing Tiamat 12 times before I figured out that my thief only had 10 luck. I changed around some equipment and got it up to 17 then managed to pop 2 settings in the next 3 kills. Coincidence or the affect of the enigmatic luck statistic? It's always exciting making items. To make the rings you need to hand them to the wizard in the tower as follows:

You give an empty ring setting to a powerful mage.
A powerful mage gasps in astonishment.
A powerful mage tells you 'I made this once long ago for the great dragon Tiamat.'
A powerful mage tells you 'If you have the five stones, I can make the ring once again.'
You give a snow-white opal to a powerful mage.
You give a radiant-red ruby to a powerful mage.
You give a blazing-blue sapphire to a powerful mage.
You give a pitch-black onyx gemstone to a powerful mage.
You give a gleaming-jade gemstone to a powerful mage.
A powerful mage carefully fits each stone into one of the claws in the setting.
A powerful mage drops the ring of the dragons.
You get the ring of the dragons.
Saved...

The ring is nice for pretty much any character. There are alternative rings for a good thief which I will work on later but for now these will do. After making the two rings I finished the final level and ended up with a hit point base of 745 - my best thief by far.

Next on the list of equipment needed is more good scales of alpha & omega... More grinding... I always seem to need more of this. I've done another 10 kills since my last post and interestingly I ended up with the exact same results from 10 kills - 2 good scales, 2 evil and 6 neutral.

Pop rates

For the last couple of weeks I've been working on equipping some of my underdressed character I use less. Part of this has been something that most people have done plenty of times - killing Justice in the Tower of Enlightenment. I usually kill Justice using just one of my thieves. It takes around 100 heals and a couple of true sights per kill. Fairly straight forward just need to watch the circle lag. Eventually the result is this:

Your pierce tears Justice!
Justice is DEAD!!
As the final blow is struck, a necklace of shimmering scales falls from
Justice's neck.
Justice splatters blood on your armor.
You get a gold coin from the corpse of Justice.
The corpse of Justice holds:
     (Humming) the Blindfold of Clarity
     (Glowing) (Humming) sword of equilibrium
     (Glowing) (Humming) scales of alpha & omega

The big mystery is once you've killed Justice what alignment the scales of alpha and omega are. Good aligned ones are the most useful and the most rare. In my experience I find that out of every 6 kills I get 3 neutral align, 2 evil and 1 good. In the last two weeks I've done 10 kills resulting in 6 neutral, 2 evil and 2 good aligned scales. I was wondering how likely this result was so started thinking about killing Justice as a Bernoulli trial. In a Bernoulli trial we have an event which has probability of occurring and can be repeated. In this case the event is getting a good aligned scale or not and can be repeated as in each kill. Looking at an individual binomial distribution table using a probability of 0.15 (roughly 1 in 6) for each kill the number of good align scales being popped in 10 kills is:

• 0 good scale - 0.272
• 1 good scale - 0.385
• 2 good scales - 0.238
• 3 good scales - 0.084
• 4 good scales - 0.018
• 5 good scales - 0.003
• 6 good scales - 0.000

Looking at the above getting 2 good scales out of 10 kills is quite lucky - but this is making the assumption that the pop rates are 1 in 6 each kill.

Earlier this year I donated 20 Unfettered Deliriums to the Guild of Vampires. The aim was to see how many Maniacal Tendencies we could make from them and use them as prizes for guild quests. The pop rate for them is lower than for good aligned scales. In the end we managed to get 2 MT's out of 20. My guess for the pop rate from experience would be either 1 in 20 or 1 in 10. Again using an individual binomial distribution table to guess how many Maniacal Tendencies we should have popped gives different probabilities.

Using 1 in 20 gives:

• 0 MT's - 0.358
• 1 MT's - 0.377
• 2 MT's - 0.189
• 3 MT's - 0.060
• 4 MT's - 0.013
• 5 MT's - 0.002

While 1 in 10 gives:

• 0 MT's - 0.122
• 1 MT's - 0.270
• 2 MT's - 0.285
• 3 MT's - 0.190
• 4 MT's - 0.090
• 5 MT's - 0.032

The question is which is more likely to result in popping 2 MT's out of 20 attempts? Hard to tell - might need to try and make some more.