Guild Wars 2: How Many Days of Beetle Racing Does It Take?

I wanted to post this yesterday but... whelp. When writing an introduction talking about the difficulty of each race and their rank in difficulty I noticed it getting big real-time. Thus I decided to split it into two posts with the first one - the introduction - talking about the difficulty and their ranks and this one to actually be about how long it takes now.

Why Going Through The Racing?

Is it to win the car? To win some hardware from ArenaNet? No. Not at all. We're doing it for the completionist in us. We're getting all the novelties and skins! Okay, now, what do we need to do?

The races reward us with a new currency called Racing Medallions. This is only the case for the six new races to my knowledge. With these Racing Medallions, you can buy stuff from a prize NPC that's standing next to the time challenges or race start points. This means we need to get those medallions.

This raises the question.

How Do We Get Racing Medallions?

After actually looking at how many I get for once I noticed the following pattern. Doing the daily achievements rewards you five for every single daily and ten for the meta-achievement. So that's 

3 * 5 + 10 = 25 already. Each racing event gives you three. This means doing the daily rewards you with at least an additional nine. Additionally, there's the time trial or racing adventures. These have a bronze, silver and gold chest that each reward a different amount of Racing Medallions. Also, there's a different type of chest with the same name awarded at the practice run in Kessex Hills. Here's the result from them:

• Gold Chest (without Kessex Hills) - 5
• Silver Chest (without Kessex Hills) - 3
• Bronze Chest (without Kessex Hills) - 2
• Any Kessex Hills chest - 1

Summing it all up we have (5 * 5) + (5 * 3) + (5 * 2) + (3 * 1) =  53 in total. Why? We've got five races that award a gold chest that contains five, a silver chest that contains three and a bronze chest that contains two. Additionally, we have the Kessex Hills racing chests that award one for gold, silver, and bronze. Now if we take the difficulty into account and you only go for one try daily then anything at the level of Mount Maelstrom and higher is out of the question for the gold chest. Now we're going with (2 * 5) + (5 * 3) + (5 * 2) + (3 * 1) =  38. Cool and all, but...

How Many Do We Need?

There are multiple items that we can buy...

Item name	Cost	Skin	Item name	Cost
Mini Roller Beetle	150		Endless Mystery Fanciful-Cat Tonic	250
Racing Goggles (Heavy)	150	Racing Goggles	Endless Mystery House-Cat Tonic	250
Racing Goggles (Light)	150	Racing Goggles	Endless Mystery Dog Tonic	275
Racing Goggles (Medium)	150	Racing Goggles	Endless Mystery Choya Tonic	300
Racing Helmet (Heavy)	150	Racing Helmet	Endless Mystery Bear Tonic	325
Racing Helmet (Light)	150	Racing Helmet	Endless Mystery Fowl Tonic	350
Racing Helmet (Medium)	150	Racing Helmet

To sum it up we need to be careful with the helmet and goggles as those share the same skin. That means we only need to buy one of those. With that in mind, we get a total cost of:

150 + 150 + 150 + 250 + 250 + 275 + 300 + 325 + 350 = 2200

With that, we have everything we need to answer the question.

How Many Days Does It Take?

If we do all dailies and each race on gold once a day we get 53 + 9 + 25 = 87 Racing Medallions each day. This means getting our 2200 Medallions takes 2200 / 87 = 25.29 or rather 26 days.

Now if we do our daily but only the daily races and time trials of those we miss out on two gold chests, two silver, chests, two bronze chest, and the Kessex Hills chests. This means we miss out on 

(2 * 5) + (2 * 3) + (2 * 2) + 3 = 23 medallions. In this case, we only get 87 - 23 = 64. Hence it will take 2200 / 64 = 34.375 or 35 days.

Assuming we don't want to wait for the races and just do the daily time trials we need 

2200 / 53 = 41.51 or 42 days.

Well, let's say we can't do gold on Mount Maelstrom, Brisban Wildlands, and Snowden Rifts...

Doing all dailies and each race once a day we get 38 + 9 + 25 = 72 Racing Medallions. With this, it will take us 2200 / 72 = 30.56 or 31 days.

Only doing the daily and the time trial of the respective races will let us miss out on two gold chests. But there's only a 1/5 and a 1/5 chance for that to happen. So we have a 1/5 * 1/5 = 1/25 chance to miss two gold chests and a 1/5 chance to miss one. With each gold chest being 5 medallions. On average we will lose 1/5 * (1 * 5) + 1/25 * (2 * 5) + (2 * 3) + (2 * 2) + 3 = 14.4 medallions. That means on average we will get 87 - 14.4 = 72.6 Racing Medallions. With this amount it will take 2200 / 72.6 = 30.30 or 31 days.

Okay, almost done... if we only do the time trials we need 2200 / 38 = 57.89 or rather 58 days.

Last but not least.. if we only do the daily events without the time trials (not recommended). It will take a whopping 2200 / 36 = 61.11 or more like 62 days.

Efficiency Is The Best!

And to make it even easier for you here's a trick. If a race event is starting, say you participate in it and wait for it to begin, or talk to the NPC to participate if it already has started and then start the time trial. This way you will do both the event and time trial at the same time, reaping the rewards of the time trial after the first round and the event rewards at the end. This way you don't need to do the race twice. This does not work perfectly on each map though, however, there's no special reward for being first in the goal in the race event, nor for second or third place. Thus, who cares about the place as long as you finish the event with gold.

A Little Addition

Assuming you only do the same race event over and over it will require you to do 2200 / 3 = 733.33 or 734 times the same race event. With the events taking place about every 15 minutes and a start timer of about 5 minutes it takes 20 * 733 = 14660 minutes without taking the actual race into consideration. That's 14660 / 60 = 244.33 hours which is 244.33 / 24 = 10.18 days or 11 days.

If you do this please blog or vlog the whole ordeal.

Magick Aptitude Test

So I've been thinking about the research I wanted to do on the One For All and energy control. To keep it short: If I really can control my energy and it works like One For All from Boku no Hero Akademia, I should be able to do a sprint in a shorter period in comparison. However, as I mentioned in the respective post this takes quite some time even if I keep it short and the results may not even be worth it so to say. However, I came up with another extremely simple test that takes a lot less time for every single execution but may take longer in the long run.

The Idea

If you read the magick oriented posts you should know this already but let's go into the details anyways. I remember from reading almost a year ago, Vrater V. D. wrote in the book "Schule der Hohen Magie" (approx. in engl.: school of high magic), that magic changes the chances of an occurrence by will. The example taken in the book assumes you want a meteor to hit exactly where you perform the ritual. The chance of a meteor hitting the earth, even more, hitting the earth exactly at this place is extremely low. Yet, using magic this chance can be increased.

I'm Not Planning on Suicide

Now, I'm not going to make that happen, I'm not planning on dying yet and I have no fun in having meteors crush down into the earth, even worse my home. The meteor thingy is just an example. I'm planning on something less dangerous that still can be extremely infuriating. I'm talking about dice. If you paid attention during the class in math - if you had stochastic... - you will know that dice has the same chance to land on each side. (Of course, this assumes a perfect dice, if you have one with holes in it or worse, numbers on it this might affect the balance, additionally damage done to it will also influence this). With every occurrence having the same chance this is called a Laplace experiment, by the way.

Throwing a Dice and Magic; How Is This Related?

If you combine both concepts explained in the paragraphs you may come upon this theory:

If throwing a dice infinitely results in each side showing up at the top equally often, this means that when using magick to influence the chances regardless of how often you throw it will occur more often. Even better, the higher the chance diverges the stronger the actor's aptitude to magic should be. At least that's the idea or concept behind.

Live/Life Research

I'm actually planning on posting all my ongoing research on my blog in the projects category under research. This project will listen there soon too probably. I mean the pure idea of this is ridiculous. You will need tons of dice throws for it to ever reach an equal distribution and secondly I doubt that my own magical power is strong enough to influence the chances so much that it's outside of the error margin.

Well, I guess we'll see.

WildStar: Proc Chance of Prime Drops Result Update

This was a bad idea and I'm kinda running out of time to write this post so here we go in three, two, one...

Recap

So you might or might not remember that I was wondering about the proc rate of items in prime expeditions, or any prime content for that matter, in WildStar. So to check whether or not the myth of it being 25% is correct I started my drop research. Of course, starting off the sample size is small so the values are anything but accurate. I've now continued for another week to get more samples and that's why I'm here now.

Research State

So the current state is almost as I planned it. My goal was to reach a total of 100 samples. I've... reached 96 samples. I know, I know, 100 samples are still like nothing. However, it's at least a number I have proof of and that's something that matters to me. Well without further ado let's look up my old research and start the comparison! That's something I haven't done yet on my blog.

So back in my first research, I had

• 44 samples
• 35 without a proc
• 5 with only one proc
• 4 with a double proc

The current state is 

• 96 samples
• 68 without a proc
• 19 with only one proc
• 8 with double proc
• 1 with quadruple proc

Calculating the Chances

It's nice looking at those numbers but we want to see chances so let's go calculate the chances. The only interesting values are how many items of these samples had at least one proc and how many didn't.

In our first example it were 4 + 5 = 9 items so 9 / 44 = 0.204545 or 20.45%.

Currently we've got 19 + 8 + 1 = 28 items with at least one proc from 96 samples so 28 / 96 = 0.2917 or 29.17%.

As you can see our proc rate jumped by about 8.7% and is now far above the 25% people believe it to be. Well with only 96 samples the number still fluctuates a lot.

Concept of Checking

We use math to check if everything went as it's supposed to be and whether or not we've made mistakes. We can use this checking to see if our number is accurate and how far it might be off.

If we assume to have a 25% chance to proc an item and the chance does not change, additionally we can proc an item multiple times, it's safe to say that our chance to get two procs is the chance for the proc to occur and then the same chance again. This means our chances in this scenario are the following:

The chance for no proc: 75%

Chance to proc: 25%

Chance for two procs: 25% * 25% = 6.25%

Chance for three procs: 25% * 25% * 25% = 1.5625%

Chance for four procs: 25% * 25% * 25% * 25% = 0.390625%

and so on. This means if we calculate the chance on how many items at least proc'd twice the chance we get here must equal the chance for one proc multiplied by itself. We can continue this throughout all our occasions. You can call this forward checking.

In our example: 

25% * 25% should equal 6.25%. If not our check fails. If it does, perfect.

Well obviously if I'm naming this "forward checking" there must be another type of checking. Not hard to guess, the opposite I'll call it backward checking. Backward checking works by doing what we just did backward. We take the chance of for example two procs and divide it through the chance to proc at least once. The result should be the lower value.

In our example:

6.25% / 25% should equal 25%. If not our check fails. If it does, perfect.

Forward Check

So let's apply this forward check to our newest numbers.

Our chance for one proc is 29.17%. So the chance for two procs should be 29.17% * 29.17% = 8.51%. So let's check out what the chance actually is. We got nine items that have at least a double procs from 96 samples, that's a chance of 9 / 96 = 0.09375 or 9.375%. So as you can see our chance for double procs isn't too far off from the chance for only one proc. Of course with our sample size, this could just be a coincidence.

We can do the same with the quadruple proc. The chance for this one should be our chance for at least one proc multiplied by itself four times.

29.17% * 29.17% * 29.17% * 29.17% = 0.7240%

With us having only one such proc from 96 samples that's a chance of 1 / 96 = 0.0104 or 1.04%. This one is a bit too high. Now let's do the other check.

Backward Check

Without chance being 9.375% for at least a double proc if we divide this through our chance of at least getting one proc the result should be the same chance we divide through. If not our numbers are still off of what they should be. It's important for them to match up but more to this later.

9.375% / 29.17% = 32.14%

Now that's off by about 3%.

Conclusion

So as you can see all our checks failed forward and backward. This was to be expected though. A sample size of 96 is still not enough. So what do these checks tell us? If the numbers don't match up we can assume one of two things.

• The system does not work as we assumed (the chances change)
• Our chances are off, wrong or incorrect

So what went wrong? In our first forward check, the chance we've calculated was 8.51% but we got 9.375%. This means we've gotten more at least two times procs than we were supposed to if we assume the at least one proc chance of 29.17% to be correct. Same with our second forward check. We've got more quadruple procs than our proc chance of 29.17% for at least one proc allowed. So we can say 29.17% is wrong. So what must change for our number to get accurate? We need to get either

• less at least double procs
• more at least one procs and more without any proc

Our backward check more or less tells the same. The resulting chance from our calculation is slightly higher. This is the result of our at least double proc being too high or our at least one proc being too low.

So what can we take from this? The research kicks us in the face with a "keep on researching".

and with this, I'll leave for now. If I make another post on this it's most likely going to be a test of significance.

Diablo III: Primal Ancient Hellfire Chance

Correction Statement
So apparently the drop rate of primal ancients isn't 10% of the ancient rate as I picked up back when it came out. Additionally, the attributes or stats that are rolled for items aren't evenly distributed. Both these facts render the used variables and parameters of the calculation to being false. Since the amount of work to correct everything is higher than I'd like I'll leave this post as a 'what if' kind of post. I might pick up the topic again later someday using the data that was posted on Reddit. Thanks to everyone. 

I've always been a fan of mage classes. In Diablo III, however, I play a demon hunter. It's weird but the demon hunter is a lot more fun in my opinion. Especially the multishot build with the unhallowed essence set. Though there is a really annoying thing.

The Hellfire Amulet

Hellfire amulets, oh sorry, The Hellfire Amulet is a special item that can only be crafted. Being able to craft it requires you to buy a recipe from the Squirt. It doesn't stop there though, obviously, we need the crafting materials as well. The materials for this craftsmanship drop from the uber bosses. To fight the uber bosses you have to get the infernal machines from the keywardens and use them in the heretic's abode in Tristam in Act I. So we have to defeat the keywardens in Act I to Act IV, kill the uber bosses and then we can basically craft the hellfire amulet.

RNG

Unfortunately forging this hellfire amulet may or may not be in vain. The unique property of this item is that it gives you one of your class's passive abilities. Usually, you're limited to four passive abilities but thanks to the amulet you can have five. This is also the reason why it's so interesting for certain classes. Well as you may notice you'll want an amulet that has rolled one of those five passive abilities you want to take with you.

So let's check out our chances to get what we want. When we craft a hellfire amulet we get a hellfire amulet with 100% certainty. So the first limiting factor will be passive. There are 19 different passive abilities, the amulet has only one of these and 5 are okay. So the chance to get one of these five we want is 5 / 19 = 0.2632, 26.32%. Well, that sounds... doable.

Once we have our hellfire amulet for a while over time we start to build on ancient pieces. At some point you also want your hellfire to be an ancient item. So let's see what the chance is for us to get our passive and an ancient hellfire amulet. The chance for a legendary item to roll ancient is 10%. So we want two chances to hit at the same time. We can use stochastic to calculate this further.

A = "Chance to get our passive" P(A) = 0.2632

B = "Chance for it to be ancient" P(B) = 0.1

We want both at the same time so:

 P(A and B) = P(A) * P(B) = 0.2632 * 0.1 = 0.0263 = 2.63%

Our chances just dropped drastically.

Unfortunately, this is not the end.. I'm sorry but.. there's still the chance for it to be primal ancient. Primal ancient items are the creme de la creme, they always roll top value on all stats. However, there are two limiting factors for getting these.

1. We need to have done a greater rift 70 or higher solo
2. They have a drop chance of 0.01 or 1%

Well if we go with the odds our chance change from 2.63% to 0.2632 * 0.01 = 0.0026 or 0.26%

Still Not Done!

Even if we get a primal ancient item, it may have stats we don't want. We can only switch one stat but if we roll badly twice it'll look bad. Luckily there isn't much to roll around. There are five attributes on it aside from the passive ability. Two of these attributes are fixed. It will always have a socket, which we need and it will always have the main stat, for demon hunters its dexterity, that we choose when crafting. This means we have two of five variables we don't need to worry about. Leftover is the three others from which two are primary and one is secondary. Which stat combination is the best, of course, depends on your current stats, most often you will see amulets rolled with critical hit chance and critical hit damage as primary stats though. The secondary effect is your personal preference, never the less I'd assume reduced damage from ranged attacks would most likely be the best. To determine the chance we need to know how many options we want and how many options are available. For our secondary stats, there are 15 different attributes and we want one of those. So the chance to get this is 1 / 15 = 0.0667, 6.67%. For our primary attributes, we have each 16 available and we want two, however, once we got one of these our chance changes. This means our first primary attribute roll has a 2 / 16 = 0.125, 12.5% chance to be successful and our second one has a 1 / 15 = 0.0667, 6.67% chance to be successful.

For our perfect roll we want all possibilities to happen at the same time. Multiplying them we get:

0.2632 * 0.01 * 0.0667 * 0.125 * 0.0667 = 1.4637 * 10^-6, 0.0000014637 or 0.00014637%.

No Worries! We Still Have Rerolls

We can reroll one of the stats. One and only one. This means our chances improve! If we assume one of our primary attributes rolls successful and one doesn't we have a 2 / 16 = 0.125, 12.5% chance to get the successful one and our 1 / 15 = 0.0667, 6.67% chance for the other fails yet our secondary attribute succeeds with a 1 / 15 = 0.0667, 6.67% chance. So we have a 2 / 16 * 1 / 15 = 0.0083, 0.83% chance for this to be the case. If both our primary attributes roll successfully we have a 2 / 16 * 1 / 15 = 0.0083, 0.83% chance for this to occur. Adding both calculations together we get 2 / 16 * 1 / 15 * 2 = 0.0167, 1.67% . Now since we want a primal ancient item with the correct passive we do the following calculation:

0.2632 * 0.01 * 2 / 16 * 1 / 15 * 2 = 4.3867 * 10^-5, 0.000043867 or 0.0043867%

One Day

Don't worry if you won't be able to farm it this season, someday you'll have this on your account, forever, next to your 10000 paragon levels.

Guild Wars 2: Magic-Warped Bundle - Worth

I did a post on the Magic-Warped Packets. It was bound to happen that I'm going to make a post about the Magic-Warped Bundles. And yes, I know by now that people say the new volatile magic is better but hey! I have my infinite unbound magic tools and I like my farming route through Bitterfrost!

What's the Difference?

So what makes these Magic-Warped Bundles different from the Packets? Well, they are more expensive. Logically more expensive things must come out? That's actually true. The bundles include rare items like lodestones, tier six materials, and unique upgrades. In total 30 different items can be collected via these bundles.

These items include:

10 ancient bones 10 armored scales 10 elaborate totems 10 karka shells 10 piles of crystalline dust 10 powerful venom sacs 10 pristine toxic spore samples 10 vials of powerful blood 10 vicious claws 10 vicious fangs

2 charged lodestones 2 crystal lodestones 2 destroyer lodestones 2 evergreen lodestones 2 glacial lodestones 2 molten lodestones 2 Mordrem lodestones 2 onyx lodestones 2 mystic clover

1 amalgamated gemstone 1 black diamond 1 ebony orb 1 flax blossom 1 freshwater pearl 1 giant eye 1 maguuma burl 1 maguuma lily 1 moonstone orb 5 globs of ectoplasm

To recap more expensive and different loot. Actually checking the prices the value is more distributed than with the Magic-Warped Packets.

Drop Research

I did some drop research of my own and got 640 samples. Back when I checked it was more than on wiki now it's the opposite around. The wiki now has 7764 samples. Out of curiosity, I'm still going to compare my results with the wiki results but I'll use the wiki results for the calculation later on.

Of course, the calculation is the same as usual. We open X samples or bundles and see how often the item type comes out. Then we're dividing the number of occurrences through the number of samples. Keep in mind the actual amount that comes out does not matter we want the item type. That means 10 ancient bones are not handled as 10 but as one. This is also the reason why we have to divide the amount that has dropped in the wiki research through the amount we get. In our ancient bones example, the wiki notes a drop amount of 3620 from 7764 bundles. However, 10 ancient bones dropped only 3620 / 10 = 362 times from those 7764 bundles. So in the end, we calculate
totalAmount / droppedStackSize / bundles = dropRate or in our example 3620 / 10 / 7764 = 0.0466. That's 4.66%. Doing this for every single item we get the following table.

Item My drop rate Wiki drop rate 10 ancient bones 2.97% 4.66% 10 armored scales 4.69% 4.31% 10 elaborate totems 6.41% 4.97% 10 karka shells 6.09% 4.73% 10 piles of crystalline dust 5.16% 4.70% 10 powerful venom sacs 3.44% 4.52% 10 pristine toxic spore samples 4.69% 4.50% 10 vials of powerful blood 4.22% 4.81% 10 vicious claws 3.13% 4.78% 10 vicious fangs 4.53% 4.39% 1 black diamond 1.72% 1.30% 1 flax blossom 0.94% 1.52% 1 giant eye 2.81% 1.39% 1 maguuma lily 1.56% 1.34% 5 globs of ectoplasm 4.53% 4.24%

Item My drop rate Wiki drop rate 2 charged lodestones 2.66% 2.61% 2 crystal lodestones 4.53% 3.05% 2 destroyer lodestones 2.66% 2.77% 2 evergreen lodestones 2.81% 3.08% 2 glacial lodestones 7.34% 6.16% 2 molten lodestones 3.13% 2.77% 2 mordrem lodestones 3.13% 3.14% 2 onyx lodestones 2.97% 3.13% 2 mystic clover 1.72% 1.87% 1 amalgamated gemstone 2.66% 3.98% 1 ebony orb 1.09% 1.64% 1 freshwater pearl 1.25% 1.52% 1 maguuma burl 1.25% 1.58% moonstone orb 1.09% 1.65%

Something you notice when comparing the numbers is that the data from the wiki is more evenly distributed and fluctuates less between the drops.

Calculating the Value

Determining the worth we need to look at each item type that can drop from the bundle. Here we're looking at the whole stack we get. So if we get ten tier six materials we got ten times the price of one. Additionally selling items on the trading post costs a fee of 5% for placing the item into the trading post and 10% for the transaction. So what we're calculating is the value the item has in the market - I'm going to use the selling price instead of the buy price since it's higher and materials always sell good - minus the trading post fee of 15% and then multiply this with the amount we get. In the example of ancient bones, it has a selling price of  2571 copper the fee is 377.4 copper. So we get 2571 - 377 = 2193.6. Multiplying it with the amount we get 2194 * 10 = 21936 copper or 2 gold 19 silver and 36 copper. You may notice that I'm rounding the numbers. This is what the trading post does as well.

Item Single value TP fee After fee Total value 10 ancient bones 2571 386 2185 21850 10 armored scales 2605 391 2214 22140 10 elaborate totems 2845 427 2418 24180 10 karka shells 1009 151 858 8580 10 piles of crystalline dust 1143 171 974 9740 10 powerful venom sacs 2510 377 2133 21330 10 pristine toxic spore samples 380 57 323 3230 10 vials of powerful blood 3300 495 2805 28050 10 vicious claws 2589 388 2201 22010 10 vicious fangs 2600 390 2210 22100 1 black diamond 7399 1110 6289 6289 1 flax blossom 2129 319 1810 1810 1 giant eye 2101 315 1786 1786 1 maguuma lily 84991 12749 72242 72242 5 globs of ectoplasm 2006 301 1705 8525

Item Single value TP fee After fee Total value 2 charged lodestones 11886 1783 10103 20206 2 crystal lodestones 5692 854 4838 9676 2 destroyer lodestones 5767 865 4902 9804 2 evergreen lodestones 10839 1626 9213 18426 2 glacial lodestones 3807 571 3236 6472 2 molten lodestones 5099 765 4334 8668 2 mordrem lodestones 148 22 126 252 2 onyx lodestones 6395 959 5436 10872 2 mystic clover 640 - 640 1280 1 amalgamated gemstone 18311 2747 15564 15564 1 ebony orb 2556 383 2173 2173 1 freshwater pearl 65407 9811 55596 55596 1 maguuma burl 2210 332 1878 1878 1 moonstone orb 1972 296 1676 1676

Notice that I calculate the mystic clover by their vendor value. To determine the value of mystic clover that's quite a bit harder so we're going with this. This also assumes that you don't want or don't need mystic clovers! Anyways with the whole table filled up and all the values in copper known we can start to calculate the actual worth of our bundle.

Calculating the Worth

To do this we simply say that each valued drop has a certain relevance. The relevance is the weight of how much it plays a role in our worth. This weight is the chance for the respective item stack to drop. Thus we're going, to sum up, all our total values multiplied by their specific drop chances from the first table. The end result will be the worth of our magic-warped bundles.

21850 * 4.66% + 22140 * 4.31% + 24180 * 4.97% + 8580 * 4.73% + 9740 * 4.70% + 21330 * 4.52% + 3230 * 4.5% + 28050 * 4.81% + 22010 * 4.78% + 22100 * 4.39% + 6289 * 1.30% + 1810 * 1.52% + 1786 * 1.39% + 72242 * 1.34% + 8525 * 4.24% + 1280 * 1.87% + 20206 * 2.61% + 9676 * 3.05% + 9804 * 2.77% + 18426 * 3.08% + 6472 * 6.16% + 8668 * 2.77% + 252 * 3.14% + 10872 * 3.13% + 15564 * 3.98% + 2173 * 1.64% + 55596 * 1.52% + 1878 * 1.58% + 1676 * 1.65% = 14212.32

The percentages need to match the prices of the same item or else it may result in errors or deviations from the result we want.

So now we know that we can expect to get 1 gold 42 silver and 12 copper when selling the materials we get from the bundle. The buying price is either 1 gold and 500 unbound magic or 40 silver and 1250 unbound magic. If we're only looking at our gold we would make 14212 - 10000 = 4212 copper buying the expensive one and 14212 - 4000 = 10212 copper buying the cheaper one. So we have a plus of either 42 silver and 12 copper or 1 gold 2 silver and 12 copper by paying another 750 unbound magic.

What Now, Captain?

Next, we can compare bundles and packets! If anyone cares.. but now in this post. These posts get big enough and very time-consuming. Of course, I could leave all those tables away and focus on the calculation... hmm I don't know.

WildStar: Proc Chance in Primals [On-Going]

I've been wondering about the proc chance or chance of items to drop with a higher item level before and asked friends what the proc chance is. Some mentioned that someone tested it on the PTR (public test realm) and shared their results on the Reddit or forum but I couldn't make that data show up. The others said a death mentioned the chance as an example chance. So I guess it's up to myself to test it myself.

Checking Drop Rates

Loot tables, drop rates, etc. are really tedious to check. The reason these things are so tedious is if you have no vendor or alternative to get the drops you need to farm. This means repeating the same content over and over again to check every single instance of the drop.

Calculating the chance of something to happen works via stochastic. We divide the number of instances or cases through the number of all possibilities. So if we say our item dropped three times and we ran the content 25 times we have a chance of 3 / 25 = 0.12, 12% to get that item.

However, what we want is the rate of procs. For this, we're going to assume a few rules that may or may not be given.

1. The proc chance will always be the same
2. Items can proc several times
3. There's a limit to the procs 

The limit is determined by the base item level. Each proc increases the item level by five. The maximum item level is 170. So that means a prime level 0 item, which has an item level of 65 can proc (170 - 65) / 5 = 21 times.

To get the proc chance we're gonna ignore any multi procs for now and just look at any item that procs at least once. We divide this number through the number of items we've gotten in total. The counter chance is the chance to get an item that has no proc, as in an item that has the base item level.

To correct errors and check the values, a double proc must have the chance of the single proc chance multiplied by itself. Vice versa, the double proc divided by the single proc chance must result in the single proc chance.

Gathering Samples

To gather the samples we need to run easy and fast content. It would be even better if we do the same content with the same circumstances to prevent from getting unwanted values in. The fastest prime content is prime level 0. One of my favorite instances to get through fast is the expedition infestation. My runs were around five to six minutes. So I've been running through this expedition in the past days and trying to get a small number of samples:

• 44 items in total
• 35 without a proc
• 5 with only one proc
• 4 with double proc

Knowing this we also know the number of items that have at least one proc is 5 + 4 = 9. We can already calculate the chance of getting an item that has no proc. To do this we divide the number of items without proc through the total amount of items.

P("no proc") = 35 / 44 = 0.7954, 79.54%

We can easily calculate the other ones as well:

P("only one proc") = 5 / 44 = 0.1136, 11.36%

P("only double proc") = 4 / 44 = 0.0909, 9.09%

Though these are only nice to know.

The actual chance that would be relevant is how often we get a proc. There are three ways to calculate this.

P("at least one proc") = 1 - P("no proc") = 1  - 0.7954 = 0.2046, 20.46%

P("at least one proc") = P("only one proc") + P("only double proc") = 0.1136 + 0.0909 = 0.2045, 20.45%

P("at least one proc") = (5 + 4) / 44 = 9 / 44 = 0.2045, 20.45%

Running our checks.

Applying our rules:

P("at least one proc") * P("at least one proc") = P("at least two procs")

Since we had no proc above two we can take P("only double proc") which is 0.0909. Filling everything in we get 0.2045 * 0.2045 = 0.0909, 9.09%. Calculating it gives us 0.2045 * 0.2045 = 0.0418, 4.18%. If we're assuming the rules we've created apply, these numbers will draw nearer.

If we reverse calculate from the double proc to the single proc we divide the double proc through the single proc. Keep in mind:

P("at least two procs") / P("at least one proc") = P("at least one proc")

The actual P("at least two procs") we have is 0.0909. So if we calculate 0.0909 / 0.2045 = 0.4445 we'll get 44.45%. Again the numbers 0.2045 or 20.45% and 0.4445 or 44.45% will draw closer to each other. So we could assume the drop chance may be between 20.45% and 44.45% at this point.

The Myth

I heard the drop chance was 25%. If we assume 20.45% and 44.45% draw closer equally we can find the middle by taking the difference and subtracting half of the difference form the higher value. 

44.45% - 20.45% = 24%

24% / 2 = 12%

44.45% - 12% = 32.45%

This is just an estimate that might not be accurate at all.

On-Going

The sample size we have consists of 44 items which means there are going to be huge fluctuations in percentages for each new item we get. To be certain we need to keep on collecting data until we have enough so that the fluctuations are low enough and the difference in our checks is small enough. Most optimal would be a fluctuation lower than 0.0001 since we've rounded up to 0.01%.

Bottom Line

I'm gonna continue my research and make a new post on this next week since I had this topic planned twice accidentally. Whelp :P If you have the information somewhere I'd be glad if it's shared. Well... I'm off to get more samples now evening or night. :P

Guild Wars 2: Magic-Warped Packet - Worth It?

Back in the old days (Living World Season 3) many people were skeptical. I looked up what dropped from them and I was hooked. They drop an interesting bunch of materials, they can't be that bad, can they?

Magic-Warped Packet

These bag items include a handful of different materials and can be bought for different prices at the vendors in the Living World Season 3 areas. (Bloodstone Fen, Ember Bay, Bitterfrost Frontier, Lake Doric, Draconis Mons, and Siren's Landing) The prices for this one are always 50 silver and 250 unbound magic. So let's see what we get from it.

We have a chance to get one of these:

10 copper ore 10 iron ore 10 silver ore 10 gold ore 10 platinum ore 10 mithril ore 5 orichalcum ore	10 green wood log 10 soft wood log 10 seasoned wood log 10 hard wood log 10 elder wood log 5 ancient wood log	10 jute scrap 10 wool scrap 10 cotton scrap 10 linen scrap 10 silk scrap 5 gossamer scrap
10 rawhide leather section 10 thin leather section 10 coarse leather section 10 rugged leather section 10 thick leather section 5 hardened leather	1 deldrimor steel ingot 1 bolt of damask 1 spiritwood plank 1 elonian leather square 1 mystic clover

Now to determine whether or not these packets are worth it, we need to know how much the content is worth. This should be no problem we can check it out in the trading post or via the API. Since we can simply look at the prices let's wait with actual numbers until we start our calculation, since the prices may change while we're going throughout our theorycrafting.

Drop Research

We can't expect the packet to drop all of those items we've listed at the same time. Especially since that's not the case. We only get one of the items listed above. The question here is what is the chance to get each of them. We could assume the chance to be equal for every. Though making some research is better. So how does the research work? It's quite simple to believe me. It's done straight forward:

• buy packets
• open them
• look what comes out
• take notes

So if we say we open 50 packets and from these, we get 30 times the iron ore, we say the chance to get the iron or is 30 / 50 = 0.6, 60%. We continue this for each item to get our drop rates.
Back when the magic-warped packets and bundles first came out I started to make this research once I've bought everything I wanted for the unbound magic. By now the Guild Wars 2 wiki has some drop research too.

So let's compare the drop research from me to the one from the Guild Wars 2 wiki. For that, we need to convert the Guild Wars 2 wiki numbers into a drop chance. This is done by checking the drop research and dividing the drops through the total containers. Copper ore, for example, they got 20 copper from 195 containers during the writing of this post. Though you get 10 coppers instead of 1 so they had two 10 copper ore drops, which means it has a drop chance of 2 / 195 = 0.0103 or 1.03%.

On a side note. My research opened 375, theirs is 195. Assuming neither had any errors or false entries my research should be more accurate since I had more trials or more data.

Drop GreenyNeko GW2 Wiki 10 copper ore 0.80% 1.03% 10 iron ore 6.67% 7.69% 10 silver ore 1.60% 2.05% 10 gold ore 1.60% 1.54% 10 platinum ore 4.27% 2.56% 10 mithril ore 4.80% 3.08% 5 orichalcum ore 1.87% 2.56% 10 green wood log 2.67% 2.05% 10 soft wood log 2.93% 5.64% 10 seasoned wood log 6.93% 3.08% 10 hard wood log 5.33% 5.13% 10 elder wood log 3.73% 3.59% 5 ancient wood log 4.00% 7.69% 10 jute scrap 1.87% 3.08% 10 wool scrap 3.20% 2.56%

Drop GreenyNeko GW2 Wiki 10 cotton scrap 6.93% 6.67% 10 linen scrap 3.73% 4.62% 10 silk scrap 1.33% 1.03% 5 gossamer scrap 2.67% 1.03% 10 rawhide leather section 0.53% 3.08% 10 thin leather section 3.47% 5.13% 10 coarse leather section 5.60% 3.59% 10 rugged leather section 2.93% 3.59% 10 thick leather section 2.93% 3.08% 5 hardened leather 8.27% 4.62% 1 deldrimor steel ingot 2.93% 5.13% 1 bolt of damask 2.40% 1.54% 1 spiritwood plank 1.33% 4.10% 1 elonian leather square 2.67% 4.62% 1 mystic clover 0.00% 0.00%

Since the wiki only has 195 opened packets their research fluctuates much more than mine but you can see that here and there both numbers behave similarly. Of course, the drop chance is the same for every player so similarities are bound to happen.

So let's go with the research that has more data since it is more likely to be accurate and a small error or a small amount of false data doesn't affect a big data pool that much. Though you know.. never trust a statistic you didn't fake yourself so if you do not trust my data collection for yourself. Whether or not it's worth doing that.. we will find out now.

Determining the Value

We can use our drop research to determine the value of the packets. If you have a coin flip and you get $1 from heads and lose $1 from tails assuming both have a 50% chance to drop you have a 50% chance to get $1 and a 50% chance to lose one. So you could say with each turn you have a plus of 0.5 * $1 = $0.5 and a minus of 0.5 * $1 = $0.5. Summing it up you get +$0.5 and -$0.5 which equals zero. So on average, there is no win nor loss. This is the expected value. You could also say the chance of a case happening is the weight of the amount you get. A number with a higher chance or a higher rate of occurrence has more relevance to a higher weight.

With this defined we can now use the drop chances from our drop research as weights and multiply them with the value of the items themselves. Summing it all up we get the worth of a package. Then we can subtract the buy price and we get the plus. So let's do this. For the prices, I'm going through the current trading post prices using the instant sell. That means if you make sell orders it's you're getting more than written here.

Item	Drop Rate	Total Value in copper	Expected Value in copper
10 copper ore	0.80%	10 * 80 = 800	0.008 * 800 = 6.4
10 iron ore	6.67%	10 * 171 = 1710	0.0667 * 1710 = 114
10 silver ore	1.60%	10 * 6 = 60	0.016 * 60 = 0.96
10 gold ore	1.60%	10 * 31 = 310	0.016 * 310 = 4.96
10 platinum ore	4.27%	10 * 152 = 1520	0.0427 * 1520 = 64.90
10 mithril ore	4.80%	10 * 38 = 380	0.0480 * 380 = 18.24
5 orichalcum ore	1.87%	5 * 89 = 445	0.0187 * 445 = 8.32
10 green wood log	2.67%	10 * 14 = 140	0.0267 * 140 = 3.74
10 soft wood log	2.93%	10 * 56 = 560	0.0293 * 560 = 16.41
10 seasoned wood log	6.93%	10 * 147 = 1470	0.0693 * 1470 = 101.87
10 hard wood log	5.33%	10 * 95 = 950	0.0533 * 950 = 50.63
10 elder wood log	3.73%	10 * 142 = 1420	0.0373 * 1420 = 52.97
5 ancient wood log	4.00%	5 * 211 = 1055	0.04 * 1055 = 42.2
10 jute scrap	1.87%	10 * 81 = 810	0.0187 * 810 = 15.15
10 wool scrap	3.20%	10 * 278 = 2780	0.032 * 2780 = 88.96
10 cotton scrap	6.93%	10 * 91 = 910	0.0693 * 910 = 63.06
10 linen scrap	3.73%	10 * 278 = 2780	0.0373 * 2780 = 103.69
10 silk scrap	1.33%	10 * 33 = 330	0.0133 * 330 = 4.39
5 gossamer scrap	2.67%	5 * 12 = 60	0.0267 * 60 = 1.60
10 rawhide leather section	0.53%	10 * 75 = 750	0.0053 * 750 = 3.97
10 thin leather section	3.47%	10 * 272 = 2720	0.0347 * 2720 = 94.38
10 coarse leather section	5.60%	10 * 169 = 1690	0.056 * 1690 = 94.64
10 rugged leather section	2.93%	10 * 488 = 4880	0.0293 * 4880 = 142.98
10 thick leather section	2.93%	10 * 65 = 650	0.0293 * 650 = 19.04
5 hardened leather	8.27%	5 * 1245 = 6225	0.0827 * 6225 = 514.81
1 deldrimor steel ingot	2.93%	48069	0.0293 * 48069 = 1408.42
1 bolt of damask	2.40%	42103	0.024 * 42103 = 1010.47
1 spiritwood plank	1.33%	36573	0.0133 * 36573 = 486.42
1 elonian leather square	2.67%	76360	0.0267 * 76360 = 2038.81
1 mystic clover	0.00%	640*	0.0000 * 640 = 0

* this is the vendor sell price, economically the value of mystic clover depends on how important it is for you.

Now we have the expected value of each drop. Next, we need to sum it up to get the expected value of the packet.

6.4 + 114 + 0.96 + 4.96 + 64.90 + 18.24 + 8.32 + 3.74 + 16.41 + 101.87 + 50.63 + 52.97 + 42.2 + 15.15 + 88.96 + 63.06 + 103.69 + 4.39 + 1.6 + 3.97 + 94.38 + 94.64 + 142.98 + 19.04 + 514.81 + 1408.42 + 1010.47 + 486.42 + 2038.81 + 0 = 6576.39

So after all this calculation, we can say according to our research so far we can expect 65 silver and 76 copper for each magic-warped packet. Since they cost 50 silver we are left with a plus of 15 silver and 76 copper. This answers our question of whether or not they're worth it. Let's even go one step further.

BUT! Trading Post

Huge "but" and something I forgot myself. A fellow Reddit user was so kind as to remind me. Thanks to rude_asura. Selling items on the trading post costs a fee of 10% of the selling price. Listing items, or more like placing items into the trading post costs a fee of 5% of the selling price. So in total, we have to pay a fee of 15% of what we would get from selling the item. We could subtract that 15 %. However, we can just say we are left with 85% of the gold. This makes it easier to calculate it. So now we have to multiply every single number with 0.85 or instead we multiply our result the 6576.39 with 85%.

Selling all our items gives us 6576.39 * 0.85 = 5589.93 copper.

That means we expect to get 55 silver and 90 copper from every packet. Since they cost 50 silver we are left with a plus of 5 silver and 90 copper. So they're still worth it at the current market prices. Even if not much.

Value of Unbound Magic

If we say we make no plus on this item the rest of the money we get is the unbound magic part of the items price. Then we're saying 250 unbound magic equals those 25 silver and 76 copper. Doing this we can say one unbound magic has a value of 2576 / 250 = 10.304 copper. Though there might be better deals for unbound magic, so we should look at those first before claiming the unbound magic value to be 10.304 copper.

Picross - How Many Possibilities?

One of my favorite games back in the old days was Mario Picross. It introduced me to the Japanese Nonograms. A puzzle that requires you with the help of a few numbers as hints to fill out squares. In the end, the result will resemble a picture of something.

Here's an example of what it would look like:

				1	1
				1	1	1
			5	1	1	1	0
		4
		1
		3
		1
		4

And solved it looks like this:

				1	1
				1	1	1
			5	1	1	1	0
		4
		1
		3
		1
		4

As you can see this one is five times five in their size. In Mario Picross, there were three different sizes in Mario Picross: five times five, ten times ten and 15x15. Though you could technically make them any size.

The game features 256 puzzles in total but that's not all you can make. You can probably make a lot more puzzles. So...

Let's-A-Go!

Let's start with the smallest size. We have five times five, which results in 5 * 5 = 25 squares. Each square can be either filled or empty. So our first one would be to leave all empty. Our second bunch would be filling one square. We have 25 squares that could technically be filled so 25 possibilities here. Next up is filling the 25 squares with two. There are 2 out of 25 possibilities or C(25, 2) = 300 to fill it up. Our next case is filling the 25 squares with 3. This time it's 3 out of 25 possibilities or C(25, 3) = 2300. Now without going through each calculation you already notice something? The only difference is that we increase the X out of 25 or C(25, X). So we can just do this:

C(25, 0) + C(25, 1) + C(25, 2) + C(25, 3) + C(25, 4) + C(25, 5) + C(25, 6) + C(25, 7) + C(25, 8) + C(25, 9) + C(25, 10) + C(25, 11) + C(25, 12) + C(25, 13) + C(25, 14) + C(25, 15) + C(25, 16) + C(25, 17) + C(25, 18) + C(25, 19) + C(25, 20) + C(25, 21) + C(25, 22) + C(25, 23) + C(25, 24) + C(25, 25) = 33554432

or alternatively we can write it like this: 

25

Σ C(25, i) = 33554432

i = 0

However, having none of the squares filled is not a valid option. So we have to subtract one, which means 33554432 - 1 = 333554431 levels could be possible. That's.. extremely many. Unfortunately, many of these don't make much sense. Anyways that's how much we have for the size of five times five.

What About 10 Times 10?

We're definitely not going to iterate through 100. So let's see if we can find a different way to calculate it. Let's look at how they behave if the first number changes.

5

Σ C(5, i) = C(5, 0) + C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4) + C(5, 5) = 32

i = 0

6

Σ C(6, i) = C(6, 0) + C(6, 1) + C(6, 2) + C(6, 3) + C(6, 4) + C(6, 5) + C(6, 6) = 64
i = 0

That's interesting it doubled. It could be a coincidence though. Let's go through the list. 7 would be 128, 8 would be 256, 9 would be 512, 10 would be 1024. Let's try it with ten:

10

Σ C(10, i) = 1024
i = 0

Okay. 1024 that's 2^10 and 2^5 is 32. So the previous number we've calculated for a five times five field should be 2^25. Let's see: 2^25 = 33554432 and that's exactly the number we had before.

Makes sense. We have a chance for a field to be either filled or not filled. That means we have two states for each field. You can show these fields like a binary number. Using the example of a Picross or Nonogram I gave it would be 11110 10000 11100 10000 11110.

That's funny, this is basically how QR-codes work.

Calculating the Rest

Well since we know this now we can easily calculate the rest.

So for a ten times ten field we have: 2^(10 * 10) = 2^100 = 1.2676506 * 10^30 that's about one Nonillion (US) or one Quintillion. Though don't forget to subtract one, since an empty field would be an instant win.

And for 15 times 15 we get even more: 2^(15 * 15) = 2^225 = 5,391989333 * 10^67 that's over 53919 Vigintillion (US) or 53 Undecillion. Again don't forget to subtract one.

Those numbers...

The Best Part Last

There are Nonograms and Picross games or puzzles that even use colors. So each color adds a new set of possibilities, but it's easy to calculate that with what we know. We calculate two to the power of n, where n equals the number of squares we have. The two resembles the number of states a square can have. So far we only had filled or not filled. With different colors, we could say it could be either red, green, blue or black. So that's four states plus none of those. Five states total. So we would calculate five to the power of n, where n equals the number of squares we have. Our example with a 5x5 field would be:

5^(5 * 5) = 5^25 = 2.980232239*10^17 

That's 298 Quadrillion (US) or 298 Billiard instead of the previous 333554432 possibilities.

Guild Wars 2: PvP Season - How Many Matches?

The PvP Season ends in about two days. A bit late to make the post now. Luckily you know for the next season! But...

Why Should I Play the PvP Season?

Like the World vs World skirmish reward chests/tracks or however you want to call them, the PvP season also has season rewards next to the usual reward tracks. We've got 6 reward chests which reward Shards of Glory, Unidentified Dyes, Transmutation Charges, Silver and Gold as well as PvP League Tickets and Ascended Shards of Glory in each last chest per tier. Additionally the last 3 tiers (persimmon, amaranth, and Byzantium) reward Boxes of Grandmaster Marks, which contain the tokens required for ascended gear. Oh and the all beloved Llama Mini Choice Box from the last chest. The last chest is also repeatable with lower rewards.

Completing all the chests without repetition rewards you with:

• 560 Shards of Glory
• 34 Unidentified Dyes
• 83 gold 85 silver
• 44 Transmutation Charges
• 100 PvP League Tickets
• 400 Ascended Shards of Glory
• 3 Boxes of Grandmaster Marks
• 1 Llama Mini Choice Box

Alright, let's go! So...

What Does It Take?

To get through all the chests without repeating the last one it takes 670 pips. Pips are awarded for each match and differ depending on several factors like in WvW but a little bit different here. The factors are:

• Winning / Losing the match
• At least one top stat
• Close match
• Division

If you win a game you get ten pips if you lose you get three pips. Having at least one top stat awards an extra pip. If you lose the game but you were close to winning, you're awarded two extra pips. Also depending on which division you play in you may get two to four extra pips. That's two pips for platinum and four pips for legendary.

Simple Maths

Since we can't say whether or not we win the match or how the match will be going we need to calculate with a range assuming the worst and best-case scenario. Something we can do, however, is calculated for each division we play in.

For lower than platinum division we get three to eleven pips each match. Requiring to get 670 pips that means we need between 670 / 3 = 223.33 and 670 / 11 =  60.91 matches. So 61 to 224 matches.

Playing in the platinum division will earn you five to 13 pips each match. With the requirement of 670 pips in this division we need 670 / 5 = 134 to 670 / 13 = 51.54 matches. That's 52 to 134 matches.

As a player of the legendary division, the reward will be from seven to 15 pips each match. These players will still need 670 pips but only 670 / 7 = 95.71 to 670 / 15 = 44.67  matches. This is only 45 to 96 matches.

On the other hand, if we assume the 50-50 rule works as intended we expect to win 50% of our matches and losing the other 50% as it should be. Then we expect to get 3 * 50% + 10 * 50% = 6.5  pips each match without the extra pips. So between 6.5 on average. In the best case, we would get 1 extra pip always and 2 pips from the close one if we lose. So it's 6 * 50% + 11 * 50% = 8.5 pips now.

Going with this we have between 670 / 6.5 = 103.08 and 670 / 8.5 = 78.82 or 79 and 104 matches for players below platinum division.

For the platinum division itself, we just need to add 2 to both our numbers. That means we get 670 / 8.5 = 78.82 to 670 / 10.5 = 63.81 or 64 to 79 matches for players in the platinum division.

And last but not least we have the legendary division who now only need 670 / 10.5 = 63.81 to 670 / 12.5 = 53.6 so 54 to 64 matches.

What About Time Consumption?

Calculating the time consumption is kinda difficult as it differs from each time you play in. Though you can take the average duration of each match and multiply this with the number of matches you need, I want to keep that calculation for another post. If you want you can see this as homework and the next post as a solution to that homework, heh. :P

Daily Matches 

I always do similar calculations to this when a new season starts to check out how many daily matches I need to complete the season in the end. Same like I did with the Wintersday achievements. 

This season started on the 7th of November and ends on the 1st January according to the wiki or 2nd January according to my in-game PvP interface. That's 56 days. We know how many matches we need so let's go down the list:

Non-expected range lower than platinum:

61 / 56 = 1.09 to 224 / 56 = 4: win 1-2 matches a day or lose 4 matches a day

Non-expected range in the platinum division:

52 / 56 = 0.93 to 134 / 56 = 2.39: win 1 match almost every day or lose 3.

Non-expected range in the legendary division:

45 / 56 = 0.80 to 96 / 56 =  1.71: win 1 match or lose 2 matches a day.

Expected range lower than platinum:

 79 / 56 = 1.41 to 104 / 56 = 1.86: win up to 2 matches or lose up to 2 matches each day.

Expected range in the platinum division:

64 / 56 = 1.14 to 79 / 56 = 1.41: win 2 matches each day or lose 2 matches.

Expected range in the legendary division:

54 / 56 = 0.96 to 64 / 56 =  1.14: win 1 match or lose a little bit more than 1 match a day.

As you can see, a win a day is a safe way to get through the season.

Leveling: Tutorial or Part of the Game?

Ah yes, you start a new MMORPG and the first thing you'll have to do is level your ass up to the end game, what a great way to start off your game. No wonder some games scare people away. Sometimes the leveling goes too fast, sometimes it goes too slow, but why?

Leveling As Tutorial

Some might argue leveling is a tutorial. The problem with this statement is that leveling takes a lot of time in many games. Tutorials usually take a few seconds up to some minutes in other games and now you want to tell me these tutorials take days and up to or more than 40 hours? What am I supposed to learn? Well, I guess there's a lot in some MMORPGs. Let's check out what you can learn in WildStar.

WildStar Tutorial

WildStar has a tutorial but that hasn't gotten much to do with leveling. So let's just look at what you unlock when leveling.

There are 50 levels. The first two levels do not unlock anything with level 3 you get the looking for group-tool, Player vs Player, the skill tree basically and two new zones. Level 4 and 5 each unlock one new skill and another skill slot. Level 6 unlocks three skills of your alternative role (e.g. healer), your first instance and the first PvP instance, as well as two new maps. Level 7 gives you the 6th skill slot and two new abilities. Level 8 unlocks salvaging and another skill. Level 9 gives you 2 new abilities and a 7th skill slot. Level 10 unlocks crafting, two skills, the last skill slot and the first point for the skill tree and the first point for upgrading your skills. From here on out every level unlocks another point each. Level 12 gives you the ability to create guilds, the next instance, and two more skills. With level 14 we get two more skills, housing and two new areas including our main city. Level 15 gives us the ability to craft upgrades for our gear, the ability to upgrade our skills further and a new PvP and PvE instance. The next level unlocks just a new skill, followed by unlocking of another instance. Two more skills with level 18. With level 20 our skills can be upgraded even further, we get two more skills and access to a new PvE instance. New area and two more skills are unlocked with level 22. Two more skills with 24. 25 allow us to upgrade our skills further and we get two more PvE instances, followed by another instance at level 26. Now it takes a while until we unlock more upgrade possibilities for our gear as well as raising our skills further, two PvE instances, one PvP instance and a new map with level 30. 31: a new PvE instance. Now it takes until 35 to unlock another PvE instance and the ability to upgrade our skills further and a new map. With level 40 we get skilled riding, the ability to further improve our skills, three PvE instances and a new map. Level 45 gives us the ability to push our skills to the maximum and a new map. Another map with level 46. Two new maps with level 49. And we did it. Level 50 with PvP arenas, more PvE instances, raids,  improved riding, special quests (contracts) and some more maps.

Alright, that's a bunch. But as you might have seen some levels do not unlock anything but points for the skill tree. Nothing wrong with this, but for a tutorial hardly meaningful. However, there is a reason leveling may take this long. Let's look at the possibilities you have.

Build Possibilities

You start off with three skills and three skill slots. Only one possibility for your build. With level 4 and 5 we get each another slot and another skill. We have five skills and five skill slots now. With level 6 we unlock three skills. Now we have eight skills but only five skill slots. The number of combinations is now:

C(n,r) = C(8,5) = 8! / (5! * (8 - 5)!) = 56.

So with level 6 we already have 56 combinations. With level 7 we get a 6th slot and two new skills. We now have 10 skills and 6 skill slots.

C(n,r) = C(10,6) = 10! / (6! * (10 - 6)!) = 210

210 possibilities now. Of course, not every possible build is also useful or makes sense. Anyways the next change we have is at level 8 with another skill:

C(n,r) = C(11,6) = 11! / (6! * (11 -  6)!) = 462

To speed things up here's a list of levels and combinations:

• Level 10: C(15,8) = 6435
• Level 20: C(24,8) = 735471
• Level 30: C(28,8) = 3108105
• All abilities: C(32,8) = 10518300

This is only taking into account the skill bar. The skill tree and the ability points that can be spent on upgrading our skills allow for many more combinations. Especially since they go hand in hand with the combinations above.

Guild Wars 2 Tutorial

Like in WildStar the actual tutorial only consists of a small instance. The leveling here goes up to 80.

The level rewards can be found here: Guild Wars 2 Wiki: Level Rewards

In Guild Wars 2 it's even more complicated than in WildStar. We have a lot more combinations here. For example, you can wear a two-hand weapon or a one-hand weapon in the main hand and off-hand. Each weapon gives you class and weapon-specific skills. There are already several different combinations here and that's only the start. There is even more with the utility skills, heal skill and elite skills you get and you can combine one weapon set with another weapon set.

Well Sounds Like a Lot

And it is a lot and learning to use it all takes some time, but it might not take as long as the developers may have anticipated. In some cases like Guild Wars 2, the developers want people to test different builds and skills creating a higher leveling time but also having the time not to level too fast enjoying the area and beauty of the world.

Guild Wars 1 Tutorial

Anyone who has played Guild Wars 1 knows: Once you have reached the maximum level you're done with the tutorial. Now the real game starts. This tutorial only took a few minutes to a few hours. Nothing compared to the leveling nowadays. This is a fine example of how leveling as a tutorial works

Path of Exile Leveling

Path of Exile is an extreme opposite of this. Here the leveling doesn't stop even in the end game. At level 90 the continued leveling is extremely tedious and time-consuming. Especially since you lose the experience of your current level when dying. So it often happens that people don't reach the maximum level of 100 in a season.

Is Leveling a Tutorial or Part of the Game?

Going through all these examples I'd say it can definitely be used as a tutorial and also as a part of the game. Whether you like leveling or not is something everyone needs to know for themselves. There are ups and downs to this system. Also, it helps out to prolong unlocks to not overwhelm the player. Especially in MMORPGs which nowadays should and partly do focus on offering people all kinds of different content from achievement hunt to costumes to difficult content and even a little grind here and there. So with growing content and possibilities for the players to come these need to be introduced slowly. However, developers should keep in mind that the leveling doesn't go too slow nor too fast. Finding the right speed for the players is hard though.

Another way to use leveling would be like in real life. You never stop learning new things, you never stop leveling in real life. So you could make a leveling system in similar games. Keep in mind that this doesn't work well with people who seek to "complete" everything though. They might not like something infinite.

Guild Wars 2: Christmas Without Procrastination

Ah, yes. The Wintersday patch of Guild Wars 2 went live on Tuesday. Another round of cold, karmic, tooth hurting Wintersday fun. Just like every time a limited event with achievement points is going on or when a new Player vs Player and/or World vs World season starts, I always calculate how much I have to do each day. I don't wanna do everything on the last day (procrastination) and I don't want to do everything on the first day (inefficient).

What Do We Have Here?

So we have three categories of achievements now.

• The Wondrous Workshop of Toymaker Tixx
• Wintersday Traditions
• Winter's Presence

The first category includes one-time achievements that basically want you to do everything Wintersday has to offer.

Wintersday Traditions contains repeatable achievements for every year. Some give achievement points and some don't.

Winter's Presence is a handful of achievements that were one time, rewarding you with collectible items that are consumable for karma at the same time. This collection gave a shoulder skin that gave your character a snow effect.

Since the Wintersday Traditions are the only achievements that seem to repeat every year let's see what it takes to complete them.

What Do We Need To Do?

First things first we need to know how much we have to do in total. Many of the achievements only reward presents. That's nice but we could just farm them forever without end. (aside from the end of the Wintersday event). So let's go for achievement points only. The achievements that reward achievement points in the Wintersday Traditions category are:

• Toypocalypse Survivor
• A Season of Merriment
• Wintersday Wonderland Mastery
• The Bells of Wintersday
• Dauntless Donator
• The Giving Spirit
• Ulla's Rival

And aside from this category if you've done the non-repetitive achievements in the last years the only new one is Holiday Food Drive.

So let's look into the achievements in detail.

Toypocalypse Survivor

The achievement rewards 5 achievement points with a cap of 25. For each 5 achievement points, we need to do 30 rounds of Toypocalypse. So we can repeat this 5 times to cap the achievement points. That means we need to do 5 * 30 = 150 rounds. A full game consists of 10 rounds. So 15 full runs.

A Season of Merriment

This achievement requires us to do 3 dailies 5 times to get 10 achievement points. It is capped at 100 achievement points. That means we can repeat it 10 times so we need to complete 3 dailies 5 * 10 = 50 times. You could say 150 dailies.

Wintersday Wonderland Mastery

Ah yes, the jumping puzzle. This achievement rewards 5 achievement points and is capped at 25. It requires 3 runs to complete once. That equals 5 * 3 = 15 runs to do.

The Bells of Wintersday

Though it was bugged the first days it is now fixed and doable again. It also rewards 5 achievement points each and is capped at 25. We need to complete 20 songs for one iteration. So 20 * 5 = 100 songs in total.

Dauntless Donator

This may sound wrong but let's see the minimum amount of children we need to give presents each day. I already feel bad... anyways, This achievement also gives 5 achievement points per repetition and caps at 25. We need to satisfy 30 orphans. That's 5 * 30 = 150 orphans to give gifts to.

The Giving Spirit

Talking about giving. 25 achievement points in total 5 for each repetition and in old Halloween fashion the Quaggan Drooburt wants 1000 snowflakes per iteration. That's 5 * 1000 = 5000 snowflakes.

Ulla's Rival

Last but not least, Ulla's race. Like most other, we're awarded 25 achievement points with 5 every time we repeat it. We need three races to repeat so we have to do it 3 * 5 = 15 times.

And additionally: Holiday Food Drive

This is not repetitive but we get 15 achievement points when donating 150 wintersday food items.

How Are We Going To Do It Now? 

We know what to do, how much to do, but how are we going to do it now? We're going to check how much we need to do every day to complete it. Thanks to Artumes I now know the Wintersday event goes until the 2nd of January. So let's go again to do the math. I'm going to make two calculations now. One expecting you to start from patch day and one expecting you to start working on the achievements from today.

So let's start with the first one.

What Does Arenanet Expect On Average

Not saying they do expect this but this is how it has been programmed. The patch was released on Tuesday the 12th of December. Until the 2nd of January, that's one month. We have 22 days if we get to play on the 2nd January before that patch is removed. So let's go with 21 days instead.

Now some small math and we got our results.

Toypocalypse

150 rounds of Toypocalypse over 31 days is 150 / 21 = ~7.14 so 7-8 rounds a day.

A Season of Merriment

Whelp. 150 dailies over 21 days that's again ~7.14. However, 3 dailies a day is the maximum that counts. So we'll be doing 3 dailies each day. That's all we can do here. The rest.. we have to wait for next year. If we do the 3 dailies every day we'll iterate the achievement every 5 days. So 21 / 5 = 4.2 that's 4 iterations this year. That means we need 4 more iterations next year and another 2 the year afterward.

Wintersday Wonderland Mastery

15 runs over 21 days that's 15 / 21 = ~0.71 so one run about every 2-3 days. What we can do here now is say that we run it every time it is daily. Chances are high we'll be able to finish it before Wintersday ends. Since there are 11 dailies, the meta daily is always active and the orphan daily is always active as well we have only 9 possible. Thus it has a 1 / 9 chance to occur. If it didn't the next daily has a 1 / 8 chance to be this one. If not the next one has a 1 / 7 chance... 1 / 6 chance, if not the last daily has a 1 / 5 chance to be this one.

With our chances being:

First achievement slot A = 1/9

Second achievement slot B = 1/8

Third achievement slot C = 1/7

The fourth achievement slot D = 1/6

Fifth achievement slot E = 1/5

P(A or B or C or D or E) 

= P(A or B or C or D) + P(E) - P((A or B or C or D) and E)

= P(A or B or C) + P(D) - P((A or B or C) and D) - P((A or B or C or D) and E)

= P(A or B) + P(C) - P((A or B) and C) - P((A or B or C) and D) - P((A or B or C or D) and E)

= P(A) + P(B) - P(A and B) - P((A or B) and C) - P((A or B or C) and D) - P((A or B or C or D) and E)

= P(A) + P(B) - P(A) * P(B) - P(A or B) * P(C) - P(A or B or C) * P(D) - P(A or B or C or D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A and B) * P(C) - P(A or B) + P(C) - P((A or B) and C) * P(D) - P(A or B or C) + P(D) - P((A or B or C) and D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A) * P(B) * P(C) - P(A or B) + P(C) - P(A or B) * P(C) * P(D) - P(A or B or C) + P(D) - P(A or B or C) * P(D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A) * P(B) * P(C) - P(A) + P(B) - P(A and B) + P(C) - P(A) + P(B) - P(A and B) * P(C) * P(D) - P(A or B) + P(C) - P((A or B) and C) + P(D) - P(A or B) + P(C) - P((A or B) and C) * P(D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A) * P(B) * P(C) - P(A) + P(B) - P(A) * P(B) + P(C) - P(A) + P(B) - P(A) * P(B) * P(C) * P(D) - P(A or B) + P(C) - P(A or B) * P(C) + P(D) - P(A or B) + P(C) - P(A or B) * P(C) * P(D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A) * P(B) * P(C) - P(A) + P(B) - P(A) * P(B) + P(C) - P(A) + P(B) - P(A) * P(B) * P(C) * P(D) - P(A) + P(B) - P(A and B) + P(C) - P(A) + P(B) - P(A and B) * P(C) + P(D) - P(A) + P(B) - P(A and B) + P(C) - P(A) + P(B) - P(A and B) * P(C) * P(D) * P(E)

= P(A) + P(B) - P(A) * P(B) - P(A) + P(B) - P(A) * P(B) * P(C) - P(A) + P(B) - P(A) * P(B) + P(C) - P(A) + P(B) - P(A) * P(B) * P(C) * P(D) - P(A) + P(B) - P(A) * P(B) + P(C) - P(A) + P(B) - P(A) * P(B) * P(C) + P(D) - P(A) + P(B) - P(A) * P(B) + P(C) - P(A) + P(B) - P(A) * P(B) * P(C) * P(D) * P(E)

Inserted:

= 1/9 + 1/8 - 1/9 * 1/8 - 1/9 + 1/8 - 1/9 * 1/8 * 1/7 - 1/9 + 1/8 - 1/9 * 1/8 + 1/7 - 1/9 + 1/8 - 1/9 * 1/8 * 1/7 * 1/6 - 1/9 + 1/8 - 1/9 * 1/8 + 1/7 - 1/9 + 1/8 - 1/9 * 1/8 * 1/7 + 1/6 - 1/9 + 1/8 - 1/9 * 1/8 + 1/7 - 1/9 + 1/8 - 1/9 * 1/8 * 1/7 * 1/6 * 1/5

= 0.8687

So it has a chance of ~86.87% to appear in our dailies.

The Bells of Wintersday

100 songs in 21 days though 3 days were bugged. That's 100 / 21 = ~4.76 so 4-5 per day. With 3 bugged days we have 100 / 18 = ~5.55 so 5-6 every day.

Dauntless Donator

This one requires us to give 150 gifts. Give gifts, give life. We have 21 days so that's 150 / 21 = ~7.14 every day. However, if you want the daily done for the reward you will have to do 15 every day anyway.

The Giving Spirit

The good sir Quaggan wants 5000 snowflakes and gets 5000 / 31 = 238.1 snowflakes every day from us.

Ulla's Rival

Just like Wintersday Wonderland Mastery we only need 15 runs of this and we have 21 days. So 15 / 21 = ~0.71 per day. Or every second to the third day more or less. The same as the Wintersday Wonderland Mastery. You can do this when it's daily and it should be done at the end of Wintersday.

Holiday Food Drive

We need 150 foods for this and with 21 days that's 150 / 21 = ~7.14 or 7-8 food items per day.

Wintersday! Totally forgot! How much Do I Need Now?

The only thing that changes now is the number of days we have. From the 12th December to the 2nd January we had 21 days. So from the 16th December to the 2nd January, we have 17 days. Let's calculate everything with 17 days!

• Toypocalypse: 150 / 17 = ~8.82. That's 8-9 per day.
• A Season of Merriment: This doesn't change much.
• Wintersday Wonderland Mastery: 15 / 17 = ~0.88. That's every 2-3 days.
• The Bells of Wintersday: 100 / 17 = ~5.88. That's 5-6 every day.
• Dauntless Donator: 150 / 17 = ~8.82. That's 8-9 every day.
• The Giving Spirit: 5000 / 17 = ~294.12. So 294-295 per day.
• Ulla's Rival: 15 / 17 = ~0.88. That's every 2-3 days.
• Holiday Food Drive: 150 / 17 = ~8.82. That's 8-9 every day.

"You're A Wacky Little Dolyak Aren't You?"

I didn't expect the calculation to contain stochastic.. heh. Anyways time goes continue working on the achievements. Happy Wintersday everyone!

Updated

I've updated the posts with newfound information. Thanks to Artumes for letting me know on Reddit that the Wintersday event only goes 'til the 2nd of January.