16 December 2017

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. 

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I'm a junior game developer and software developer and I created this blog to share my ideas, thoughts and whatever I'm working on or doing.