WINTER EVENT - SET BUILDINGS YOU MAY NOT GET

[DeletedUser5139]

Which makes the "bust" chance 0.00001% higher with small boxes? Just guessing at the zeros, but I'm sure there's many.

I've given you good simulations for multiple scenarios. Now, you want to guess at the zeros? Can we discuss real data instead of making up numbers to suit our view?

My point is that 99% of the time it is very possible to use all 100% of the 6,000 keys on set buildings.

Again -- where did "99% of the time" come from? Another guess? I'm trying to have a discussion based on actual data here.

While I believe your intentions are good, your statement that you think almost all players should go for the big box is misleading at best, and if players listen to you, ultimately they will get fewer buildings.

I too believe your intentions are good, if misleading. You're making up percentages and passing them off as facts. Directionally, it's not terrible advice since the two boxes are fairly close in terms of performance. However, it's still not a golden rule as it has been stated.

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You should at least show both sides and mention that if they open all big boxes that they will spend 450 extra keys on buildings, not just 86.

Where did you get the 450? I keep "touting" a stat that is out of the simulation. You keep inventing numbers out of thin air. No scenario results in spending 450 more keys.

Less than 1% increased chance of failing to get a GH with small boxes, but on average 1 more building.for the event, and you honestly recommend they shouldn't choose that?

...

If there are 10,000 players, each with 2K keys your idea of going big boxes saves 16 of them from failing to get the GH, but if they all go small boxes 10,000 more buildings will be won in the event.

Fine. Here is a case that I can model. Above, you're claiming a very precise case, so I assume that you already have calculated it and are using real numbers. Let's see if that's the case! I will use 1,000,000 iterations instead of 10,000 to increase the stability of the data. (I hope you understand that this is important...I'm not trying to change your case). This will mean that we should expect 1600 more people to bust using small boxes and we should expect to see 1,000,000 more buildings in the game. Further, it means that the people that didn't bust using small boxes on average all got 1 extra building.

Let's see if that's right...

1,685 more people ran out of keys before getting any buildings by going for the small box. So, this modeled as expected! No surprise as this was pulled from my previous simulations.

There are 330,000 more buildings...not 1,000,000. The per player average is shown in parenthesis. The average player using small boxes got 4.89 set buildings. The average player using big boxes got 4.56 buildings. We can restate that to say that 1 out of 3 small box people got an extra building. Surprised? You promised everyone an extra building, but only 1 in 3 will get one. In exchange for that, 1,685 more people walk away with zero buildings.

With that, here is the final assessment:

If you want to maximize the number of buildings you might get, you should open the small boxes with the understanding that you will take an increased risk of 1.7 in 1000 to not get any buildings at all. There is a 1 in 3 chance you'll get can extra set building!

OR

If you want to play it safe, you should open big boxes until your balance is below 140. Then, you should open small boxes to use up your last keys. You will take the least risk of busting with zero buildings, but you will not have a 1 in 3 chance at an extra building.


...

With that, I'm done with simulations. I've given you a simulation that you set up and also given you an unbiased assessment of it. It is my opinion that this assessment should be the answer to the question, "Which box should I open given I have 2,000 keys and want set buildings?" Give the player the correct information and allow the player to make the choice which route they take.

 

[SoggyShorts]

@Nenelar
Yeesh, so aggressive.

First of all no, I'm not doing my own sims, I'm just using your data. (I'm far too lazy to teach myself PHP like you did, which is very impressive BTW)
You gave numbers for 4,000 keys on day six.
That was a increase of 174 in 10,000,000 or 0.0017%
I could have had 4,800 keys on day six (4449+(35*6)+50 to start+collections)
So yes, I "guessed" at 0.0001%

Spoiler: how I got that number

Based on your data, the change from
1k keys 1.03%
2k keys 0.16%
3k keys 0.02%
4k keys 0.0017%
4.8k keys 0.0001% ? (a better estimate would probably be 0.00025%)
I didn't pull the number from me bum, I ballparked it based on data you have given, and openly admitted it was a guess (should have said "estimate") Feel free to change the line in your sim from 4,000 to 4,800 and give a more accurate number. If you think it is relevant.
My own personal bias is that anything under a 1 in 10,000 chance is insignificant, but you are right, we should strive for accuracy.

regarding my 450 number, I thought that was obvious from previous posts.

Spoiler: how I got that number

6,000 keys = 15 buildings for small boxers
400 keys per box for small boxers
430 keys per box for big boxers
430-400=30
30x15=450
This is all from your data as well.

On to the next one, "99% of the time it's possible to spend all 6k keys on set buildings"

Spoiler: how I got that number

If you don't bust (which only happens 1% of the time) you can spend all of your keys on set buildings
100-1=99
My assumption was that if you bust that you wouldn't finish the event spending your remaining keys on set buildings, hence "99%"
Again, I thought that was clear, sorry for not spelling it out before.

And lastly, onto the latest sim:

If there are 10,000 players, each with 2K keys your idea of going big boxes saves 16 of them from failing to get the GH, but if they all go small boxes 10,000 more buildings will be won in the event.

There are 330,000 more buildings...not 1,000,000.

Your sim shows what happens with your first 2k keys perfectly, but you are ignoring that players get 6k keys, (hence my use of the words "in the event") so you need to triple the results to get the whole picture. 0.99m is close to 1m, and the rounding is due to my using your data from your previous sims.

"Which box should I open given I have 2,000 keys and want set buildings?" Give the player the correct information and allow the player to make the choice which route they take.

Your final assessment above is nearly perfect imo, and would be perfect if you tripled the results to reflect the entire event.

Something like this:

Based on having 2K keys* on day 6,19, and 30:
If you want to maximize the number of buildings you might get, you should open the small boxes with the understanding that you will take an increased risk of 1.7 in 1000 to miss each set building, but on average you'll get an extra set building over the course of the whole event.

*If you have fewer than 2k keys on set days, your chance of missing a set building with small boxes increases (but total number of buildings remains higher than big boxes)
*If you have more than 2k keys on set days, your chance of missing a set building with small boxes decreases (but total number of buildings remains higher than big boxes)

 

[DeletedUser5139]

@Nenelar
Yeesh, so aggressive.

Admittedly, I can find debating of more interest than the topic at times. Re-reading your replies, I suspect you may share that with me.

First of all no, I'm not doing my own sims, I'm just using your data.
You gave numbers for 4,000 keys on day six.
That was a increase of 174 in 10,000,000 or 0.0017%
It's possible to have 4,800 keys on day six (4449+(35*6)+50 to start+collections)
So yes, I "guessed" at 0.0001%

You "guessed" 0.00001% (note the extra zero in your original post) ... which is a factor of 10 off.

(a better estimate would probably be 0.0002%)
I didn't pull the number from me bum, I ballparked it based on data you have given, and openly admitted it was a guess (should have said "estimate") Feel free to change the line in your sim from 4,000 to 4,800 and give a more accurate number.

Now it's off by a multiple of 20. That's a large ballpark. If you can't see my frustration as reasonable after working to put together actual analysis and have it answered with guesstimates so far off...

regarding my 450 number, I thought that was obvious from previous posts.
6,000 keys = 15 buildings for small boxers
400 keys per box for small boxers
430 keys per box for big boxers
430-400=30
30x15=450
This is all from your data as well.

This is a failure to understand your own case. If you're spending all 6,000 keys on buildings, you spend all 6,000 keys. I thought that was obvious too! There are no "extra" 450 keys in this scenario. There are only "extra" keys when you stop early. You will open more small boxes than big boxes, but in both cases, you spend all 6,000 keys.

On to the next one, "99% of the time it's possible to spend all 6k keys on set buildings"
If you don't bust (which only happens 1% of the time) you can spend all of your keys on set buildings
100-1=99
My assumption was that if you bust that you wouldn't finish the event spending your remaining keys on set buildings, hence "99%"
Again, I thought that was clear, sorry for not spelling it out before.

100% of the time it's possible to spend all 6k keys on set buildings. It's just that 1% of the time, you get no return -- but you spent the keys in all of the cases.

Your sim shows what happens with your first 2k keys perfectly, but you are ignoring that players get 6k keys, (hence my use of the words "in the event") so you need to triple the results to get the whole picture. 330Kx3 is close to 1m, and the rounding is due to my using your data from your previous sims.

I used parameters you defined, not me. If you want to say that you chose to ignore that players get 6k keys, great! Don't say I did it. You're making it seem that I am trying to hide something by setting up an incomplete case and that isn't fair.

Your final assessment above is nearly perfect imo, and would be if you tripled the results to reflect the entire event.

Something like this:

Based on having 2K keys on day 6,19, and 30:
If you want to maximize the number of buildings you might get, you should open the small boxes with the understanding that you will take an increased risk of 1.7 in 1000 to miss each set building, but on average you'll get can extra set building over the course of the whole event.

If you have fewer than 2k keys on set days your chance of missing a set building with small boxes increases (but total number of buildings remains higher than big boxes)

If you have more than 2k keys on set days your chance of missing a set building with small boxes decreases (but total number of buildings remains higher than big boxes)

This is nearly perfect except:

This is a non-linear inverse function so you shouldn't just multiply by 3. The more keys you have, the smaller the chance of missing a building. The fewer keys you have, faster the chance of missing a building increases!

This is a critical point: As keys decline, the chance of missing the building increases at a faster rate. This suggests that at some point toward the end of the event, even a small box approach should switch to a big box when the key balance falls below some break-even number that would need to be determined. (A quick multiple scenario search says it's around 560 keys -- but it would take more effort to nail down the exact tipping point).

For example, suppose you've spent 5,700 of your keys on small boxes. You now have 300 keys left. You'd like to try to get 1 more set building. Should you open more small boxes or switch to big boxes? You might think that 6 tries on a small box is better than 2 tries on a large box. Well, 1,000,000 simulations says should switch to big boxes because small boxes pay out 49% of the time while big boxes pay out 54% with so few keys. You get both a greater chance at one last building and 10 more crowns by using big boxes at such a low key balance.

...

Hopefully you follow the situational nature of the question, "Which box is better?". This is what I have been saying, maybe poorly ... the choice is not black and white. It should not be said that small boxes are always better. The answer is that NO box is always better (although it appears that the middle box is always worst). Since key balances for all of us changes -- even if you magically hit 6k keys on Day 6, you will spend down to a point where big boxes are the better choice to finish your run if you still want more buildings. That will be after you have fallen to ~560 keys. Above that, the question is "Do I care more about the chance to get an extra building or more about walking away empty-handed?"

As for your request to change the scenario to 4,800. I have provided the PHP source code. It's very straight-forward. Again, I had to teach myself PHP while writing it. It was worth learning. Please feel free to modify it and run your own scenarios as you wish.

 

[SoggyShorts]

You "guessed" 0.00001% (note the extra zero in your original post) ... which is a factor of 10 off.
Now it's off by a multiple of 20. That's a large ballpark. If you can't see my frustration as reasonable after working to put together actual analysis and have it answered with guesstimates so far off...

It most certainly is. Huge error on my part. I do understand your frustration, my apologies for that.
I wish you'd focused on my next point that due to my personal bias, I just don't feel there's a significant difference between 1 in 10,000 or 1 in 100,000.(which might explain my lack of double checking and being off by a factor of 10 or even 20)

This is a failure to understand your own case. If you're spending all 6,000 keys on buildings, you spend all 6,000 keys. I thought that was obvious too! There are no "extra" 450 keys in this scenario. There are only "extra" keys when you stop early. You will open more small boxes than big boxes, but in both cases, you spend all 6,000 keys.

Lemme put it another way: if your goal is x buildings, you will have more keys left over after reaching that goal by opening small boxes.
Roughly 450 more towards the end of the event at roughly 14-15 buildings.

100% of the time it's possible to spend all 6k keys on set buildings. It's just that 1% of the time, you get no return -- but you spent the keys in all of the cases.

nitpicker.
rephrasing again: 99% of the time it's possible to spend all 6k keys on a full set, 1% of the time your set will be broken.

If you want to say that you chose to ignore that players get 6k keys, great! Don't say I did it. You're making it seem that I am trying to hide something by setting up an incomplete case and that isn't fair.

That wasn't my intention. My goal was to look at one picture (the 2k keys scenario) and then also zoom out and apply it to the event as a whole. I don't mind taking responsibility for my failure to communicate that, my bad.

For example, suppose you've spent 5,700 of your keys on small boxes. You now have 300 keys left. You'd like to try to get 1 more set building. Should you open more small boxes or switch to big boxes?

You've solidly proven that when you have a low key count and your goal is 1 (more) set building the big box is better. the lower the key count the more important it is to open big boxes to avoid failure.

Admittedly, I can find debating of more interest than the topic at times. Re-reading your replies, I suspect you may share that with me.

I can't imagine how anyone could get that impression of me from my posts.....

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I'm actually going to be in an interesting situation on one account in a few minutes.
2230 keys, and I want 2 buildings, anything else is a fail.
Does the big box scenario for bust work on this?
The other account that I care about is at 3300 keys, so I'm not too worried.

Edit:
5 big boxes on first account to get 2
4 big boxes to get 2 on second account.
TBH my main motivation for going big boxes was completely unrelated to the math... I just wanted to know if I would get my buildings or not ASAP, and opening 50-60 boxes seemed like a chore.

Next question: What are the odds of getting the 3rd grand prize?
1630 Keys
5x35 dailies
5x20 collections
------
1905 keys for double day, and I need 655 crowns
So I just need 3x 140 keys from 13 boxes, right?

 

[rvtdragon1]

Are you fin kidding me. 10 tries using every key I have been saving for days and NO Orc Vortex. You got my last nickel INNO. Bite me.

 

[SoggyShorts]

Are you fin kidding me. 10 tries using every key I have been saving for days and NO Orc Vortex. You got my last nickel INNO. Bite me.

Thank sucks mate, sorry about your luck.

 

[rvtdragon1]

I deleted the other three buildings. Did not need the culture. The number of good and supplies was not worth the space. I am on the way to Dwarves and the space for expansion is a whole lot more important than a few useless buildings that do nothing to advance my city other than take up a huge amount of space in one corner.

 

[DeletedUser5139]

I'm actually going to be in an interesting situation on one account in a few minutes.
2230 keys, and I want 2 buildings, anything else is a fail.
Does the big box scenario for bust work on this?

And, the answer from 1,000,000 sims is...

Bust means you will spend all 2,230 keys and have zero buildings.

Going small box from 2230 will award an average of 1.97 buildings with 0.34% chance to bust.
Going big box from 2230 will award an average of 1.98 buildings with a 0.24% chance to bust.

The average small box player will get their 2 buildings having spent 794 keys.
The average big box player will get their 2 buildings having spent 853 keys.

With that, you can make your decision as to which to do!

 

[DeletedUser5139]

I deleted the other three buildings. Did not need the culture. The number of good and supplies was not worth the space. I am on the way to Dwarves and the space for expansion is a whole lot more important than a few useless buildings that do nothing to advance my city other than take up a huge amount of space in one corner.

It sucks to not get the building you wanted. Good news is, if you're moving into Dwarves, anything you'd have got would be quickly replaced anyway!

 

[SoggyShorts]

With that, you can make your decision as to which to do!

I went big boxes and won everything I wanted almost instantly.

 

[DeletedUser5521]

I had 786 keys to play with...hit the small box 10 times. Got 2 Vortexes plus 90 keys twice, so I still have 466 keys to play with for something else. On to the next world..

 

[DeletedUser5139]

I went big boxes and won everything I wanted almost instantly.

Then it was a good choice.

As the sim showed, it was slightly better to go big box in that case ... but only slightly.

 

[DeletedUser5139]

I started with 3,226 keys:

Big Box = 25 KP
Big Box = Set
Big Box = Set

...and there I stopped with 2,806 remaining for the last double day.

 

[DeletedUser3507]

Ah they are if your in chapter 11, Actually kept 2 of the set buildings to up my culture I may or may not keep the grand prize is still up in the wind, but at least I finally one one.

 

[rvtdragon1]

Well, clearly you are all better than me. You win.

 

[SoggyShorts]

...and there I stopped with 2,806 remaining for the last double day.

Guaranteed 3rd prize?
I need 3x keys on one account in 13 tries

Well, clearly you are all better than me. You win.

"I was once luckier than someone else due to random chance"
I should put that on my business card.

 

[DeletedUser5139]

Want to maximize crowns on the last double day?

Open big boxes. Even if you haven't spent a single key and have all 6,000 ... big boxes win on crowns.

So, you should:

• Open big boxes.
• Once you fall below 140 keys, open small boxes.
• Never open a middle box.
• Should you get lucky on a small box and win enough keys to open a large box, do it.

Good luck! Remember that nothing is a guarantee. The above strategy has the best average outcome for crowns.

 

[SoggyShorts]

Want to maximize crowns on the last double day?

Open big boxes. Even if you haven't spent a single key and have all 6,000 ... big boxes win on crowns.

So, you should:

• Open big boxes.
• Once you fall below 140 keys, open small boxes.
• Never open a middle box.
• Should you get lucky on a small box and win enough keys to open a large box, do it.

Good luck! Remember that nothing is a guarantee. The above strategy has the best average outcome for crowns.

For those of you who have been following our back and forth about which box to open:
There is no question about the accuracy of the above statement: Big boxes = more crowns.

 

[samidodamage]

I've been following the convo about the boxes, but it was really hard for me to change my mindset about 'more daily buildings opening the small chest' as I could wrap my mind around the idea of smoothing out the randomness with more tosses of the coin. I wanted 2 of the orc vortexes and had ~2350 keys to work with. I didn't keep up with any of the extra rewards I won, including keys, but here is what happened: 24 times the small chest = zero buildings. 13 times the large chest = 2 buildings. Keys left = 315. I did wait until I had used over half my keys with no buildings to start trying the large box. I'm nowhere near to getting the 3rd GP, so double crowns don't have any appeal to me. I may just wait for the last day and throw everything I have at the Candy Cane tree, because pretty, sparkly and shiny get me every time.

 

[DeletedUser5139]

I've been following the convo about the boxes, but it was really hard for me to change my mindset about 'more daily buildings opening the small chest' as I could wrap my mind around the idea of smoothing out the randomness with more tosses of the coin. I wanted 2 of the orc vortexes and had ~2350 keys to work with. I didn't keep up with any of the extra rewards I won, including keys, but here is what happened: 24 times the small chest = zero buildings. 13 times the large chest = 2 buildings. Keys left = 315. I did wait until I had used over half my keys with no buildings to start trying the large box. I'm nowhere near to getting the 3rd GP, so double crowns don't have any appeal to me. I may just wait for the last day and throw everything I have at the Candy Cane tree, because pretty, sparkly and shiny get me every time.

This is an interesting case for me because it is similar to what I initially set out to illustrate. You want to exit the box opening on a success condition (2 orc vortex buildings) rather than spending all of your keys. Let me show you what my simulation of 1,000,000 of each box would look like:

A bust means you spend all 2,350 keys you had and get zero buildings.

Big boxes have a 1.5 in 1,000 chance of busting in your case but will cost 58 more keys.
Small boxes have a 2.5 in 1,000 chance of busting in your case but will save you an average of 58 keys..

If you knew this in advance, what would you have done? Would you have tried to save 58 keys for more risk of busting or would you have said, "For 58 keys, I'll take a little extra insurance."

Please don't misunderstand me here. This is all just chance at the end of the day. What I'm interested in is whether knowing this would have helped "wrap your mind around it" as you said?

PS - Man, am I a sucker for running more simulations after I said I was done or what?