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Events : which is best chest ?

tonton-des-bois

Illusionist
You can get some nice buildings from the long events daily rewards, globaly better than the solo grand prizes...

But which Chest gives the best probability to get the more buildings ?

To calculate that, you must keep in mind the chances to get extra items that will give you more tries, so, this is what is called a "recursive"(*) function : you first calculate what your starting collected items will give you as buildings and extra items, then you must calculate what you'll get as buildings and extra items from the first extra items, then... this nested function only end when you can't do any more try.

REMARK
Statistically, the 1st chest gives more chances to get buildings out of the same items amount BUT statistics are for huge numbers and you need thousands tries for the random results to approach the statistical numbers...
You can't compare your 10-15 tries with the statistics !
The statistics only say : averagely, all the people, all together, will get a higher probabilty with the 1st chest, not that you will get them...


No matter how much item you have at the moment you do your tries, the winner is always the 1st chest as you can see below...there is an unsignificant advantage for chest 2 (half a percent of a building) if you have only between 90 and 139 items (nuts, bets, snowflakes, etc)

In the following tables I've tried differents amounts of items to show what changes or not.
The 1st "pass"(*) matches with what you receive from your starting items, the following passes are what you'll get from the extra items you've got from the previous ones...
Each recursive calculation ends when you can't afford one full try, after that, the values are greyed...

Less than 50 items
You got nuts :p

50 to 89 items
Chest 1 wins by default of opponent. No math required ;)

90 to 139 items
Unsignificant advantage for chest 2 (less than half a percent of a building)


140 items and over
The winner is always 1st chest







(*) Recursivity and "passes"
A recursive function means (in this case) "an action that will have as result to do this action again... and again..."... We have nuts, they provide chests openings, those openings can give more nuts that will give more openings, etc... until you can't do one opening.
Each step provides less product for next step so you fast reach too few products for a single try.
It's like if you were doing tries using your first "pot" of nuts and putting the nuts you gain in a second pot, that's the first "pass", then you do a second pass with the second pot and fill a third one, etc
 
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Brienne

Necromancer
I simply see that the rewards for the 140 chest are greater per nut , so only open them and only on days I don't mind winning the daily prize. Personally I have enough buildings already with no space to place them. :(
 
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Poacher

Conjurer
I must admit i have been pretty lazy during this event, maybe because i had just got into Dwarves so was concentrating on that more, but even just playing the first chest i have managed to gain a pretty fair amount of buildings and instants.
3x Nutcrackers 1x Squirrel Square 1x Spheric Stub 1x Eldasil''s Holy Halls. I Won't gain the last building Eldrasil's Village.. might be a good thing too as i have nowhere left to put it:p but all in all it's been pretty good and i'm looking forward to the Halloween event.. gotta make some room in case i gain more buildings..:eek:you could evict some tenants and demolish their homes to make room.:confused:eek.
 

TomColBadil

Adventurer
I analyzed the expected rewards for the Harvest Festival Cornucopias, following @tonton-des-bois approach.

Here you can see an example with 6000 moon splinters:
Conclusions:
  • Small Cornucopia is better if you are interested in event buildings (you earn more of both Sun Flares and Daily Buildings).
  • Medium Cornucopia is better if you are interested in coin and supplies.
  • Large Cornucopia is better if you are interested in Knowledge Points and Time Boosts.
Results don't change significantly with the amount of splinters spent, so it didn't feel worth to post examples with different amounts.

I hope this is on point. Ask if you have any question, and message me if you want the link to the spreadsheet.

EDIT: Rewards chances come from event page on the wiki

Here I went with my approach: instead of recursive purchases, I used the reduced price for each Cornucopia, which is calculated from the initial price minus the expected splinters gains.

This is the example still with 6000 splinters. As you can see numbers are slightly higher, and are the same that you'd get with the recursivity approach if you considered also the iterations where you purchase less than 1 cornucopia. This way, the rewards are exactly proportional to the splinters spent, so the ratios are fixed.
 
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tonton-des-bois

Illusionist
First, thank you to TomColBadil to put his maths here, you are welcome and this is my no-sarcasm day... ;)

Of course, we are back to the old system with some minor fixes about the amounts but the rest of the recipe is still working the same way : you can get some "extra balls" from the chests so you have a "bonus" in the results, decreasing in value "with time"...

Even if I get some minor (but constant and unsignificant) variations in my own results (compared to yours), the ratios are kept and i arrive to the same conclusion as you : small chest is best for daily buildings or flares, medium is good for extra coins or supplies, big is best for time boosters and KPs...

PS : I used the same starting amount of items (6000 but I got the same ratios with 3000, 2000 and 1000) like you to have a consistant point of comparison and I explored the recursivity effect to the point where the amount of won splinters wasn't enough, anymore, to get a new try...

Thanks for reading :)
 
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TomColBadil

Adventurer
The Bonus Days don't make any difference, and here's why: the amount of sun flares for each chest is equally amplified by a factor x2, so if you compare the sun flares yields you'll still see that small cornucopia is better.

Getting both sets is indeed very difficult if you don't spend money. On the other hand, if you focus on a specific set you should be able to get it with the rigth strategy:

- SET 1: purchase cornucopias only when a set building is offered, and stop as soon as you get a copy of that building. You should get enough sun flares for the 1st main prize so when you unlock the whole set you can use your shards for whatever you want.
- SET 2: purchase cornucopias only when a set building is offered, and stop as soon as you get a copy of that building. Spend the spare shards on double sun flares days and you should get enough to unlock all main prizes.