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Best Chests - Event Strategy calculators

MinMax Gamer

Well-Known Member
Edit: Updated up to and including Rise of the Phoenix Cult event (March 2021)

Another major Elvenar event – Summer Solstice – is rapidly approaching, and it is time to do some analysis of what chest opening strategy we should employ, and what rewards can we get as outcomes of that. But instead of doing analysis on some specific strategies only, how about a couple of calculators that can answer many of those questions for any particular strategy or targeted rewards?

So take a look here for the detailed writeup on how to use these calculators:
https://minmaxgame.com/elvenar-event-chest-strategy-analysis/

Or you can jump right in here:
  • Manual Event Chest Strategy calculator
    • Here you define your own Elvenar event chest-opening strategy manually (i.e. you specify priorities for chests), and this calculator can tell you what are the expected outcomes of this strategy for all the rewards.
  • Optimal Event Chest Strategy calculator
    • But why would you want to figure out a strategy by yourself? Ultimately, you just want to focus on particular rewards, and this calculator can figure out an appropriate Elvenar event chest-opening strategy specific for the rewards you are targeting. And yes, you can target more than one reward!
I did validate results with the full simulation, and they look pretty close. Not much else was tested, especially UI ;) I am strongly considering to focus 100% on Portal Profits this time around, as I haven't seen a lot of PPs/Trading Outposts in the recent events, and my stockpile is running critically low. That, and other prizes look rather meh.
 
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DeletedUser23031

Guest
Great calculators. Thanks.
The chests seem more expensive this time therefore the chance to get daily rewards seems lower over all. Am I reading this correctly?

edit: using the calculators for a few test runs, chests cost more, therefore fewer opened and 1/3 fewer Daily prizes will be won. Compared to the last event. :(
I think I'll go for the portal profits
 
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MinMax Gamer

Well-Known Member
Basically, you're right. With the same amount of event currency, you could expect a lot more daily prizes from the last event. And you actually could get more event currency (essence) the last time around - at least with the extra added quests. You can take a look at adjusted expected cost per daily prize for individual chests:

AdjustedCostPerDailyPrize.png


As you can see, chests in the Solstice event are strictly worse than the ones from the last event.
 

Black watch

Well-Known Member
Quote from MinMax Gamer

"Basically, you're right. With the same amount of event currency, you could expect a lot more daily prizes from the last event. And you actually could get more event currency (essence) the last time around - at least with the extra added quests. You can take a look at adjusted expected cost per daily prize for individual chests:

index.php


As you can see, chests in the Solstice event are strictly worse than the ones from the last event."



I'm on SS quest 58 so far and had targeted a few buildings I wanted to upgrade older ones. So far I've been completely shut out on this event and if I see another coin instant or supply windfall, I might scream at my monitor. The only bright spot in not getting my buildings up graded with replacements is I've been able to use the Time instants to bring up my troop strength, which was nice. Other than that, I'm not happy with this event compared to all the others I've done since I joined this game in 2017.
To say I'm disappointed is a major understatement.
Perhaps someone else knows why INNO decided to mess with their formula.
I've followed the Gems suggestions and even tried the chest suggestions from Phoenix too. Both don't seem to be particularly accurate.
Disappointed and resigned to just keep building my army.
Blackie
 

Ashrem

Well-Known Member
I've followed the Gems suggestions and even tried the chest suggestions from Phoenix too. Both don't seem to be particularly accurate.
The problem with any estimate of what you'll get from a random is that you have to approach hundreds of the same pick before you can be guaranteed to get close to the expected result. The charts are accurate, but they are not particularly useful for specific cases.
 

MinMax Gamer

Well-Known Member
What Ashrem said is true, averages are just that - averages. You can do significantly worse than average - and you can do significantly better. This doesn't mean averages are wrong ;)

With quest 58 you're probably about only at a quarter of total event currency available. So keep on rolling the dice. As an anecdote, in the last event my rolls with the first quarter of event currency were terrible - only about 3% chance of being that bad or worse. Yep, tons of coin and supply instants - and not much else. Yet by the end of the event I went to even slightly above average. There is still plenty of time.
 

Ashrem

Well-Known Member
The last 35 quests give as many points as the first 78. When you factor in that there are still 18 daily quests to go, you're not even half way to the total points even if you're at quest 80.

If you can finish the event, and get 20 points in the flare-booger pickups (about 15-18 pickups with some having more than one) and finish the daily quests, you should end up with more than 6500 flare-boogers to spend
 

DeletedUser23255

Guest
Am I missing something with these calculators?

Everything I read says purple is the worst for grand prizes but it’s a cost of 142 with 5 flowers. 142 / 5 is 28.4 flares per progress towards a grand prize. Red chest is 85 with 3 flowers or 28.33 flares per progress. Some of the other chests only give 1 flower and cost more then 28 or equal to 28.
 

MinMax Gamer

Well-Known Member
Am I missing something with these calculators?

Everything I read says purple is the worst for grand prizes but it’s a cost of 142 with 5 flowers. 142 / 5 is 28.4 flares per progress towards a grand prize. Red chest is 85 with 3 flowers or 28.33 flares per progress. Some of the other chests only give 1 flower and cost more then 28 or equal to 28.
Yes, you're missing a few things. One is that several chests have a chance of producing extra flares, so you need to adjust for that. E.g. adjusted cost for the purple chest is 117, with 23.4 adjusted cost per flower. But you can't simply order chests by this adjusted cost and call it the optimal strategy. You need to take into account that you lock in this average cost for the cost of the whole chest. To make long story short, this means that you want to prioritize good value chests with high total cost, and bad value chests with low total cost.

E.g. bronze chest with 26 adjusted cost per flower is ranked higher than purple with 23.4 because you lock in bad value of 26 only for 26 flares, and then roll again for another chest which is expected to be significantly better. Now the purple chest has better average, but you lock it in for the whole 117 flares. This is suboptimal. You're better off taking a short burst of bad value and move on.
 

Enevhar Aldarion

Well-Known Member
Am I missing something with these calculators?

Everything I read says purple is the worst for grand prizes but it’s a cost of 142 with 5 flowers. 142 / 5 is 28.4 flares per progress towards a grand prize. Red chest is 85 with 3 flowers or 28.33 flares per progress. Some of the other chests only give 1 flower and cost more then 28 or equal to 28.

This same discussion has happened in the past couple of events also. Some people base their calculations on what you could get as a reward from the chest, the extra flares, and some people just go by the actual cost of each chest for what is best. Take me for example. In the Phoenix event I got zero of the essences as prizes from the chests, so for me, the cheap chests were a better value that the one that cost 85. But if you included the variable of actually getting some essences from that chest, then it became the best cost for other people.
 

NightshadeCS

Well-Known Member
In the Phoenix event I got zero of the essences as prizes from the chests, so for me, the cheap chests were a better value that the one that cost 85. But if you included the variable of actually getting some essences from that chest, then it became the best cost for other people.

That was truly a run of extraordinary bad luck! :eek::eek:

I was an example of the other side of that coin in the last event, hitting the +200 essence with what felt like good regularity (I did not count, so can just go off of my general impression). I ended up with one extra evolution artifact after getting that Fire Chicken up to 10, so my impression is backed up there, at least. As with all probabilities, there have to be some folks at the edges of the curve.

I hope you experience better luck this time, @Enevhar Aldarion ! :D:p:D:p
 

StarryElf

Guest
I usually just go with my gut on these kinds of events. Too much variation in the chest prizes and chest occurrences to try to determine what can be best for me. I will still most likely avoid the green chest though and always go for the light wood chest when I can.

Yes, you're missing a few things. One is that several chests have a chance of producing extra flares, so you need to adjust for that. E.g. adjusted cost for the purple chest is 117, with 23.4 adjusted cost per flower. But you can't simply order chests by this adjusted cost and call it the optimal strategy. You need to take into account that you lock in this average cost for the cost of the whole chest. To make long story short, this means that you want to prioritize good value chests with high total cost, and bad value chests with low total cost.

E.g. bronze chest with 26 adjusted cost per flower is ranked higher than purple with 23.4 because you lock in bad value of 26 only for 26 flares, and then roll again for another chest which is expected to be significantly better. Now the purple chest has better average, but you lock it in for the whole 117 flares. This is suboptimal. You're better off taking a short burst of bad value and move on.

You have to be very careful making this assumption because the law of large numbers does not necessarily apply here. A risk-taking player that opens the purple chest can obtain the 500 sun flares with relatively few tries, which is more cost effective than a risk-averse player only opening the less expensive chests. The adjusted chest costs simply give a cost ratio that is expected from that moment in time. However, risk-taking players can still be more lucky than risk-averse players and vice versa.

Another way to look at it as that every time you are taking the risk-averse option, you are also forfeiting that risk to reward option.
 
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MinMax Gamer

Well-Known Member
You have to be very careful making this assumption because the law of large numbers does not necessarily apply here. A risk-taking player that opens the purple chest can obtain the 500 sun flares with relatively few tries, which is more cost effective than a risk-averse player only opening the less expensive chests. The adjusted chest costs simply give a cost ratio that is expected from that moment in time. However, risk-taking players can still be more lucky than risk-averse players and vice versa.
I am actually not making any assumptions about risk-tolerance. Tool calculates averages, and optimizes averages (as stated). It doesn't show nor even calculates variance. Now, it is indeed true that you don't have to aim for averages, or even have a symmetrical gain/loss value function. If you want to maximize a particular outcome (say, achieving L10 Stonehenge), then optimal strategy might be different than maximizing the mean.

Trivial example of that would be two grand prize strategies: one has mean of 15 and standard deviation of 0 (i.e. you will always get 15), another one has mean of 10 and standard deviation of 5. Now, if you simply want to maximize your expected number of grand prizes, then strategy 1 is a no brainer. That's what the tool optimizes for. However, you may consider that you only care about hitting L10 for your evolving building (needs 17 grand prizes or more). Anything less you consider worthless. Now, all of the sudden strategy 2 is the optimal strategy for you. Because while you still expect to get fewer GPs with this strategy, now you have some non-trivial (albeit small) chance of hitting your L10 or more (as there is a lot of variability in the results). Strategy 1 is useless to you as it will never get you to L10, so all outcomes are bad (again, to you).

Such analysis requires looking at full distribution, which is hard to do analytically and is best done with the full simulation. I did similar analysis for several strategies (not optimization) for the last event: https://minmaxgame.com/evolution-of-the-phoenix-event-analysis/

There you can see variability and percentiles of the distribution. I may do something similar for this event.
 
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