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#1 2018-08-30 02:42:53

CapBlarry
Member
Registered: 2018-08-27
Posts: 221

Failstacking with armor

A popular strategy used by players enhancing endgame gear is deliberately downgrading armor to build stacks for more important components, such as weapons. Today we will examine the soundness of this strategy from a financial point of view.
We will only examine downgrading DUO and TRI fodder tier armor today. In other words, the mathematics will be done with Heve/Grunil equivalent armor at DUO/TRI.
The concept of what we’re doing here is best illustrated with a tree diagram. Tree diagrams allow us to examine possible outcomes based on the odds, and make inferences based on them.

In mathematical terms:
[ulist]
[*]The failstack cost analysis for armor enhance can be calculated as
[ulist]
[*]( CostArmorFail + CostEnhanceAttempt) * FailChance + (CostXFailstack + CostEnhanceAttempt – ExtraArmorValue) * SuccessChance
[*]That equation calculates the expected outcome per action, but of course to reach your failstack goal you need to retry the outcome multiple times until you fail the enhancement.
[*]The entire thing has to be divided by the probability of enhancement fail to give you the final equation:
[ulist]
[*]((CostArmorFail + CostEnhanceAttempt) * FailChance + (CostXFailstack + CostEnhanceAttempt – ExtraArmorValue) * SuccessChance) / FailChance
[/ulist]

[/ulist]

[/ulist]
[ulist]
[*]The failstack cost analysis for blackstone fodder can be calculated as
[ulist]
[*](CostXFailstacks + AverageStonesLost) * SuccessChance + AverageStonesLost * FailChance
[*]That equation calculates the expected outcome per action, but of course to reach your failstack goal you need to retry the outcome multiple times until you fail the enhancement.
[*]The entire thing has to be divided by the probability of enhancement fail to give you the final equation:
[ulist]
[*]((CostXFailstacks + AverageStonesLost) * SuccessChance + AverageStonesLost * FailChance) / FailChance
[/ulist]

[/ulist]

[/ulist]
 
Next we need to figure out the multiple variables we need to complete the equations. We will examine this at 30 and 40 failstacks using DUO/TRI armor for the first strategy.
The cost of 30 failstacks and 40 failstacks can be worked out using combinatorics. This is too complex to summarize in this article, so I’ll just write the answers instead.
[ulist]
[*]30 Failstacks – 274.5 blackstones with Reblath+14
[ulist]
[*]At 250k per stone and repair, this comes out to 68.6mil
[/ulist]

[*]40 Failstacks – 1417.5 blackstones with Reblath+14
[ulist]
[*]At 250k per stone and repair, this comes out to 354mil
[/ulist]

[/ulist]
The cost of DUO/TRI/TET Grunil as dictated by the market is:
[ulist]
[*]PRI->DUO – 40m
[*]DUO->TRI – 80m
[*]TRI->TET – 120m
[/ulist]
Using this and the KR enhancement table, it is now possible to work out all 8 scenarios and the cost of building additional failstacks using these.
DUO Grunil 30 stacks
((40 + 4) * 0.8 + (68.6 + 4 – 80) * 0.2) / 0.8 = 42.15m for 4 more stacks
TRI Grunil 30 stacks
((80 + 4) * 0.905 + (68.6 + 4 – 120) * 0.095) / 0.905 = 79m for 5 more stacks
DUO Grunil 40 stacks
((40 + 4) * 0.75 + (354 + 4 – 80) * 0.25) / 0.75 = 136.67m for 4 more stacks
TRI Grunil 40 stacks
((80 + 4) * 0.88 + (354 + 4 – 120) * 0.12) / 0.88 = 116.5m for 5 more stacks
 
And of course the cost using Reblath method.
[ulist]
[*]Average stones used for 4 stacks = 1 + 0.85 + 0.85^2 + 0.85^3 = 3.19
[*]Average stones used for 5 stacks = 1 + 0.85 + 0.85^2 + 0.85^3 + 0.85^4 = 3.71
[/ulist]
How the above is derived can be found in an earlier article: https://bdomaths.wordpress.com/2016/07/15/demythifying-failstacks/
Reblath 30 stacks -> 34
((68.6 + 3.19 * 0.25) * (1-0.85^4) + 3.19 * 0.25 * 0.85^4) / 0.85^4 = 64.3m for 4 more stacks
Reblath 30 stacks -> 35
((68.6 + 3.71 * 0.25) * (1-0.85^5) + 3.71 * 0.25 * 0.85^5) / 0.85^5 = 88.1m for 5 more stacks
Reblath 40 stacks -> 44
((354+ 3.19 * 0.25) * (1-0.85^4) + 3.19 * 0.25 * 0.85^4) / 0.85^4 = 325.7m for 4 more stacks
Reblath 40 stacks -> 45
((354+ 3.71 * 0.25) * (1-0.85^5) + 3.71 * 0.25 * 0.85^5) / 0.85^5 = 445.9m for 5 more stacks
Conclusion:
The numbers are self-explanatory. The values used in the market prices of various Grunil pieces are before tax, so they slightly understate the cost of building stacks using the high enhance armor fail method.
Because of how simple these equations are, I’m not going to elaborate on these findings in more detail. Feel free to play around with them by substituting different armor costs and come up with your own conclusions.
Additional thoughts:
Given these numbers, it’s pretty obvious anyone with their hands on the enhancement equations can easily manipulate this mechanic with Value Pack. This is also a proof of concept on how to directly accumulate a Valk’s Cry effect on your enhancement through buying and selling gear with Value Pack. In order to prevent the market from being ruined more than it is already, I have no intention of releasing the specifics of this strategy at this point in time.

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