#### Laozi

##### Member

Introduction

Cape is a GB that produces FPs only. There has been much debate over whether one should build Cape (e.g. see the comments on the Cape wikia page), since it seems to cost more FPs than it generates. The problem is actually straight-forward: given the amount of FPs needed to level Cape, can a player reach break-even within a reasonable time frame? However, there has been no quantitative analysis to date, which is the purpose of this guide.

Method

Consider the following scenario that allows us to obtain a rough estimate on the shortest time required to reach break-even. Assume that all reward spots are taken by free donors with 1.8 - 1.9x Arc boost and that the owner contributes the remaining FPs. The total investment on each level can thus be obtained. By

Results

Before presenting the complete results let us examine 2 cases which will illustrate how the algorithm works.

A target level of 1 simply means bringing Cape out of mud and letting it sit at level 1. At level 0, there are 2 free donors, contributing 19 FP for 1st place and 10 FP for 2nd. The owner contributes the remaining 60 - 19 - 10 = 31 FP. The total investment is 31 FP. Remaining at level 1 gives the owner 2 FP per day without further investment. Therefore, this will require 31 / 2 = 15.5 days to reach break-even. In other words, Cape becomes profitable beyond day 16.

Cape is often benchmarked against SoK. Cape occupies 20 tiles, equivalent to 5 SoKs. Therefore, in terms of space efficiency, Cape should generate 5 FPs per day just to be on par with SoK. This is accomplished with a target level of 5, where the net total investment by the owner is 618 FPs. This will require 618 / 5 = 123.6 days, or about 4 months, to reach break-even.

The following figure shows the number of days to reach break-even (denoted as D hereafter) for target levels 1-79 and free donors with 1.8x, 1.85x, and 1.9x Arc boost. The black point at level 5 is the benchmark with respect to SoK as discussed above.

We make the following important observations:

Close-up around 0 line:

Strategies on target levels

Best strategy: target level 60

Fastest for break-even (8 months); profits are better than even level 80 within a time frame of 1.5 years.

Worst strategy: target level 21

Slowest for break-even (1 year); profits are very poor, even worse than level 10 within a time frame of around 450 days.

Practical strategy

In practice, I believe few players would wait to amass 50 sets of blueprints and the required 14135 FPs before building Cape. A practical way is to rush level in 2 stages. In stage 1, build Cape and end at level 10. In stage 2, upgrade to level 60 as fast as possible.

Concluding Remarks

While the presented model ignores (i) other sources of donors (e.g. goods buyers, competitive bidders, altruistic friends), (ii) alternative modes of leveling (e.g. swap-based leveling instead of self-leveling), and (iii) possible setbacks (e.g. owner bought goods with FPs to build Cape, denial of 1.9x donors due to snipers or mistakes), it provides a controlled and well-defined estimate for D.

So, "Is Cape worth building?" If you plan to play longer than the corresponding D of your target level, the answer is yes. Moreover,

As a final note, this analysis only provides a working strategy of getting a return on FPs from Cape within the least amount of time. It does not mean that one should never level Cape beyond 60.

Cape is a GB that produces FPs only. There has been much debate over whether one should build Cape (e.g. see the comments on the Cape wikia page), since it seems to cost more FPs than it generates. The problem is actually straight-forward: given the amount of FPs needed to level Cape, can a player reach break-even within a reasonable time frame? However, there has been no quantitative analysis to date, which is the purpose of this guide.

Method

Consider the following scenario that allows us to obtain a rough estimate on the shortest time required to reach break-even. Assume that all reward spots are taken by free donors with 1.8 - 1.9x Arc boost and that the owner contributes the remaining FPs. The total investment on each level can thus be obtained. By

*ansatz*, assume that the owner flips Cape to a target level using the said FP allocation within 1 day, reinvests all the FPs generated upon leveling, and collects every day afterwards, waiting for the day of break-even. (The reason for adopting this strategy will become apparent after seeing the complete results.)Results

Before presenting the complete results let us examine 2 cases which will illustrate how the algorithm works.

__Case study: Target level 1__A target level of 1 simply means bringing Cape out of mud and letting it sit at level 1. At level 0, there are 2 free donors, contributing 19 FP for 1st place and 10 FP for 2nd. The owner contributes the remaining 60 - 19 - 10 = 31 FP. The total investment is 31 FP. Remaining at level 1 gives the owner 2 FP per day without further investment. Therefore, this will require 31 / 2 = 15.5 days to reach break-even. In other words, Cape becomes profitable beyond day 16.

__Case study: Break-even with respect to Shrine of Knowledge__Cape is often benchmarked against SoK. Cape occupies 20 tiles, equivalent to 5 SoKs. Therefore, in terms of space efficiency, Cape should generate 5 FPs per day just to be on par with SoK. This is accomplished with a target level of 5, where the net total investment by the owner is 618 FPs. This will require 618 / 5 = 123.6 days, or about 4 months, to reach break-even.

__Complete results__The following figure shows the number of days to reach break-even (denoted as D hereafter) for target levels 1-79 and free donors with 1.8x, 1.85x, and 1.9x Arc boost. The black point at level 5 is the benchmark with respect to SoK as discussed above.

We make the following important observations:

- D increases dramatically at the lower levels.
- The dent at level 10 is caused by an increase of 2 FP from level 9, reducing the rate of increase in D.
- The rate of increase in D slows down beyond level 10. This is due to the increased ratio of rewards, which reduces the portion of investment by self-leveling.
- D obtains a local maximum (blue points) at a target level of 21 (1.9x) or 22 (1.8x, 1.85x). The owner needs to wait for almost a year before s/he gets a return on FPs.
- D decreases to a local minimum (red points) at level 57-60 for 1.8-1.9x donors, corresponding to 302 days (10 months) down to 236 days (8 months).
- Going to higher levels, the drop in reward ratio causes D to increase again. Currently there is no evidence that D will ever drop again.

Close-up around 0 line:

Strategies on target levels

Best strategy: target level 60

Fastest for break-even (8 months); profits are better than even level 80 within a time frame of 1.5 years.

Worst strategy: target level 21

Slowest for break-even (1 year); profits are very poor, even worse than level 10 within a time frame of around 450 days.

Practical strategy

In practice, I believe few players would wait to amass 50 sets of blueprints and the required 14135 FPs before building Cape. A practical way is to rush level in 2 stages. In stage 1, build Cape and end at level 10. In stage 2, upgrade to level 60 as fast as possible.

Concluding Remarks

While the presented model ignores (i) other sources of donors (e.g. goods buyers, competitive bidders, altruistic friends), (ii) alternative modes of leveling (e.g. swap-based leveling instead of self-leveling), and (iii) possible setbacks (e.g. owner bought goods with FPs to build Cape, denial of 1.9x donors due to snipers or mistakes), it provides a controlled and well-defined estimate for D.

So, "Is Cape worth building?" If you plan to play longer than the corresponding D of your target level, the answer is yes. Moreover,

**if you go beyond level 10, it is important not to sit at around level 20 (worst) but to reach level 60 (optimal) as soon as possible**, where D is about 8 months with 1.9x free donors and the net total investment is 14135 FPs;**otherwise, the day of profitability could be significantly delayed**.As a final note, this analysis only provides a working strategy of getting a return on FPs from Cape within the least amount of time. It does not mean that one should never level Cape beyond 60.

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