Magic/calculations

Based on the information from Magic.

Based on that we might need to make a calculator (when the investments pay off?).

Take into account, we don't have the formula of hired-mage increase, so the calculator could only give some approximate time then (if created).

Plan A. First hire 1 mage; then 1/3/6 to catch up
Maths of Upgrading Mages.

Two projects.

Before.

VARIABLES

- budget = 50k

- main mage: shards per hour = 66

- main mage: % chance to get 2x shards = 8%

- shard per hour upgrade cost = 5.7k

- hiring mage: cost per hour1 = 730 (at 66 + 8%)

* - hiring mage: cost per hour2 = 734 (if upgraded 66->67 + 8%)

COUNTING VARIABLES:

NOW (if 66 + 8%)

1) - hiring mage: shards per hour1 = 66/2 = 33

2) - hiring mage: % chance to get 2x shards1 = 8%/2 = 4%

3) - main mage: shards per hour, adjusted on %-chance1 = 66*2*8% + 66*1*(100%−8%) = 71.28

4) - hiring mage: shards per hour, adjusted on %-chance1 = 33*2*4% + 33*1*(100%−4%) = 34.32

NEW (if 67 + 8%)

1) - hiring mage: shards per hour2 = 67/2 = 33.5

{it is now correct, because it will be floored to 33, but whatever}

2) - hiring mage: % chance to get 2x shards2 = 8%/2 = 4%

3) - main mage: shards per hour, adjusted on %-chance2 = 67*2*8% + 67*1*(100%−8%) = 72.36

4) - hiring mage: shards per hour, adjusted on %-chance2 = 33.5*2*4% + 33.5*1*(100%−4%) = 34.84

===

Project 1.

Invest in one mage (50k).

Project 2.

Buy one upgrade (5.7k). Invest in one mage the rest (50k − 5.7k).

{Tip: Hiring one or seven mages will give the same amount of shards}

{Tip: Though the mefail's calculators says that there is difference. Hm. If it because of flooring?)

===

Calculations.

Project 1.

Hours_hiring_mage_works1 = 50k / 730 = 68.5 hours (with 34.32 shards per hour, adjusted).

Total_hiring_mage_makes1 = 68.5*34.32 = 2350.92

Total_main_mage_will_make1 = 71.28*68.5 = 4882.68

SubSubtotal1 = 2350.92 + 4882.68 = 7233.6 (in 68.5 hours)

Project 2.

Hours_hiring_mage_works2 = (50k−5.7k) / 734 = 60.35 hours (with 34.84 shards per hour, adjusted).

Total_hiring_mage_makes2 = 60.35*34.84 = 2102.59

//Hours_that_main_mage_will_be_alone = 68.5 − 60.35 = 8.15

Total_main_mage_will_make2 = 72.36*68.5 = 4956.66

{Tip: to harmonize the time, we took the main mage time as constant, 68.5. So if project 2 main mage will work alone for a long time}

SubSubtotal2 = 2102.59 + 4956.66 = 7059.25 (in 68.5 hours)

SUBTOTAL

All hired mages dissapeared.

7059.25 − 7233.6 = (−174.35) shards lost in 68.5 hours.

====

{How many time do we need to recover those 174.35 with a new efficiency?

That is when the number of mages matter}

With no hired mages:

174.35 / (72.36 − 71.28) = 161.44 (7 days)

With three hired mages:

174.35 / ((72.36 − 71.28) + 3*(34.84 − 34.32)) = 66.04 (3 days)

With all (six) hired mages

174.35 / ((72.36 − 71.28) + 6*(34.84 − 34.32)) = 41.51 (2 days)

Plan B. First hire 6 (all) mages; then 1/3/6 to catch up
Maths of Upgrading Mages.

Two projects.