[Calculation] Builders Without Buying Gems Or Maxing All Achievements

Due to the new achievements added in the last few updates, you can now afford all five builders. Completing all the achievements will now give you 6,432 gems, enough to buy all 5 builders. However, some of the high-yielding achievements such as "Unbreakable" and "Firefighter", are very tough to achieve for most people. So I am going to calculate how long it would take you to get all 5 builders on removing obstacles alone.

Every 8 hours, a new obstacle spawns in your village (Provided that you do not have 40 obstacles already). When you remove an obstacle, you have an equal chance of receiving 0, 1, 2, or 3 gems per obstacle.

Expected Value = 0 (0.25) + 1 (0.25) + 2 (0.25) + 3 (0.25)
Expected Value = 0 + 0.25 + 0.5 + 0.75
Expected Value = 1.5 gems

On average, over the course of a long time, you would get an average of 1.5 gems per tree, bush, or trunk removed. Let's see how long it would take you to get a third, fourth, or fifth builder on removing obstacles alone.

Third Builder: 500 gems
500 gems / 1.5 gems = 333.33 obstacles needed to be removed (On average).
333.33 obstacles * 8 hours = 2,666.67 hours
2,666.67 hours / 24 hours = 111.11 days
111.11 days = 3.7 months (approximately)

Fourth Builder: 1000 gems
1000 gems / 1.5 gems = 666.67 obstacles needed to be removed (On average).
666.67 obstacles * 8 hours = 5,333.33 hours
5,333.33 hours / 24 hours = 222.22 days
222.22 days = 7.4 months (approximately)

Fifth Builder: 2000 gems
2000 gems / 1.5 gems = 1,333.33 obstacles needed to be removed (On average).
1,333.33 obstacles * 8 hours = 10,666.67 hours
10,666.67 hours / 24 hours = 444.44 days
444.44 days = 14.8 months

To get all three extra builders, you will need to play for 777.78 days, which is around 25.9 months.

Achievements are good, aren't they?

Here's a little extra thing:
How about the XP points you will get for removing all these obstacles? The possible obstacles that will spawn are: Mushroom, Bush, Trunk (1), Trunk (2), Trunk (Fallen), Tree (Small), Tree (Medium), Tree (Large).

Expected Value = 3 (0.1) + 3 (0.2) + 5 (0.1) + 5 (0.1) + 5 (0.2) + 5 (0.2) + 6 (0.05) + 7 (0.05)
Expected Value = 0.3 + 0.6 + 0.5 + 0.5 + 1.0 + 1.0 + 0.3 + 0.35
Expected Value = 4.55 XP

4.55 * (333.33 + 666.67 + 1,333.33) = 10,616.6515 XP points.

That's a lot of XP points. :)

10 characters
:p
Attachment 25339

That is crazy! Thank goodness for achievements.

Just wow..

I guess if anyone ever wondered.... now they know. :)

More acheivents We want more!

:eek:




















:rolleyes:

Quote:

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Originally Posted by AntarcticTern

Due to the new achievements added in the last few updates, you can now afford all five builders. Completing all the achievements will now give you 6,432 gems, enough to buy all 5 builders. However, some of the high-yielding achievements such as "Unbreakable" and "Firefighter", are very tough to achieve for most people. So I am going to calculate how long it would take you to get all 5 builders on removing obstacles alone.

Every 8 hours, a new obstacle spawns in your village (Provided that you do not have 40 obstacles already). When you remove an obstacle, you have an equal chance of receiving 0, 1, 2, or 3 gems per obstacle.

Expected Value = 0 (0.25) + 1 (0.25) + 2 (0.25) + 3 (0.25)
Expected Value = 0 + 0.25 + 0.5 + 0.75
Expected Value = 1.5 gems

On average, over the course of a long time, you would get an average of 1.5 gems per tree, bush, or trunk removed. Let's see how long it would take you to get a third, fourth, or fifth builder on removing obstacles alone.

Third Builder: 500 gems
500 gems / 1.5 gems = 333.33 obstacles needed to be removed (On average).
333.33 obstacles * 8 hours = 2,666.67 hours
2,666.67 hours / 24 hours = 111.11 days
111.11 days = 3.7 months (approximately)

Fourth Builder: 1000 gems
1000 gems / 1.5 gems = 666.67 obstacles needed to be removed (On average).
666.67 obstacles * 8 hours = 5,333.33 hours
5,333.33 hours / 24 hours = 222.22 days
222.22 days = 7.4 months (approximately)

Fifth Builder: 2000 gems
2000 gems / 1.5 gems = 1,333.33 obstacles needed to be removed (On average).
1,333.33 obstacles * 8 hours = 10,666.67 hours
10,666.67 hours / 24 hours = 444.44 days
444.44 days = 14.8 months

To get all three extra builders, you will need to play for 777.78 days, which is around 25.9 months.

Achievements are good, aren't they?

Here's a little extra thing:
How about the XP points you will get for removing all these obstacles? The possible obstacles that will spawn are: Mushroom, Bush, Trunk (1), Trunk (2), Trunk (Fallen), Tree (Small), Tree (Medium), Tree (Large).

Expected Value = 3 (0.1) + 3 (0.2) + 5 (0.1) + 5 (0.1) + 5 (0.2) + 5 (0.2) + 6 (0.05) + 7 (0.05)
Expected Value = 0.3 + 0.6 + 0.5 + 0.5 + 1.0 + 1.0 + 0.3 + 0.35
Expected Value = 4.55 XP

4.55 * (333.33 + 666.67 + 1,333.33) = 10,616.6515 XP points.

That's a lot of XP points. :)

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You just made my brain explode with math

Quote:

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Originally Posted by comandodude101

You just made my brain explode with math

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Your welcome :)

Thank you SC for achievments

Quote:

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Originally Posted by AntarcticTern

So I am going to calculate how long it would take you to get all 5 builders on removing obstacles alone.

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Stopped reading here. Pointless calculation.

Might as well calculate the time needed to max TH10 using gold from collectors only.

Quote:

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Originally Posted by Sandalhat

Stopped reading here. Pointless calculation.

Might as well calculate the time needed to max TH10 using gold from collectors only.

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Please do this AntarcticTern!:rolleyes:

Quote:

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Originally Posted by Sandalhat

Stopped reading here. Pointless calculation.

Might as well calculate the time needed to max TH10 using gold from collectors only.

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Collectors don't make gold so it's impossible

Quote:

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Originally Posted by AntarcticTern

Total Cost (Gold, With Walls) - 2,841,861,450 Gold
Total Cost (Gold Without Walls) - 636,561,450 Gold


Total Cost (Elixir, With Troops/Spells) - 299,062,850 Elixir
Total Cost (Elixir, Without Troops/Spells) - 159,212,850 Elixir


Total Cost (Dark Elixir) - 8,720,000 Dark Elixir

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21,000 gold an hour with townhall 10 maxed mines, 504,000 gold a day, 2841861450/504000 is 5,638 days, or 15.5 years to max gold

21,000 elix an hour, 504,000 elix a day, would take 593 days, or a little over 1 and a half years to max elixir

300 de an hour, 7,200 de a day, would take 1,211 days, or a little under 3 and a half years

don't forget these are all approximates which means you can be either really lucky and clearing obstacles and getting 3 gems everytime which totals to 9 a day, or you can get nothing.
500/1000/2000.
best possible outcome. 3500/9=388.88 days

Also, where did you find the extraction that the probability of getting gems are equal? I would assume there is a distribution.
Something along the lines of.
50% chance of getting gems, 50% not getting gems.
If Gems ->
25% chance for 1 gem
15% chance for 2 gems
and 10% chance for 3 gems

the expected # of gems for each obstacle removal is 1 gem. they might have unequal chances of getting 0, 1, 2 and 3 gems.
i think it is stated in the wiki.

Quote:

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Originally Posted by sexysoup

the expected # of gems for each obstacle removal is 1 gem. they might have unequal chances of getting 0, 1, 2 and 3 gems.
i think it is stated in the wiki.

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Hmm, maybe you're right :)

I'm pretty sure there's an equal chance though.

That's why achievments help a TON.

the best calculation is..
get to 1260 trophies by sniping (3rd builder 500gems)
go to 2600 trophies by sniping (4th builder 1000gems)
less than 2 months

Quote:

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Originally Posted by Yoshimuraxx

the best calculation is..
get to 1260 trophies by sniping (3rd builder 500gems)
go to 2600 trophies by sniping (4th builder 1000gems)
less than 2 months

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Assuming you can trophy push to Master League :)