Beards of Power

“

Locally sourced from a fat goblin's armpit hair.

”

Beards of Power is a feature that is unlocked by using UUG's Armpit Hair, which is a guaranteed drop from UUG, The Unmentionable.

It enables you to grow different kinds of beards using the excess energy generated after the resource has capped (aka mostly based on bars), which each give different kinds of temporary bonuses. If a beard slot is active at rebirth, a part of that temporary bonus then becomes permanent. You can only have as many Beards active as you have Beard Slots. There are 7 beards and 7 beard slots.

Permanent Levels

Permanent levels gained on rebirth is given by

$\min( \lfloor\sqrt{\mathit{temporary\ beard\ level}} \times \mathit{timefactor} \rfloor , temporary\ beard\ level )$

The time factor is 0 initially, and increases additively by 1/3 every hour until the maximum of 8 after 24 hours of rebirth time (-1 hour for every level of the Five O'Clock Shadow perk, to a maximum of 12 hours).

If the permanent level gained on rebirth calculated with the above equation is higher than the temporary level, the permanent level gained will be equivalent to the temporary level instead. For example, at 50 temporary level, 56 permanent level will be supposedly gained on rebirth with a time factor of 8. Since that is higher than the temporary level, only 50 permanent level will actually be gained.

Graph (v6)

Progress

Progress per tick is defined by formula:

$\dfrac{Bars \times \sqrt{Power} \times (1 + Equip_{BeardSpeed})}{SpeedDivider \times (level + 1) \times Beards_{SameResource}} \times Digger_{Beards} \times Quirk_{Beards}$

Bars and Power refer to resource used by the beard (Energy or Magic). Beardverse (set) reward reduces Beards_SameResource penalty by 10% (0.9 of beards count with same resource). Speed dividers differ per beard and are as follows:

Beard	Speed divider
The Fu Manchu	10000000 (1e7)
The Neckbeard	30000000 (3e7)
The Reverse Hitler	30000000 (3e7)
The Beard Cage	100000000 (1e8)
The LadyBeard	100000000 (1e8)
The BEARd	300000000 (3e8)
The Golden Beard	300000000 (3e8)

The Beards

There are currently 7 beards, which grow using either Energy or Magic. (EM Bars multiplied by EM Power square root). 

The Fu Manchu

• Grants an Attack/Defense bonus.
• Magic based.
• Bonus:$f(L) = L \times 5\%$
• Permanent Bonus:$f(L) = L \times 1\%$

The Neckbeard

• Grants a Drop Chance bonus.
• Energy based.
• Bonus:$f(L) = \begin{cases} L \times 0.05\%, & L \le 1000 \\ L^{0.3} \times 125.9 \times 0.05\%, & L > 1000 \end{cases}$

• Permanent Bonus:$f(L) = \begin{cases} L \times 0.05\%, & L \le 1000 \\ L^{0.33} \times 102.4 \times 0.05\%, & L > 1000 \end{cases}$

The Reverse Hitler

• Grants a NUMBER bonus.
• Magic based.
• Bonus:$f(L) = \begin{cases} L \times 1\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 1\%, & L > 1000 \end{cases}$

• Permanent Bonus:$f(L) = \begin{cases} L \times 0.1\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.1\%, & L > 1000 \end{cases}$

The Beard Cage

• Grants a NGU speed bonus.
• Energy based.
• Bonus:$f(L) = \begin{cases} L \times 0.01\%, & L \le 1000 \\ L^{0.3} \times 125.9 \times 0.01\%, & L > 1000 \end{cases}$
• Permanent Bonus:$f(L) = \begin{cases} L \times 0.02\%, & L \le 1000 \\ L^{0.3} \times 125.9 \times 0.02\%, & L > 1000 \end{cases}$

The LadyBeard

• Grants a Wandoos speed bonus.
• Magic based.
• Bonus:$f(L) = \begin{cases} L \times 0.1\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.1\%, & L > 1000 \end{cases}$

• Permanent Bonus:$f(L) = \begin{cases} L \times 0.2\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.2\%, & L > 1000 \end{cases}$

The BEARd

• Grants an Adventure stats bonus.
• Energy based.
• Bonus:$f(L) = \begin{cases} L \times 0.1\%, & L \le 1000 \\ L^{0.3} \times 125.9 \times 0.1\%, & L > 1000 \end{cases}$

• Permanent Bonus:$f(L) = \begin{cases} L \times 0.05\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.05\%, & L > 1000 \end{cases}$

The Golden Beard

Unlocked by completing the 7th Troll Challenge.

• Grants a Gold (Time Machine) bonus.
• Magic based.
• Bonus:$f(L) = \begin{cases} L \times 0.2\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.2\%, & L > 1000 \end{cases}$

• Permanent Bonus:$f(L) = \begin{cases} L \times 0.5\%, & L \le 1000 \\ L^{0.5} \times 31.7 \times 0.5\%, & L > 1000 \end{cases}$

Extra Slots

There are 7 total beard slots, found via the following methods:

• 1 upon unlocking feature
• 1 from Troll Challenge, completion 4
• 1 from EXP shop (50,000 EXP)
• 4 from 4G's Sellout Shop

Beards of Power upgrades

There are several upgrades that improve different aspects of Beards of Power:

• Normal Troll Challenges 4 and 7

4G's Sellout Shop

Name	Effect	Price (AP)
An Extra Beard Slot!	+1 Beard Slot.	110,000 (first) 225,000 (second to fourth)

Perks

Name	Effect	Price (PP)	Levels	Difficulty
Five O'Clock Shadow	The time factor will reach its maximum 1 hour sooner per level, to a minimum of 12 hours.	10	12	Normal
Beard Temp Level Bank I	Banks +10% of temp Beard level for the next rebirth.	3	10	Normal
Beard Temp Level Bank II	Banks +10% of temp Beard level for the next rebirth.	10	10	Normal
Beard Temp Level Bank III	Banks +10% of temp Beard level for the next rebirth.	25	10	Evil
Beard Temp Level Bank IV	Banks +10% of temp Beard level for the next rebirth.	50	10	Evil
Beard Temp Level Bank V	Banks +10% of temp Beard level for the next rebirth.	100	10	Evil

Quirks

Name	Effect	Price (QP)	Levels	Difficulty
The Beast's Special Beard Tonic	+1% Beard Speed per level.	50	50	Normal
Beard Temp Level Bank I	Banks +5% of temp Beard level for the next rebirth.	100	10	Normal
Beard Temp Level Bank II	Banks +5% of temp Beard level for the next rebirth.	250	10	Normal
Beard Temp Level Bank III	Banks +5% of temp Beard level for the next rebirth.	500	10	Evil
Beard Temp Level Bank IV	Banks +5% of temp Beard level for the next rebirth.	1,000	10	Evil
Beard Temp Level Bank V	Banks +5% of temp Beard level for the next rebirth.	2,000	10	Evil

Items

Item	Effect	Source
Armpit Set	+10% Beard Speed	UUG, The Unmentionable
Beardverse Set	10% reduced penalty to levelling speed, when equipping multiple beards that use Energy or Magic at the same time!	The Beardverse
Build Beard Speed	Gain Beard Speed.

Other features

• Energy/Magic Beard Digger

Figures

The following graphs show the diminishing returns for beards up to level 10,000:

https://imgur.com/a/RmNSX2C