Subject

[Research] RNG as a paywall [Analysis, Paywall]

Posting this to the forum so I can reference it in the future.

==HOTM==

For a 99% chance of getting the hero of the month, you would spend $1,049.89 USD in gems.

Note: used wrong example of 1 in 100 chance, find a better one than poker.

With 10,000 players, 100+ will fail to get the Hero of the month even if they spend $500 USD.

==Elemental Summons==

Note: find out odds after October challenge event.

==Seasonal Event==

Note: find out odds Oct 22.

==Epic Token==

==yellow 5* Joon==

If you earned 1 Epic Token per day,

for a 99% chance of getting yellow 5* Joon, you would need to wait 16.8 years.

With 10,000 players, 100+ will fail to get yellow 5* Joon even if they get 1 Epic Token per day for 8 years.

==yellow 4* Wu Kong==

If you earned 1 Epic Token per day,

for a 99% chance of getting yellow 4* Wu Kong, you would need to wait 1 year.

With 10,000 players, 100+ will fail to get yellow Wu Kong even if they get 1 Epic Token per day for 6 months.

==Legendary Training==

==yellow 5* Joon==

If you collect 1 legendary training per 2 days,

for a 99% chance of getting yellow 5* Joon, you would need to wait 10 years.

With 10,000 players, 100+ will fail to get yellow 5* Joon even if they collect 1 legendary training every 2 days for 5 years.

==yellow 4* Wu Kong==

If you collect 1 legendary training per 2 days,

for a 99% chance of getting yellow 4* Wu Kong, you would need to wait 1 year and 4 months.

With 10,000 players, 100+ will fail to get yellow 4* Wu Kong even if they collect 1 legendary training every 2 days for 1 years.

MY PERSONAL OPINION

I would prefer a way of directly buying a hero, like buying a Magic The Gathering card. Gryphonkit is sitting on 5x green 4* Hanzel and Noblessa is sitting on 3x yellow 5* Delilah, so trade would greatly enhance their Empires experience. Or enhance everyone’s experience and do both direct purchase and trade. This also ties into other another paywall, summoning heroes at tier 1, level 1.

EQUATIONS

==HOTM==

HOTM 1.3%

X Summons for 99% chance

( 1 - .013 ) ^ x = 0.01%

0.987 ^ x = 0.01

x = log ( 0.01 ) / log ( 0.987 )

= 351.93

Check

0.987^ 351.93 = 0.01

351 summons * 300 gems = 105,000 gems

10k gems = $99.99 USD

( 105k / 10k ) * $99.99 USD = $1,049.89

==Epic Token==

Legendary 1.5%

Purple 4 Sartana

Yellow 4 Joon

Blue 4 Magni

Green 4 Leggylass

Red 4 Marjana

= 20 = 0.075% each

0.075% Joon

X Summons for 99% chance

( 1 - 0.00075 ) ^ x = 0.01%

0.99925 ^ x = 0.01

x = log ( 0.01 ) / log ( 0.99925 )

= 6,137.92

Check

0.99925^ 6,137.92 = 0.01

1 epic token per day= 6,137 / 365 = 16.8 years

Epic 26.5%

Purple 4 Rigard

Yellow 4 Wu Kong

Blue 4 Grimm

Green 5 Melendor

Red 5 Boldtusk

= 22 = 1.2% each

1.2% Wu Kong

X Summons for 99% chance

( 1 - 0.012 ) ^ x = 0.01%

0.988 ^ x = 0.01

x = log ( 0.01 ) / log ( 0.988 )

= 381.45

Check

0.988^ 381.45 = 0.01

1 epic token per day= 381 / 365 = 1 year

==Legendary Training==

Legendary ~5%

Purple 4 Sartana

Yellow 4 Joon

Blue 4 Magni

Green 4 Leggylass

Red 4 Marjana

= 20 = ~0.25% each

~0.25% Joon

X Summons for 99% chance

( 1 - 0.0025 ) ^ x = 0.01%

0.9975 ^ x = 0.01

x = log ( 0.01 ) / log ( 0.9975 )

= 1,839.76

Check

0.9975^ 1,839.76 = 0.01

1 legendary training per 2 days = 3,678 days / 365 = 10 years

Epic ~20%

Purple 4 Rigard

Yellow 4 Wu Kong

Blue 4 Grimm

Green 5 Melendor

Red 5 Boldtusk

= 22 = ~0.91% each

~0.91% Wu Kong

X Summons for 99% chance

( 1 - .9909 ) ^ x = 0.01%

0.9909 ^ x = 0.01

x = log ( 0.01 ) / log ( 0.9909 )

= 503.75

Check

0.9909 ^ 503.75 = 0.01

1 legendary training per 2 days = 503 days / 31 days per mont = 16 months= 1 year 4 months

-=

### Anecdotal Example

## Click for missing Boril and Cyprian

Started 2017-Sep

Daily Summons ( 1* to 3* heroes and 1* to 3* troops ) and Gem Summons ( 3* to 5* heroes ):

Current mission Summon Heroes V= 1064 / 1500

Training camps

Legendary training since 2018-Mar

VIP Pass

Continuous since 2018-Feb

IAP from 2017-Sep to 2019-Jun

$3,020 USD

FIN