General DiscussionBye bye PRC(pseudo random chance) : simple and fair effect chance cal...

In this post i show alternate system for PRC. It is used in dota 2 mostly for bashes and in my opinion they need a better balance.
A chance of having bash on autoattack is named here effect occur chance(our effect is bash)

I will use such names like: (just go back here if u forget something)
Effect Occur Chance(EOC)
Starting EOC(sEOC) usually sEOC=AEOC
EOC Increase per effect not occur(EOCi)
EOC decrease per effect occur(EOCd)
Effect Occur(O)
Effect Not Occur(NO)
Average Effect Occur Chance(AEOC)

I will show 3 exaples: 50%,33,(3)% and most common in dota2 25%
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We start from most simple chance to easy understand it - AEOC = 50%

sEOC=50% This is not so important but we need to start with something

EOCi =20% EOCd=20%
RCi : RCd <==> 2 : 2 <==> 50:50
and thats why our choosen chance is 50 %

When our effect will occur (f.e. we will bash enemy unit) our EOC will lower it's value and when it does not EOC will become bigger

Lets start from 4 charges(sEOC=4) (50%):
50% -> NO -> 70%

When effect effect occurs (O) calculate next RC = previous RC - RCd
When it doesnt (NO) RC = RC + RCi (50% + 20% = 70%)

Effect didnt occur but now we have chance to bash 70% (EOC=70%)
Check a longer effect occur/not occur list starting from sEOC=50% and ending at same value

50% -> NO -> 70% -> NO -> 90% -> O -> 70% -> NO -> 90% -> NO -> 110%
(if EOC>=100% next time effect will surely occur )
-> O -> 90% -> O -> 70% -> O -> 50%

In this period NO count was 4 and O count also 4 so
O/NO == 4 : 4 - it's 50% chance for effect to occur

Look another example when we have much luck at beginning and our effect occurs several times:

50% -> O -> 30% -> O -> 10% -> O -> -10% ->
We got our effect twice with 50% chance first time, 30% second and 10% third so we were lucky but now
-> NO -> 10%
EOC=-10% so chance for effect = 0% and next time it will be only 10%
(if EOC<=0% next time effect will surely not occur)

The more effect occur the less it happens in future and contrary.
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Let' try now AEOC = 33,(3)%=1/3
That means on each one O we will have 2 NO
so EOCi : EOCd <==> 1 : 2

Let's say sEOC = 30% (to calculate easier, it's not interrupting balance much actually)
30% -> NO -> 40% -> NO -> 50% -> O -> 30%

NO count = 2 and O count = 1 as u see that works

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AEOC = 25%
Most important. Does it work? Let's check on exmaple on ♥♥♥♥*NG FACELLS VOID BASH

To greater balance sEOC = AEOC
sEOC = 2,5

EOCi : EOCd <==> 1 : 3 so it can also be 0,5 <==> 1,5 or 1,5 <==>4,5
and I will take the third option (but that's no matter all work)
so EOCi=1,5
and EOCd=4,5 (check that if u want AEOC=75% just takr sEOC=7,5 EOCi=4,5 and EOCd=1,5)

Let me play a bit:
25% -> O -> -20% -> NO -> -5% -> NO -> 10% -> NO -> 25% -> NO -> 40% -> NO -> 55% -> NO ->

-> 70% -> NO -> 85% -> NO -> 100% -> O -> 55% -> O -> 10% -> O -> -35% -> NO -> -20% -> NO ->

-> -5% -> NO -> 10% -> NO -> 25%

( remember that when EOC<0% next effect will not occur and when EOC>100% it will )

O count = 4 NO count = 12 so 4 : 12 <==> 1: 3 -> AEOC = 25%

Most common is that Void will not have bash 3 times and than have it but I showed extreme cases when effects occur in a row.
We can see that Void can attack without bash maximum(from -35% to 100%) 8 times which is very rare. You can calculate it by multiplying all chances on NO from -35% to to 100% but remember that
EOC = O chance
100% - O chance = NO chance
EOC<0% next effect will not occur and when EOC>100%

Void can also bash maximum 3 times in a row (100% to -35%) but remember that earlier he
hadn't bash long time and he will not get it soon in future. Actually he will have 0% bash chance next 3 times(-35% to -5%) and fourth time only 10%

BONUS
I will type this again but THIS time i typed additionally a chance of O/NO depending which happened

25% -> O -> -2 -> NO -> -0,5 -> NO -> 1 -> NO -> 2,5 -> NO -> 4 -> NO -> 5,5 -> NO ->
(25%) (100%) (100%) (90%) (75%) (60%) (45%)

I will not type further but u can see that if sEOC=-2 our chance to not have bash 8 times is
100% * 100% * 90% *75% * 60% * 45% * 30% * 15% = 9*7,5*6*4,5*3*1,5/1000000=
0,0082=0,82% so its less than 1% and even if it happens we will have 100 % chance for bash next time and big chance for nextnext bash so dont worry Void.