DID YOU KNOW? - CHANCES

How do you calculate the evasion percent if you have 4 butterfly?
How do you calculate the chances to block 40 damage having 2 vanguard?

4 Butterfly

Alot people misunderstand this,
Each butterfly gives you 30% chance to evade attack. So getting 4 butterfly will give you 120% evasion. Means you will not get hurt at all. Every hit on you will be evaded. This is godlike!!

Well, that is NOT true. If you have 4 butterfly, it will check each butterfly chances. First it check for the first butterfly whether it was evaded. If it was not evaded, it will check for the second butterfly, third , blah blah blah

So, what is the chances of evasion if you have 4 butterfly? The formula is this

% Evasion = (1 - ((1-0.3) * (1-0.3) * (1-0.3) * (1-0.3))) *100 %
= 75.99%
means for every 4 hits, there will be 3 hits which is evaded. It is still like godlike.

2 Vanguard

What if you have 2 vanguard on axe? 1 vanguard gives you 65% to evade 40 damage. Then having 2 vanguard will give you 130% to evade 40 damage. Means creep cannot hurt you at all.

Well, it is NOT true again.

% = ( 1-((1-0.65)*(1-0.65)) ) * 100 %
= 87.75 % to evade 40 damage

means that for 10 creeps that hit you, only 1 or 2 creep will effectively damage you.

1 butterfly + 1 radiance

butterfly gives you 30% evasion while radiance gives you 8% evasion. So what is the actual evasion? It seems to be 38% evasion

% = ( 1-((1-0.30)*(1-0.08)) ) * 100 %
= 35.6%

5 buriza de kyano

buriza give you 20% to critical 2.2x. So logically, 5 buriza will give you 100% to critical 2.2x. Very painful.

Well, having 5 buriza only give you

% = ( 1-((1-0.20)*(1-0.20)*(1-0.20)*(1-0.20)*(1-0.20) ) ) * 100 %
= 67.23 % to critical 2.2x

That is like for every 3 hits , there will be 2 hits which has critical.

Summary

All chances on dota is using this formula
% = (1 - ( (1-(percent)) * (1-(percent)) * (1-(percent))) * 100 )

So, If you meet a hero with 4 butterfly, you still can kill him.