Just let me give my 2 or 3 cents to this.

Doing the amth for it is pretty useless becasue there are no numbers to start with. All you can do is assume one number or another.

If you start by saying "everything is fair" than chosing a champion and banning him is equal to "choosing to win with 50% probability".

Now the statement says "counterpicking increases you chance to win". So if you not "choose to win" but instead "choose to counterpick" your chances will be 50%+x.

X is unknown and as far as i am aware there is no statistics on counterpicking. So we only can assume it. So let X be 1%.

Now the math should be doable by everyone. If one pick gets 51% of winning, the other should be 49%.

Ok, here is where the complicated stuff begins:

Let there be 20 heroes. Let every hero have at least one counterpick.(no overpowered champion). Furthermore to make it easy, let the counterpick always be the hero+1.

Lets now see the order of the picks:

[--Bans--Picks---------]

ABBA ABBAABBAAB

Worst case scenario

A picks Hero 1

B picks Hero 2

B picks Hero 13

A picks Hero 5

A picks Hero 7

B picks Hero 6

B picks Hero 8

A picks Hero 10

A picks Hero 12

B picks Hero 11

This order would give B 5 heroes with each the ability "counterpick". while A has 0 counterpicks. In forms of Math: Devastating for Team A since B now can arrange their laning with the apropiate counterpick!

Best Case scenario

A picks Hero 1

B picks Hero 2

B picks Hero 3(to make sure A doesnt get counter)

A picks Hero 4

A picks Hero 5(to make sure B doesnt get counter)

B picks Hero 6

B picks Hero 7(to make sure A doesnt get counter)

A picks Hero 8

A picks Hero 9(to make sure B doesnt get counter)

B picks Hero 10

Team A now has 2 counterpicks

Team B now has 3 counterpicks

Since it is a odd number of heroes, there will always be a chance one has more counterpicks than others!

But as it is now, team B has ALWAYS the CHANCE to be this one group!

So, lets get in there a little bit further, as draft mode is like this:

[--Bans--Picks---------]

ABBA ABBAABBAAB

Team A starts off with the bans.

Question is: waht do you want to accomplish with your banns?

Do you want to bann heroes you dont want to play against?

Do you want to bann heroes you might think are OP?

Do you want to bann heroes you know are a counterpick to your team?

if you jsut bann heroes you dont WANT to play against you are nothing more than flipping a coin.(its not a strategy: "ahhhh i dont want to play against ashe, becasue i hate big boobed women"

As team A, you definitively do __NOT__ want to bann an OP champion!. At least not the most OP one. You are first to pick a champion, so you can pick the OP champion! As team A you want to bann OP number 2 and 3.

On the other side, as Team B you want to get rid of the OP champion because team A is going to pick first!

So, lets check the math again. For easy numbers, lets say an OP champion has the winning chance of 60%. And lets assume there is no counterpick to an OP chmpion(he wouldnt be OP than, would he). Furthermore, let 4 of the 20 heroes be OP(hero 17-20, 20 beeing the most OP)

[--Bans--Picks---------]

ABBA ABBAABBAAB

Lets not check the worst case scenario, as this is something like "5 friends "just palying to win" vs "5vompetative players", its not really interesting to see who wins in this scenario. so lets assume team A and Team B are trying to make the best choices to win!

Bans:

A Bans 19

B Bans 20

B Bans 18

A Bans 5

A picks 17 (OP, no counter possible)

B picks 1

B picks 2 (to make sure A doesnt get counter)

A picks 3

A picks 4

B picks 6

B picks 7 (to make sure A doesnt get counter)

A picks 8

A picks 9

B picks 10

Lets see how it went:

A got: 1 OP; 2 counterpicks

B got: 1 counterpick!

Suddenly the chances of B winning have decreased to a minimum!

Team A winning strategy is to NOT TO BAN THE OP CHAMION AS SECOND BANN, INSTEAD BAN A COUNTERPICK OF THEIR OWN TEAM!

If there is only one OP champion, team A will not bann him! instead they will ban 2 counterpicks of their team!

Team B on the other side has to ban the OP champion.

So, what if there are no OP champions?

Well Team A has the first bann, randomly banning a champion is throwing a coin -> useless. SO Team a starts with banning counterpicks, now Team B has the chance to bann either counterpicks of themself, or the original hero so the counterpick ban of team a was useless, lets see what happens

Bans:

A Bans 2(counterpick to 1)

B Bans 1(ban of the original)

B Bans 4(counterpick of 3)

A Bans 3(ban of the original)

=> Its the same scenario as the beginning: B will end off better!

Bans:

A Bans 2(counterpick to 1)

B Bans 5(counterpick to 4)

B Bans 11(counterpick to 10)

A Bans 8

A picks 1

B picks 3

B picks 4 (to make sure A doesnt get counter)

A picks 6

A picks 7 (to make sure B doesnt get counter)

B picks 9

B picks 10 (to make sure A doesnt get counter)

A picks 12

A picks 13 (to make sure B doesnt get counter)

B picks 14

Team A:

0 counterpicks!

Team B:

1 counterpick!

So, now we can conclude:

- Two clever choosing teams will use the right ban strategy

- Having the "wrong number of OP champions" will result in an devastating disadvantage for Team B!

- Having no OP champions will result in Team B **always** beeing better of by 1 counterpick!

- Letting Team A have one ban more than team B **COULD** make the field even.

- Having __ONE__ OP champion would have the same result as having one ban more for team A

- Team A should not Bann the most OP champion in the game!

- Team B ALWAYS should ban the most OP champion in the game!

Edit:

If team B gets the one counterpick, it should always try to counterpick Team As mid lane, that would be the biggest disadvantage of Team A