We have hit the 200 games mark in the current 2v2 ladder season, that are more games then previous ladder.
I wondered if I have seen or played all possible setups and did some math.
There are 6*5*4*3=360 different 4 player setups. But from the players view, its not important if the other team is russia and asia or asia and russia.
So we have 180 unique setups to play.
From the specs view, you would neither care if Team A switches its territories or if Team B does, or if Team A and B switch roles altogether.
So we have 360/2/2/2=45 unique setups to watch.
So how many games we have to watch to have seen them all? Well at least 45 or if we are unlucky we never see all. But how many in average?
The 1st time we watch a 2v2 we certainly see a new unique setup, but the 2nd time we have a 1/45 chance to see the very same setup again and just a 44/45 chance to see a new one. After we have seen 2 unique setups, we have a chance of 43/45 to see a new one and so on, until we have a 1/45 chance to see the last one.
Thats the probability, but how many games we need to play for probability=1? (44/45)*(45/44)=1
So we need to watch 1+45/44+45/43+...+45/2+45/1 games.
I have no clue how to calculate that other then brute force, but i know how to let my pc brute force it.
And the results are (please imagin a fanfare):
We need to watch 197.8 games to see the 45 unique 2v2 setups
We need to play 1039.1 games to encounter all 180 unique 2v2 situation
If you watched every ladder game, you probably have seen them all, but no way you played them all, even The Stiffmeister has not.
I am known to myself to include errors in stuff like this, please dont nail me to the results.
