So in order to clarify this system a bit more, I'm going to walk through an example.
Let's say we have a player that played pure astro in global games and is now 1500 rated with 150 sigma. This player would now like to play this new 2v2 matchmaker he heard about. What will happen to him?
Initially, the system will rate him by taking his global rating values (1500,150) and adding additional sigma to him to account for the potential growing pains of the player. Evidently astro gameplay is quite different from traditional 2v2 gameplay, and so a slight decrease in certainty should be expected.
This player will now be considered (1500,250) by the system. Why not 300 sigma? Because it chooses the smallest value between (global sigma+150, 250).
In addition, this player, for his first 10 games, will utilize the linear interpolation method when deciding who he will MATCH against not what his actual rating IS.
We know from the equation above that this would put him at ((10-0)x500+(0x1500))/10 or 500 mu for his first game. On his second game, he will have (9*500+1x1502)/10 or 600 mu.
You can see the player gained from 1500 mu to 1502 mu. Why such a small change? Because he faced someone around 500 mu and the system would expect an individual with 1500 mu to easily trounce someone with 500 mu. The slight adjustment reflects that. The linear interpolation will continue until the player reaches 10 games.
In addition, if this player is queueing with another player that is also below 1600 mu, then these players should be matching up quite frequently due to the random matchmaking protocol.