2.0 means you have won 2 times against your opponent(and 0.2 is shown on that opponent). So, those numbers are shown only when you have played with him before.
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What do the numbers in brackets after a player's name at the end of a game represent? Only some games, not all. Typically [2.0], or in my case usually [0.0]. I know zeroes are bad and twos are good, but since they don't always appear they must have some deeper, significant esoteric conotation.