Here is how it works
If your last 23 of your last 25 wins were solo, you get the solo emblem,
OTHER WISE you get the emblem representing whether you had a preference for 2 or 3+ players.
If your last 25 wins contained 22 solo games, and 2 duo games, and 1 3+ game, you will get the dynamic icon.
If your last 25 wins had 3 solo games, 10 dynamic games, and 12 3+ games, you will get the party icon.
If your last 25 wins had 23 solo games, and 2 duo games, you will get the solo icon.
If at any point, your last 25 wins contains more than 2 of any non solo games as wins, you will lose the solo emblem until your last 25 wins contains more than 23 solo wins.