Duelist and throwing weapon adds +2. 1d8+2 is 6.5, equal to 1d12 and very near 2d6.
2d6 changing 1s and 2s to 3 is average of (3, 3, 3, 4, 5, 6)*2, or 8, which is an increase of +1. It's (3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), or 6.75 on a 1d12, which is an increase of 0.25.
+1 is less than...