Quick Alert / initiative maths

Basic probs from https://www.reddit.com/r/3d6/comments/1ad3g5u/alert_has_more_value_on_a_low_dex_character/

D is the difference between your initiative modifier and the enemies.

So if an enemy is rolling with a +0 and you have a +5 you have a 70% chance of beating their result.

D Win% Tie% Lose%

+0 47.5 5 47.5
+1 52.5 4.75 42.75
+2 57.25 4.5 38.25
+3 61.75 4.25 34
+4 66 4 30
+5 70 3.75 26.25
+6 73.75 3.5 22.75
+7 77.25 3.25 19.5
+8 80.5 3 16.5
+9 83.5 2.75 13.75
+10 86.25 2.5 11.25
+11 88.75 2.25 9
+12 91 2 7
+13 93 1.75 5.25
+14 94.75 1.5 3.75
+15 96.25 1.25 2.5
+16 97.5 1 1.5
+17 98.5 0.75 0.75
+18 99.25 0.5 0.25
+19 99.75 0.25 0
+20 100 0 0


Alert feat where you win ties, enemy dex modifier same as yours:
+0 base: 52.5% chance to win
+2 lv1: 61.75
+6 lv20: 77.25

61.75*100/52.5=117.619 -- 17.6% chance of an extra turn!
77.25*100/52.5=147.1429 -- 47% chance of an extra turn!!

With +5 mod relative to the monster, to show diminishing returns:
+5 base: 73.75
+7 alert lv1: 80.5
+11 alert lv20: 91

80.5*100/73.75=109.1525 -- 9% increase in turns
91*100/73.75=123.3898 -- 23.4% increase in turns