Initiative Math (aka opposed rolls)

[SorO_Lost]

An Opposed Check's odds are a little different than a simple check against a set value.

+0: 47.5% win, 5% tie, 47.5% loss.
+1: 52.5% win, 4.75% tie, 42.75% loss.
+2: 57.25% win, 4.5% tie, 38.25% loss.
+3: 61.75% win, 4.25% tie, 34% loss.
+4: 66% win, 4% tie, 30% loss.
+5: 70% win, 3.75% tie, 26.25% loss.
+6: 73.75% win, 3.5% tie, 22.75% loss.
+7: 77.25% win, 3.25% tie, 19.5% loss.
+8: 80.5% win, 3% tie, 16.5% loss.
+9: 83.5% win, 2.75% tie, 13.75% loss.
+10: 86.25% win, 2.5% tie, 11.25% loss.
+11: 88.75% win, 2.25% tie, 9% loss.
+12: 91% win, 2% tie, 7% loss.
+13: 93% win, 1.75% tie, 5.25% loss.
+14: 94.75% win, 1.5% tie, 3.75% loss.
+15: 96.25% win, 1.25% tie, 2.5% loss.
+16: 97.5% win, 1% tie, 1.5% loss.
+17: 98.5% win, 0.75% tie, 0.75% loss.
+18: 99.25% win, 0.5% tie, 0.25% loss.
+19: 99.75% win, 0.25% tie, 0.00% loss.
+20 or higher: 100% win, 0% tie, 0% loss.

*With Opposed Checks, if there is a tie in rolled values than the person with the higher bonus goes first. Skills also do not automatically fail, or succeed, on a naturally rolled value unlike Attacks & Saves. Original Source

As you can see there is a definitive diminishing returns effect. The greater your advantage is then the less each point gives you and the less the modifier tiebreaker matters. So to produce an at least 60/40 odds then you need a bonus of at least 3 higher than your target does. 70/30 needs +5, 80/20 needs +8, 90/10 needs +12, and a 100% success rate requires a +20 or greater advantage.

[Endarire]

An important note is that you're normally facing things with different initiative modifiers.  Thus, getting 70/30 odds against one foe may mean getting 100% odds against another.

[Garryl]

Also worth noting is that since initiative checks, like opposed checks, go to the character with the highest modifier in the case of a tie, all of those tie percentages can be added to the win percentages in the table (or split evenly to 50/50 for equal modifiers). 60/40 odds come at +2, 70/30 odds come at +4, 80/20 odds come at +7, 90/10 odds come at +11, and a 100% success rate only requires +19 over your opponents.

Also worth noting is that the first point above your opponent's modifier gives a larger benefit than normal, bringing your success rate up from 50% to 57.25%.