Yup, here goes:
The important thing to remember is that with each opposed check, the difference is applied to the leading character's DS. So if the leading character wins the difference is added to his DS, whereas if the trailing character wins, the difference is deducted form the leading character's DS. This means that you can geta "to-and-fro" situation where both hover around the 0 mark if they are approximately equally strong, and eventually Constitution will decide who wins unless one or other gets lucky early.
Round 1) Lydia wins by 5, so her DS increases by 5 (to 5).
Round 2) Ogre wins by 8, so Lydia's DS reduced by 8 (to -3)
Round 3) Ogre wins by 6, so its DS inceased by 6 (to 6)
Round 4) Lydia wins by 1, so ogre's DS reduced by 1 (to 5)
Round 5) Ogre wins by 9, so its DS increased by 9 (t0 14, not 13 as I miscalulated when writing the example).
Since the ogre's DS is currently 14, and the Target Number for arm wrestling is 20, he needs to beat her by 6 in the next round to win the match.