Of course there is always the 'luck of the dice' chance, but other than that it really makes little sense that Cyndane was able to defeat Alivia so handily.

Let's look at some of the facts.

1) Alivia was stronger than Cyndane, -maybe- even without her angreal.

2) Alivia had a fairly powerful angreal which was multiplying her strength by at least 3 times, more likely maybe 4-5 times or more. Cyndane had NO angreal.

3) Alivia had a ter'angreal to unravel any weaves directed against her directly (similar to Mat's) where she need not even spare the effort to slice it. So the possibility of Cyndane shielding her (even never mind the angreal) would be virtually impossible.

4) Alivia frightens Nynaeve with her strength, and Nynaeve has come face to face with several Forsaken.

5) Alivia is approx 400 years old, likely older than Cyndane ie Lanfear was and since the age of 12 or 13 she has been trained solely to be used as a weapon. Cyndane may know more weaves, but no reason to believe she knows more battle weaves.

6) Alivia commented that The Asha'man may be called weapons, but she was confident that she was far, far more lethal of a weapon.

Basically between her 388 years of battle experience, her ter'angreal and her quite powerful angreal it should have been like Rand dealing with Damer Flinn, ie: No Contest. Alivia should have actually been able to shield her quite easily without Cyndane being able to prevent it.

Besides luck, or the Pattern protecting Cyndane for some higher purpose how do you explain how Alivia came off as the 'loser' in that fight?

Yes she prevented Cyndane from getting to Rand, but she did not shield, capture or kill Cyndane which is what the odds are in her favor to do.