First up is the chance of just a raw dodge:
|Raw dodge chance
The chances are pretty low, and with some margin of error, seem to be in line with the general accepted 1/64 dodge chance.
Here is an important one, the chance of being hit with the enemy Surrounded (in this case I used the Light Sword):
|A Surrounded Cyclops
Surround in this game gives an additional 25% chance to dodge an enemy attack. This is pretty low and they even adjusted this rate higher in later games to be more effective, to 50% or more. It makes Surround a pretty useless spell, except for in a few select cases.
Now for equipping Clothes Hiding:
|Hero with Clothes Hiding equipped
This is the most surprising result. Clothes Hiding seems to give an additional 12.5% (or 1/8) to dodge an enemy attack. I was thinking this was much lower, and it might make getting a set of Clothes Hiding a good option at some point in the speedrun.
And to be complete, I did one more test, combining Surround and Clothes Hiding:
|Cyclops Surrounded and Hero with Clothes Hiding
The effects of both seem to stack, giving close to the combined dodge chance of both Surround and Clothes Hiding.