The expression à Dgi l'adèrt is an interesting one. The precise spelling isn't fixed, as it may turn up nowadays as à dgi l'adèrt, or à Dgi l'Adèrt, or à Dgi l'adèrt. Older writers even managed to run it together as one word, such as à dgiladèr; it being such a fixed but opaque expression.
One the face of it, it would translate as something like "by God the adroit" - but since it conveys the sense of "at random", there wouldn't seem to be much divine adroitness about it. Perhaps it has been interpreted as meaning that the choice is left to God's sense of what is fitting. The Dictionnaire Jersiais-Français speculates that it originally meant "well done" or even "perfect", then "quickly done", then "done by rule of thumb" and ending up as meaning something done badly or at random. However the dictionary also speculates that the phrase might originally have been à Dgile adèrt i.e. adroit like Giles - Giles being presumably a proverbial bumpkin.
For comparison, à la guilmargouère (the gu is there pronounced dg) means "any old how" in mainland Norman.
The origins of this expression remain mysterious - but it's a nice phrase to use!