Cowardly Codomannus?

King Darius III (380 - 330 BC) is known to history as the Persian king who twice ran away from king Alexander III (356 - 323 BC). First at the Battle of Issus and then finally at the Battle of Gaugamela.
The impression we get from the Greek historians is of a cowardly king.

A Roman depiction of Darius fleeing from Alexander at the battle of Issus. From a mosaic at Pompeii.

However, before becoming king of the Persian empire, Darius' original name was Codomannus and gained reknown for ending a long rebellion of the Cadusii in 358 BC by defeating their champion in single combat.

Okay, by the time of Gaugamela, Darius was about 49 years old, yet what he may have lacked in strength he would have to have had in intelligence in order to have become king in the first place.
Quite why he would have thought it sensible to run away makes no sense, especially as his army outnumbered Alexander's at Gaugamela and the right wing of his army was actually defeating the left wing of Alexander's.

All that can be said for certain is that the Greek historians of Alexander's day would have written for Alexander only and if they chose to differ they would have had a short life indeed.