Ancient battle accounting 101
It is quite conceivable that Alexander did face 1 million at Gaugamela, but one should be as cautious of Greek accounting as of their gifts
Firstly many in Darius' Army were client tribes that came with their camps, i.e. families.
Secondly, when Persians were asked how many troops Darius commanded, it meant, in the terms of the day, how many adult males were part of his kingdom and therefore subject to military service. The answer was 1 million. This doesn;t mean literally one million, but an expression used for 'infinately incalculable' because the mathematical concept of infinity didn;t exist yet.
Thirdly, we know from Jewish sources that the Persian empire was very large, and could master significant manpower for war. However we also have an estimation tha the total World population at the time was 50 million. It is highly unlikely that Darius could have brought 1:50th of the global population to one battlefield. Today's equivalent would be 120 million, which is way beyond the total capabilities of global transportation.
Fourthly, as much as it may surprise us today, it seems that horses were counted separatelly to people. Some people were also counted, who would not be counted today, like washers, water carriers, wood carriers, cooks, bakers, horse grooms, tent erectors, carriers, servants of officers and chiefs, etc.
So how large was the Persian army?
This si not hard to answer. We know the ancients were quite familiar withthe concept of mass. Nor did Darius underestimate an army which, not insignificant in size, had reached his Empire from such far lands. The best form of defence is of course attack, and Darius was not going to sit on his hands (which also did his public image no good). The commonly accepted minimum for numbers requiered for attacking is 3-4 to 1, so assuming Alexander had about 45,000 troops, Darius (who had ample cavalry for scouting, and therefore probably knew this) would have brought at least 135,000-180,000 troops with him. About a twentieth part would have been cavalry (as many as 14,000 horses mostly from the northern tribes), and there would have been 13-20,000 non-combatants. And of course all the camp followers of the nomadic tribes (no idea there on the numbers).
In Wiki the numbers given are
62,000 peltasts
15,000 Immortals
2,000 Greek hoplites
1,000 Bactrians
12,000 cavalry
200 scythed chariots
15 war elephants
total 93,000, quite a few short for success by numbers
Clearly what was called for was a manoeuvre of some sort
Clearly 79,000 infantry were not sufficient against the Macedonians that amounted to:
9,000 peltasts
31,000 hoplites
7,000 cavalry
Darius would have been placing major hopes on the chariots and elephants, and we know that he did (since much of the cavalry was useless against formed phalanxes, being nomadic bowmen). Traditional sources say that Alexander forced him to attack, but given he had the field cleared for chariots, he probably intended to attack all along. Why he never used the elephants is a mystery.
Cheers
Greg