A better word would be patience. Alexander took risks once battle began, but his strategy of when and where to give battle was the opposite of risk-taking.
Alexander recognized that a big Persian army could not stay in one place very long. The bigger it is, the less it can live off the land; and bringing in supplies generates the vanishing-point mathematics of pack animals and humans eating up the supplies they are carrying, not to mention clogging the available roads.
Facing huge armies, Alexander delayed accepting battle. Before Issus, Darius assembled several hundred thousands on a plain near the Syrian Gates, where the Macedonians would be expected to come out of the mountains of Asia Minor. The plain gave unrestricted maneuverability for a large army, and there had been time to stockpile ample supplies. Alexander, crossing them up, went on a 7-day campaign westward against the mountain tribes. Then he returned to a city where he was well supplied by sea, made elaborate sacrifices to the gods; held a review of the army; athletic and literary contests; even a relay race with torches. Finally Darius had to move, and went seeking Alexander in the narrow region of mountains and swamps, throwing away his advantage of open ground. After two weeks inland, no doubt hurting for supplies, Darius finally met Alexander at the Issus River, where the Persian army — now down to about 150,000 — was packed in and unable to use superior numbers to outflank or surround him.
At Gaugamela 3 years later, Darius had an even bigger army, on a wide plain supplied by the main roads of Mesopotamia. They even cleared away bushes so that their scythe-bearing chariot wheels had room to roll. Alexander brought his army, now grown to 45,000, to a hill overlooking the plain, where at night the torches seemed to go on forever. Since the Persians were not going to move, Alexander gave his army four days rest. Alexander was also playing psychological warfare, not letting the Persians fight in their first flush of enthusiasm (the adrenalin rush, we would say). Their suspense grew even worse, since they began to expect a night attack, so after several nights of this, Alexander chose to attack in the daylight.
Alexander always started the battle. His formula was to seize the initiative, establish emotional domination as quickly as possible. His open-field battles all became walkovers. The units of the Macedonian army — infantry phalanx, light troops, heavy cavalry on both wings — advanced at different times, but the key was always Alexander’s assault. Once the Companion cavalry broke the Persian ranks in an intense but usually short fight, the Persians’ advantage in numbers was turned against them.
At Issus, the Persians had large numbers of troops, realistically perhaps four times the size of Alexander’s, lined up along a river bank. But most of those tens or hundreds of thousands could never engage the Macedonians, because they couldn’t get close to them. Once their defense crumbled on the right, Alexander turned obliquely against the center; this threw the Persian army into a stampede, particularly disabling when so many men trample each other in a traffic jam. In every major battle, the Persians lost 50 percent or more, the Macedonians a small fraction, perhaps 1 percent or less. The disparity in casualties seems unbelievable, but it is commensurate with complete organizational breakdown of one side, making them helpless victims. In violence on all size-scales, emotional domination precedes most physical damage.
At Granicus, Alexander positioned himself opposite where the Persian commander was surrounded by bodyguards. He waited for the moment when he saw a wavering in the Persian line, and charged his cavalry at that point. Alexander led 2000 or so cavalry splashing through the water and up a steep bank. This might seem a risky thing to do. But psychologically, relying on favorable geography for defense is a weakness; once the advantage of terrain turns out to be ineffective, the defending side has set itself up to be emotionally dominated. In every respect, Alexander aimed at the point of emotional weakness — a point in time and space, visible to a good observer.
Alexander did not have to fight the entire Persian army; he picked a unit about his own size, and counted on the superior quality of his troops — the superiority they created by generating emotional domination.
All three of Alexander’s fateful victories — Granicus, Issus, Gaugamela — ended the same way, with the enemy commander (in the last two, the King himself) running away in his chariot, setting off a general panic retreat. At Gaugamela, the Persian forces were so large and spread out that Parmenio, commanding on the left, had a stiff fight with Greek mercenaries and other Persian forces who did not know the rest of their army was routed. It took longer but Parmenio, too — the other cavalry commander — emerged victorious without Alexander’s help. This shows that the Macedonian style was not personal to Alexander alone.
There is another respect in which Alexander attacked the weakness of the Persian army. It was an army of an empire, a polyglot of 50 different ethnic groups, with their own languages, each fighting in their own formation. The army that invaded Greece under Xerxes had 30 generals, all Persian aristocrats; the armies of Darius III were probably similar. We can surmise that central control of the army, once battle began, was minimal. We can also infer that morale and loyalty of each ethnic unit was shakey; they had been recruited by going over to the victor, and they were aware of the possibility of going over to the other side if things did not go well.* There was also the rigid hierarchy of the Persian army — something all the Greeks commented on.
*This was the pattern of warfare in India before the arrival of European officers. Battlefields were displays of ferocious weapons — chariots, elephants and so on — but outcomes were decided mostly by side-switching in the midst of battle but arranged beforehand. (Philip Mason. 1976. The Indian Army.)