Remember that the Persians did some fairly stupid things in the battle if you follow Arrian exactly. The cavalry was posted right on the edge of the river, with the infantry behind them (Arrian 1.14.4), and they were light cavalry (javelineers - Arrian 1.15.4 notes that they had “light javelins” against the Macedonian “cornel-wood spears”), not the heavy lancers. Alexander lined up with a phalanx and hypaspists in the center, and on the right flank were the Companions screened with archers and javelineers, with spear-armed Paeonian and Prodromoi cavalry between them and the phalanx. The left flank was held by Thessalian heavy cavalry and Greek and Thracian light cavalry.
The battle started with a charge by the Paeonians and Prodromoi. They reached the opposite bank, rather than being stopped in the river (Arrian 1.15.1) and disrupted the formation of the Persian light cavalry before withdrawing; the Persian light pursued and ran headlong into a charge by the heavier Companions. The rest of the battle is barely described by Arrian, but what seems most plausible is that the heavy cavalry drove off the Persian light cavalry, and then the Persian line was rolled up from left to right, with the Greek mercenary infantry not able to come up from its rearguard position to attempt to influence the outcome.
(Note: my description is influenced by Dr. Duncan B. Campbell 's article “Alexander’s Great Cavalry Battle,” in Volume 7, Issue 2 of the magazine “Ancient Warfare”)
Like I said, I’m not a historian, or even that familiar with war-games, so I just cobbled together some stuff from maps and wikipedia and so forth.
I tried to use all of the rules, but I’m sure I missed something here or there.
To keep things from being ridiculous (once I get around to playing things out on a map) I used 3x3 “epic” scale.
The Persians had 3 stands of heavy infantry and two stands of light infantry at the back that weren’t even used.
Along the riverbank were 16 stands of light cavalry and three stands of heavy cavalry.
Alexander had 4 heavy cavalry, 3 light cavalry, and three knights (companions), a stand of heavy infantry, along with a stand of archers, a stand of light javelin infantry (I think), one heavy infantry and six light infantry as phalanx.
I did give Alexander’s army the bonus BR for him being awesome, generally assuming that the guy was just super-human, but really, having to roll 20+ while the other guys roll 16+ seemed to make a significant difference.
The numbers don’t seem quite right. The Persians have 19 stands of cavalry and 5 stands of infantry. That works out to roughly 1 stand of cavalry per 500 troops and 1 stand of infantry per 1,000 troops.
Using those ratios, the Macedonians should have 4 knights (1800 Companions), 4 heavy cavalry (1800 Thessalians), and 3 light cavalry (600 Scouts, 600 Greek, and 300 Paeonian), 1 archer, 1 javelineer, 10 light infantry, and 2 heavy infantry (assuming the pezhetairoi are light and the hypaspistai are heavy), with the infantry having pike or spear, sword, shield, and leather (linothorax) or banded (metal cuirass). The Macedonians were under-equipped by 1 knight and 4 light infantry. It’s not an excessive difference, but it would have an effect.
I would be interested to know the deployment and tactics used by each side, since they may help in seeing what happened (of course, it may just be that Alexander was luckier than the commander of the Macedonians on that table - Granicus was a bit of a risky attack).