As a test, I ran 1BG of Agema (Companian Cavalry) up against 2BG of Saka Cavalry. As a basic assumption I put it that Alexander and Darius are within their required influence distances to affect the cohesion tests.
The Saka BG's are in 2 lines. They shot at the Agema while in bow range - 6 dice provided 2 hits. As this was >1 per 3 hits from shooting a cohesion test was required. They threw a 10 - no problem. As only 2 hits were taken, no death roll is required.
Dice after re-rolls. Hefty Macedonian win.
The Agema charge in. Having +POA for lancers, they hit on 4,5 or 6 (the Saka need 5 or 6). The Macedonians rolled 4 hits but 3 re-rolls (1 and 2 's) yielded 6 hits. The Saka could only get 1 hit in return - a solid Macedonian win. The Saka lost a base and the impact. A cohesion test is at +1 (Darius is close by) but -1 (1 hit per 3B in close combat) and -1 (2 more hits received than inflicted) means the Saka need an 8.
They throw a 7 and the Front BG goes Disrupted.
Melee - the extra dice count
In the Melee phase, its pretty even. Both are Armoured Swordsmen so no POA's here. But will the ability to re-roll 1's and 2's make a difference - especially as its 6 dice to 4?
The Agema get 3 hits and 3 re-rolls (all 2's). re-rolled they deliver three 6's! Ouch! The Saka respond with 2 hits and 2 re-rolls (1's) which convert into 1 more hit. The Saka lose 6-3 and lose another base. As Superior they don't Autobreak but the cohesion test will be tough. They were Disrupted (-1), took more than 1 hit per 3B in close combat (-1), lost by more than 2 hits (-1) and have lost more than 25% of bases (-1). The +1 Darius offers makes the roll needed a 10. They get a 7 and go Fragmented.
The Rear BG cannot conform by stepping forward as it is not moving into an overlap position. Therefore it must either move to the side or stand and await the outcome. Being undrilled, they can only turn 90 with a simple advance on a CMT OR turn 180 degrees and stand still. Neither of these options is particularly attractive because if the Front BG breaks (as is likely) then they Agema will contact the Rear BG in the flank or (worse) rear. But if the Saka Front BG routs through the Rear BG it will go Disrupted and be contacted in the Impact phase at a distinct disadvantage (8 dice to 6 at -POA and already Disrupted). They fail the CMT anyway and decide to stand and wait.
The melee continues. The Agema move the leftmost base around to contribute to the melee so it is now 8 dice to 2. The Saka get 1 hit in, the Agema get 5 in (after re-rolls). The Saka make another test at a whopping -4 (11 needed). They get 9 and Rout. The Death Roll is a 6 - they get a 5 and lose another base and so Autobreak.
Rout leads to additional problems!
Reading the rules, I now assume this means that the BG Routs (using a VMD) - going through the Rear BG and Disrupting it (and will then be removed in the Joint Action Phase). The Agema pursue - rolling a 1 on the VMD which means a 3MU move - thereby impacting the Rear BG.
This is 6 dice vs 4 dice. The Agema are on a +POA and as the Saka are Disrupted they lose 1 dice in 3. The Saka throw four 2's! No hits or re-rolls. The Agema steam in with a whopping 5 hits and a re-roll - for 6 hits. The Saka lose a base. They are also on -1 for 3 hits per base, -1 for being Disrupted, -1 for taking 2 more hits than inflicted and -1 for losing 25% of its bases. Darius gives them +1 though. They need 10. They get...10! They just stay Disrupted. Melee now sets in. Both have an overlap so its 6 dice to 4 with no net POA's. The Saka get 2 hits in, the Agema 6 hits (again!). The Saka lose another base and need a big throw for cohesion. A 7 doesn't do it so they drop to Fragmented.
The Front BG now autobreaks but is beyond 3MU's so the Rear BG doesn't need to test.
In the Movement phase the Agema feed a base into melee. Its 6 dice to 2. The Saka get 1 hit, the Agema just 2 (and 4 3's!). They just win. The Saka throw at -1, -2, -1 and +1 which is 10 again. They get 9 - not good enough and Rout. The VMD is 2 (oh dear) and the Agema's 3 - the Saka are caught in the rear and lose another base - forcing an autobreak. At the end of the JAP they are removed.
Summary
Interesting. The dice were very much on the side of the Macedonians in this example. The line-up of the Saka didn't help either. By forcing the Front BG to rout through it meant the Rear was Disrupted and open to slaughter at Impact (as it proved). The Agema are deadly at impact but in melee they are pretty even with the Saka - so making the impact count is all important.
Therefore I'll try the same situation but with the Saka BG's side by side.