so on battle dice rolls, your rolled symbols must match your own troops, not those of your enemy. So what is the incentive of buying cavalry at all, since there is only 1 cavalry side of the dice and 2 infantry sides....why not just use infantry since they are so much stronger a force? the only advantage to cavalry is they can move twice as fast and can pursue retreats, but to me that doesn't seem like it balances the worth of the cavalry opposed to the worth of infantry.
The idea is to encourage a combined arms approach to your armies. If you have an army that's mostly composed of infantry plus a couple cavalry and a couple of catapults as backup, you'll be hitting on most rolls of the dice and be able to inflict more casualties than a similar-sized all-infantry army.
A 'hit' occurs when the die roll matches any of the unit types that you have in your force. Therefore, having multiple types means more hits. Roman armies were primarily composed of infantry (and these were the best trained and armed), so roman infantry gets 2 facings on the die. However, an army of several types will always beat an infantry-only force of equal cost.