Wars of the Roses

Mike & Mark's Lancastrians
v.
Jim & Renfrey's Yorkists

Both armies had 3 divisions of 6 units.
York (on the right in the pics) had on the left 3 bows + 3 spear, in the centre 3 men at arms & 3 bills and on their right 3 mounted knights & 3 bows (Renfrey's division).
Lancaster had on their right 4 bows & 2 men at arms, in their centre 2 bows, 2 bills & 2 mounted knights and on their left 2 bows, 2 bills & 2 mounted knights.  Mike commanded the Lanc's left, Mark their right.

Both sides advance slowly initially.

On the far flank the Lanc's horse charged the Yorkist bowmen which had accidentally advanced ahead of their cavalry.  The cavalry on the flank rode down their target, but were counterattacked by the Yorlist horse. The cavalry near the centre were stopped by the well supported bowmen.
In the centre, the Yorkist men at arms charged the Lanc's bowmen supported by bills.
On the near flank, the Yorkist spearmen advanced past their bowmen and charged the Lanc's bowmen.

On the far flank, the Yorkist cavalry beat the Lanc's cavalry and went on the beat enough infantry behind to break the Lancastrian left flank division.  But the 3 Yorkist horse were all shaken while the Lancastrian horse destroyed all 3 bow units in that division, so the division broke as half broken & the rest shaken.
The Yorkist centre division drove back the Lanc's centre but didn't break it.  2 men at arms units turned right to attack a Lanc's cavalry unit in flank and break it.  It was too late to save the Yorkist right flank division but the Lanc's centre division was in bad shape.
On the near flank York's attack was beaten off and the spearmen rallied behind the bowmen. 

The near flank has stalemated .
In the centre, York's billmen renewed the attack on the Lanc's foot but were flanked by bowmen & beaten off.
Richard saw his only chance of victory was to beat the remaining Lancastrian cavalry, so he charged them with 2 units of men at arms.

The first infantry charge was beaten off, but they fell back leaving the horse shaken.  One men at arms unit was unshaken & renewed the charge on the shaken horse.  This time the horse broke.  This loss broke the Lancastrian centre & gave York a hard fought victory.

We used Hail Caesar with our house modification for the medieval periods.  One of the really interesting conundrums in this era comes from the mix of bow units & melee units.  You want the bows in front to shoot up the enemy, but you want the men at arms or bills in front when the lines close.  The Lancastrians had more bow units than the Yorkists who generally tried to close with bill, spear & sword, while the Lanc's relied more on their bowmen.  Neither method was decisive in this battle so we remain none the wiser as which is the best option.