Here's a shot of the battlefield from behind the Patriot lines. The Patriots are outnumbered 16 elements to 12, and their general is stuck on the opposite side of a rocky hill from the bulk of his army. The Royalists have two groups opposing the Patriots, plus a third one marching along the hills towards the key pass between them. Their general is Good, that os the Patriots is Poor.
Initial approaches saw both sides push the larger parts of their armies forward. The Royalists rushed their cavalry forward to secure the pass.
On the other flank the Patriots edged their troops forward, and got their artillery into a commanding position on the shore of Lake Titicaca.
Royalist infantry marched to reinforce the cavalry in the pass.
The Patriots switched one element of infantry to contest the pass. Their first volley routed the Royalist cavalry.
The Patriots charged ...
... and routed an element of Royalist infantry. The Royalist hold on the pass was now not so secure.
The Patriots charged with their cavalry, but the Royalist militia saw them off.
Both lines were now trading artillery fire, and casualties had been taken on both sides.
On the other flank, the Patriot general edged his troops forward. Musketry and artillery drove off some of their Royalist opposite numbers.
In the pass the Patriot infantry held off attack after attack.
An overview of the battle. On the left of the picture is the bulk of both armies. The Patriots are hampered by their general being so far away, whilst the Royalists couldn't get enough PIPs together to launch a decisive attack, as both lines were being broken up by artillery fire. On the right the Patriots were attacking.
The Patriot right went on the offensive, but a single element of Royalist militia kept holding them off.
The Royalists finally got an attack together on their right, destroying the Patriot artillery.
Both sides fed more infantry into the fight.
On their right the Patriots prevailed.
The Royalist general was captured when the unit he was leading routed.
On their far right the Royalists swept away two elements of Patriot infantry, but their army morale had now collapsed
A final shot of the battle. In the centre the Patriot infantry unit that had contested the pass had finally been destroyed, but its fight had delayed the Royalists long enough that they were unable to exploit the pass to their advantage.
On paper the Royalists should win this every time, but as can be seen, sometimes the actions of a single element and a few lucky combat rolls can be significant. The battle was very close; both sides lost 50% of their elements, but the Royalists had lost more since their 50% point was higher.