Mass Battle System
I have used the below method to handle mass battles in TTRPGs without getting too bogged down with the nitty gritty. I use it to simulate within 5 rounds a full clash of two sides.
Step 1 - Upper hands
I first assess each side, and create a list of 'trump cards' they posses. This typically is some trait (large swarms of combatants, special unit, ie. Dragons). Each trump card a side possesses earns them one point to spend during combat.
Step 2 - Fight!
I narrate the sides approaching, however the scenario is intended to occur. The first round is called for after the introduction, with each side rolling a single d6. Re-roll if a tie. After a winner is determined, I narrate some large scale event or movement that represents the victory. For example, an attacking army might breach the walls of the city.
Using trump cards
If a side has lost, but before narration begins, a side may choose to 'spend' one of their trump cards, allowing them to re-roll the round. Their trump card is spent, and both sides roll again. If this manages to change the outcome, I narrate how that aspect of the army won this moment of the battle. For example, if a side had extremely regimented or elite troops, they could have infiltrated and taken out key generals or leaders on the other side.
Step 3 - Winners
The first side to get to 3 victories wins the battle overall. Since we are doing this extremely 'zoomed out' - I narrate in large strokes how the victors win, and what losses are inflicted.