As I've been doing lately, I did a solitaire refight of a historical battle that Young General and I played using the simpler and more abstract Hold the Line with the more detailed and traditional Rebels & Redcoats game.
In this case the R&R game game to a brutally quick decision. Leaving out some secondary maneuvers and movements that didn't affect the final outcome, the key moves were an assault at 2-3 odds with a +2 die roll modifier by Mercer and his brigade of Continentals against the British 55th Regiment which resulted in a NED0 (Attacker No Effect; unmodified Defender morale check). Both halves of the 55th promptly failed their morale checks and retreated (and eventually one half even routed off the field!). This was a low probability outcome that put the British down 8 points in disruption and eliminations.
It also left Mawhood and the British 17th Regiment adjacent to Mercer and his brigade. Rather than withdraw and risk leaving half his regiment behind if it failed to disengage, Mawhood called in the Dragoon troop to help the 17th and launched a 1-1 assault with a +1 DRM on Mercer which resulted in a NE (no effect). In retrospect this was an error.
On the 0900 turn Mawhood was swarmed by all of Mercer's and Calawalader's brigades, led by Gen. Washington himself for a 3-1 assault with no modification to the die roll as Mawhood and Washington cancelled out. A die roll of 8 resulted in a DE (defender eliminated) which brought the British army far above it's disintegration level of 16. Indeed, Mawhood and the troops with him alone counted as 15 points!
This illustrates nicely a point that's often misunderstood in wargaming circles -- more dice does not equal more luck.
In the Hold the Line version of Princeton there were a total of 36 rolls of the command die between the two sides, and nearly 100 rolls of a standard die -- providing enough rolls that there's a high likelihood that the luck generally evened out. Indeed, the only real "luck roll" in that fight involved the hit on General Greene that took him out of the fight -- but even there the luck was not extreme. Washington was missed at least twice and Mawhood dodged a bullet as well.
In contrast, the traditional hex-and-counter game Rebels & Redcoats turned in dramatic fashion on just a literal handful of die rolls. In the entire 3-turn game there were just a dozen die rolls and half of those were of minor import (mostly low-factor bombardments and force marches). Seven rolls were important rolls: three assaults and four morale checks/rally attempts. Of those seven rolls fully six went against the interests of the British side and there was simply insufficient time for the rolls to even out in any way.
So despite surface appearances, Rebels & Redcoats's Princeton was much more luck dependent than Hold the Line's version of the battle.
On the other hand, R&R was closer to the actual final result than HTL, although getting there quite differently than the historical course of the action. In the R&R playing the British brigade was destroyed, where in HTL the British actually emerged victorious.
Hold the Line is a more fair scenario than Rebels & Redcoats, but probably makes it a more even fight than the historical reality would justify. Mawhood's command was seriously outnumbered and the Ameircan force was well-led with Washington, Greene and Sullivan all on the field.