Gen. Pope stood at the treeline outside Groveton, examining the Rebel line with his spyglass. If he could destroy the Secessionist Brigade opposing him, believed to be Pickett's, he could break through the enemy front. Unfortunately, despite having five brigades immediately at hand, under the commands of Meade, Butterfield, Robinson, Milroy and Hatch, experience told him there was a good chance that a full-fledged assault would merely push the enemy back, or succeed with high losses. Pope was sore tempted to send in just three brigades. The weaker attack was still guaranteed to succeed, but likely at reduced cost.
Rebel brigade is 4 combat factors. It can only be attacked from three contiguous hexes by five federal brigades totalling 21 factors for a 5-1. 33% chance of a defender retreat, 33% chance of an exchange and a 33% chance of a defender eliminated. Using just three brigades (12 vs. 4, or 3-1) provides just a 1/6 chance each of a DE or EX, while a 2/3 chance of a DR.
"Bad news, sir," said a nearby aide, a young major. "Another rebel brigade has come up in support!"
Pope could see that was true. A slightly smaller Rebel brigade was taking a position beside the first.
"Not at all!" exclaimed Pope, snapping his telescope shut. "Pickett is doomed, now. Quick. Send word to Hatch to swing around from the right flank and join Meade in attacking this new arrival. Once they've driven them back, tell Hatch to be sure to follow. Then order the rest to hit Pickett"
"But sir," the major protested. "We have Meade and Robinson already in position to attack the newly arrived brigade! Shouldn't we attack now?'
"No, no," Pope explained. "Hatch will bring an extra factor and give us exactly enough for a 3-1!"
Hatch's 5 combat factor brigade moves to stack with Meade's 4-factor brigade adjacent to the 3-factor Rebel Seddon's Brigade. Butterfield, Milroy and Robinson, total of 12 factors, stack in the remaining two hexes to attack Pickett. Hatch and Meade combine for a 3-1 against Seddon, which is guaranteed to clear the hex. Even and EX allows Hatch to advance, cutting off Pickett's retreat, meaning that the subsequent 3-1 against Pickett is guaranteed to eliminate Pickett.
The above is a commonplace scenario in traditional hex-and-counter wargames, in this case the Second Bull Run scenario from the Blue & Gray quad.
For more than 40 years I've grudgingly tolerated this aspect of the games, while never really being a fan of it, ever since discovering it in the old Avalon Hill game Stalingrad. I understand that all wargames result in some compromises for the sake of playability, but factor-counting has always grated a bit. Perhaps it's because I never really developed a knack for it, despite the fact that it's really required for good play. But I think it's largely because it's a distraction from the real art of generalship in a game. The above example illustrates the absurd nature of factor-counting. There's no equivalent in real battlefield command of counting out combat (or movement) factors in order to gain a precise advantage.
I think that's one reason why games like Memoir '44 or Battle Cry don't bother me. To my mind, a game that reduces generalship to commands like move a couple of units on the Left or fire the guns in the center seems just as authentic as a game that purports to be realistic by accounting for the slight strength differential between Hatch's brigade and Meade's.
Most infantry brigades in the Blue & Gray quads are very similar in strength, and this is no accident. Both armies generally tried to keep brigades around the same strength in order to simplify command and control. Each brigade was supposed to be able to do about a brigade's worth of work on the battlefield. I don't think you'll find many instances in the Official Records when the commanding general sent Brigade "A" on a mission because it had one more regiment than Brigade "B." That sort of detail is invisible at the battlefield command level. The Battle Cry approach where all the units are the same functional strength is really more valid than it might appear at first glance.
This opinion is likely why I've generally been pretty open to non-traditional approaches to wargames such as Up Front, Columbia's block games, Bowen Simmons' recent designs and area/point-to-point games such as A House Divided or Storm Over Arnhem. There are many great hex-and-counter wargames, but in many cases they do tend to focus the gamer's attention on minute details at the expense of larger truths.