I haven't bought Civ V yet because after the way I was burned with Call to Power 2 - a game I just played a few times before deciding I couldn't stand some of the changes - I'm reluctant to buy a game so many people are expressing misgivings about. So I can't really say anything about how well or badly the 1UPT system works in actual practice. But I can look at the conceptual issues involved.
One of the great strategic virtues in warfare is concentration of force - as General Nathan Bedford Forrest of the Confederate States of America put it, "get there firstest with the mostest." Since this virtue is important on both strategic and tactical scales, any game that wants its military model to make sense has to have a reasonable way to represent it.
Civ III and Civ IV represent this strategic virtue by the fact that defenders who win their initial battles are weakened, making it easier for subsequent attackers to finish them off. The larger an attacking force is, the better its chance of overwhelming the defenders with its weight of numbers so it doesn't suffer as many casualties as it would if a smaller force spread out an attack over a longer time. The larger a defending force is, the more it can avoid taking losses as a result of units having to fight after they are injured and the more flexibility it has to engage in preemptive strikes or in counterattacks.
Note that this "stack of doom" model is a good reflection of the way wars were fought through most of history. Without the mobility of railroads or motor vehicles, an army couldn't afford to spread itself out across a broad front that a concentrated enemy force could easily smash through. So both sides built up the biggest "stacks" they could, and the "stacks" fought against each other.
In a game played on a tactical map, concentration of force can be represented a different way. A larger force can spread out in an effort to overwhelm units on the ends of the opposing lines with flank attacks, which in turn makes it necessary for the smaller force to spread its lines dangerously thin in order to prevent the units on the ends of its lines from being overwhelmed. In this kind of game system, a limit of one or two units per tile can represent limits on how many troops it is practical to have occupy a given amount of space, but the size of the map still leaves plenty of opportunity for larger forces to take advantage of their weight of numbers.
But Civ is played on a strategic map where room to maneuver is often very limited, not on a tactical map with plenty of room to maneuver. When a player tries to capture a city, the city is represented by a single tile, not a line of tiles, so there isn't room to use superior numbers to spread an opponent's line dangerously thin or to overwhelm units on the end of the line with flank attacks if the enemy doesn't spread his line dangerously thin.
As long as the numbers of units are relatively small and bottlenecks don't restrict the amount of space available too much, a combination of 1UPT with kinds of units capable of ranged attacks can work. Under those conditions, an attack force made up of the right kinds of units can take advantage of its weight of numbers in spite of a 1UPT limit, providing a reasonable way of representing concentration of force.
The problems come when players want to involve more units than the map allows room for. Under those conditions, the 1UPT rule does not merely encourage the use of a mixture of short-range and longer-range units, but instead seriously sabotages the strategic virtue of concentration of force. This, in turn, necessitates rules deliberately designed to sabotage players' efforts to build large armies in order to prevent players from continually being annoyed and frustrated by not being allowed to concentrate their forces the way they want to.
It is also important to note that 1UPT can only make sense for land forces, not for naval forces. Throughout history, the goal of naval commanders who expect to fight major battles has been to concentrate the largest forces they reasonably could in order to maximize their advantage or minimize their disadvantage against the enemy's numbers. A 1UPT limit could make sense in a tactical naval game where tiles aren't much larger than a ship or squadron denoted by a single unit and turns represent no more than a few minutes of time. But in a game played on a strategic scale, a 1UPT limit can't even come close to depicting naval battles in a reasonable way. Ships are too expensive for any conceivable unit of ships to fill up a tile on a Civ map - unless maybe each unit represents a superpower's entire navy.
Finally, 1UPT runs into serious problems when it comes to strategic movement - that is, movement of units from one area to another. Without a "logistics officer" to take care of the details in an intelligent manner, the task of managing movement in such a way that units don't get in each other's way and the right units are in front when they reach their destination has the potential to be a serious micromanagement headache. And being unable to move units onto the same tile, group them as a stack, and move them together, takes away a valuable tool for reducing micromanagement in redeploying units to a different area.
I'd be interested to see some discussion of how these conceptual issues fit together with gameplay in Civ V.
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Conceptual Analysis of 1UPT in Civ5
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This is what 1UPT suppose to represent. It just does it withing limitation of being game, and without need of having separate screen for battle (like other games have, like Heroes of Might and Magic series). So think about co-located units as a single army (your doom stack if you will), but with the strategic depth of imitating different positioning of the units in the field. Think about it as if it represents much smaller scale (and indeed, where have you seen an archer shooting tens of miles, over the mountain?). Civ V 1UPT is simple consequence of not having separate screen to show local positioning of the troops, and instead showing it on global map. Sure, it is less realistic from scaling point of view, but it keeps everything in single screen and always visible to player.
And while the game mechanics have its own disadvantages, one of those is more tedious handling of the troops, but this is because it is more close to the actual battle, where generals have to deal with lots of tedious issues as well. And while I do think 1UPT mechanics can be improved (like allowing stacks for non-battle related activities - storage of the units and transportation) 1UPT model is definitively a step forward.