Forest penalty to Calvary?

The civ5 mounted units all have these two attributes:
  • Penalty Attacking Cities (33)
  • No Defensive Terrain Bonuses
Except for a couple unique units.
They did not start with the city penalty on release - in vanilla 5 it was added because the meta was just horseman rush; horseman were stronger and faster than anything else, so they were invaluable for attacking cities AND they could just scoot around like no ones business.

I would argue we need to reintroduce both of these penalties for our mounted units because:
Mounted units feature higher strength and movement than other unit classes but barely cost more, and sometimes cost less, than other contemporaries
There's no reason to melee attack a city and use a melee and anticav unit when you have mounted units available, especially heavy cav. They simply hit harder.

Basically, mounted units never actually pay for being so mobile. This makes them ideal attackers and defenders because you can respond so much better than using something slow like pikes.
If mounted could not get the defensive bonuses, they would still be the best units for offense, but there would be a reason you might want swords or something to be hunkered down holding the hills and forests.

The city penalty is to give the melee unit line a fair shake at existing. Why build a sword for 90 production when you can get a unit that is twice as fast, with the same strength for 80 production? Etc.
They introduced it in civ5 because we learned a hard lesson about why you don't make one unit line both the strongest and fastest.
It would also be helpful if they made the battering ram and siege tower only apply to soldiers on foot. Tank type units in civ5 lost the city penalty once upgraded from cavalry iirc. That's fine to me given how radically things change at that point in the game. Plus, you know, tanks are just armored artillery cannons on treads.

The end result of bringing back these penalties is that mounted units are still killing machines. They are the go to if you want to clobber your enemy in the field. They just aren't as effective as melee once bogged down and besieging cities. There are two resource consuming unit lines (melee and the mounted units) and there is no reason to ever use a melee unit when you have heavy cav of the same era available.
 
Been here before: Historical Negatives associated with Mounted/Cavalry units:

First, Civ VI got it backwards: the limiting factor is the extra expense in raising Heavy Horses required for Heavy Cavalry - including heavy chariots, so the Horse Resource should be required for the Heavy Cav line, not the Light Cavalry, which historically could use just about anything on four legs that wasn't bovine or woolly (or striped - nobody could ever domesticate or tame Zebras).

Second, except in cultures where the daily way of life was on horseback (Scythian, Hun, Mongol, Commanche, Lakotah, etc) Mounted Units take a lot of 'Maintenance' - horses eat, on average, about 5 - 10 times more than people per day and it can't all be 'grass'. Mounted also have to train, and keep training to stay proficient, and that includes both man and horse - which adds to the cost of keeping them around.

So, all other things being equal, Mounted will cost more than Foot to acquire, and they will cost 2 - 3 times more than Foot to Maintain.
IF you are not one of the 'mounted cultures' the cost in land devoted to pasturage alone means the bulk of your army cannot be mounted unless it is a very tiny army compared to your population - a tiny 'elite' force like the armored aristocratic feudal knights of Europe or the heavy cavalry of Tang China (1000 armored cavalry out of an army of 60,000 is the figure for one of their battles)

Finally, there are terrain types that are much more deadly to mounted units than to foot: Rain Forest/Jungle, Marsh/Swamp probably the worst, but Deserts a close second. Even 'normal' terrain and weather can get nasty: Napoleon in 1812 and the German Wehrmacht in 1941 each lost 1/4 to 1/3 of their horses to the Russian Summer: hauling heavy loads in hot sun on less-than-optimal water and fodder supplies killed them off in droves. Modeling that explicitly is beyond the scale of Civ, I think, but the problem of providing constant 'remounts' should be included in Per Turn Maintenance Costs for mounted units.

Finally, a negative modifier for cavalry attacking cities is Spot On: Even if you can get them off their horses to climb a ladder over a city wall, they forego all their advantages of mobility and the combat impact of the horse. Likewise, men on horseback do not get the same advantages out of terrain that men on foot get. For one thing, a horse charging down a slope from the top of a hill doesn't get more impetus, unless reined in he goes head over horseshoes and reaches the bottom with rider and mount both nursing broken bones. Any terrain, like forest or marsh, the restricts mobility camps horsemen far more than foot, because the cavalry relies on its superior mobility and the impact of its charge for so much of its Combat Power: horses bouncing off trees do not intimidate...

So I would add to the Civ V penalties to Cavalry increased initial cost and increased Maintenance Costs for all Heavy Cavalry, and for Light Cavalry except for such units raised by Horse Cultures: in the game now that would be Scythians and Mongols, OR the game could allow reduced maintenance (by 33 - 50%) for each Light Cavalry Unit, up to the total number of Horse Resources with pastures in your Civ - even the Aztecs, if they happen to be settling cities on lots of grasslands, plains, and Horse Resources, should be able to raise and maintain cavalry much more easily than, say, a Rain Forest enclosed Norway...
 
Mounted troops also couldn't hold a position unless they fought dismounted. You couldn't tell a unit of horse to go to that hill and hold it against attack and expect them to do so. It robs them of any combat advantage they might have until you get to WWII era tanks which is due to the fact that they have guns and thus can be entrenched to a degree. Light and Heavy horse shouldn't get defensive bonuses.
 
Mounted troops also couldn't hold a position unless they fought dismounted. You couldn't tell a unit of horse to go to that hill and hold it against attack and expect them to do so. It robs them of any combat advantage they might have until you get to WWII era tanks which is due to the fact that they have guns and thus can be entrenched to a degree. Light and Heavy horse shouldn't get defensive bonuses.

With two notable exceptions, which Civ has never accurately modeled.

First, starting in the 17th century (specifically, Count von Mansfeld organized the first unit in 1624) a new 'class' of Light Cavalry appeared in Europe: Dragoons. They were basically mounted infantry: use horses to get into battle quickly, dismount and fight on foot with muskets. They were frequently used to 'hold' special points ahead of the army, like bridges or defiles, or to cover the flanks of a defense or advance, so they relied on precisely those 'terrain advantages' that other Cavalry could not use. They also tended to be mounted on whatever cheap, small horses were available, because they weren't expected to actually fight on them, which made them cheaper to raise and maintain than 'regular' cavalry.

What makes Dragoons particularly and potentially useful for Civ is that they very quickly became used all over Europe for Reconnaissance/scouting duties. Within 100 years they also became good enough on horseback that some armies (Prussia for starters) were using them as regular 'battle cavalry' - charging enemy infantry, even (with less success) fighting regular cavalry on horseback. In other words, they could potentially be a late Renaissance-early Industrial Era Scout unit and/or the first Light Cavalry unit in the game that can actually get Terrain advantages.

Second, as rifles became the standard infantry firearm in the 1840s - 1850s, cavalry began getting off their horses more: a man on a horse was simply too big a target. The first to do this on a regular basis was the United States Cavalry, whose first 6 regiments included 2 regiments of dragoons, 2 regiments of Mounted Rifles (infantrymen on horseback) and 2 regiments of 'cavalry' - so they started with a strong bias for dismounted action.
That means that the Cavalry of the Industrial Era in Civ should get Terrain Bonuses, because they were increasingly armed with good rifled carbines (and, for instance, the 'karbin' used by the German cavalry in 1900 was almost identical to the standard infantry rifle of 1939, so in useful firepower they were almost the equal of infantry units)

Finally, interesting you should mention WWII, because the second largest cavalry force in history was the Soviet Army in WWII: in April 1943 their cavalry units included 9 Corps and just over 230,000 mounted men. Although propaganda photos almost always show 'Red' cavalry charging and waving sabers, and they certainly trained to do that, most of their combat action was dismounted. In fact, the cavalry were the first troops to have half their men armed with sub-machineguns for higher firepower in the assault, and by late 1943 every cavalry division included a tank regiment, so a 'cavalry attack' most often resembled an elite infantry attack: assault troops with submachine guns blazing, supported by tanks, self-propelled guns, and heavy mortars, all of which were part of the 'cavalry' Corps.
 
knights fought dismounted too, like in the battle of Cresy, and many other
even nomads sometimes fought dismounted, like Xionnu archers when faced by chinese crossbowmen
i think cavalry should not be much stronger than swordsmen, but get an 'attack in open terrain' bonus (and spearmen -- 'defense in open terrain')

also, on the operational level, infantry doesn't move much slower than cavarly, afaik. it can march 50 km/day, pretty same distance as cavalry. cavalry can do forced marches but infantry is capable of that too. its only when there are multiple horses per warrior, cavalry can travel significantly faster (mongols up to 150 km/day).
 
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