Chance of Norm Koger doing a sequel?

[golden delicious]

ORIGINAL: Karri

Furthemore, the Supreme Command needs to 'know' how to give objectives(instead of designer implementing those objective tracks),

How do you do this, though? How does the computer know what is important and what isn't? This is an incredibly human decision, which is why it is made by the designer
at the moment.

The key is information and how to use that information, and it should flow both ways. For example the 1st corps gives the 1st division the task of capturing the city of Kharkov. 1st division 'analyses' the situation and sends back a message that this is impossible without 2nd and 3rd division securing flanks. 1st corps then analyses the situation and decides if it can allow 2nd and 3rd division to do that.

This is how real armies work- but I think it's an inefficient and roundabout way for the computer to work. After all, I Corps, 1st division and everyone else are in fact all controlled by one staff. Further, the situation is much more complicated that deciding whether or not to attack one point and whether or not to assign support to that attack.

So to take your basic concept, I Corps decides on a list of possible actions and sets them priority ratings. It then apportions troops to these tasks according to those ratings. Then it records the highest priority rating which could not be achieved due to lack of troops, and the lowest priority rating which was achieved. GHQ then reassigns troops from areas which were able to do all their priorities to areas which have lots to do.

All of this would be very difficult to make the computer do. The virtue of my proposition is that it fits the existing model where most of the problems have already been solved. It could also apply at least partially to existing scenarios as well as new ones.

[a white rabbit]

ORIGINAL: golden delicious

ORIGINAL: a white rabbit

..you're looking at it wrong, on the right magnification, a formation, say a corps is one 'thing', with a limited number of options,

The options are finite, sure. But they number in the millions. Raise this to the power of the number of formations, and then add in the possible actions of the other side (bearing in mind sharply limited intelligence, whereas in Chess and Go intelligence is perfect).

..what toaw does now, is decide btn by btn, refering only to the pre-set objective track for that btn's formation,

This is more or less the problem. But the solution to this isn't a brute-force approach like you use for a Chess computer. You'd want a learning AI which tries to be more like a human player and less like an adding machine.

The idea I had would be for the player to design objective tracks independent of the formations. The AI would then judge how it was performing on each of these objective tracks relative to one another, and assign its formation to these tracks depending on the situation. So if the situation on one track is changing rapidly, that gets extra formations assigned to it.

..toaw is a prgram, the computer at the moment is still just a glorified adding machine..

..never the less, i can't see why it can't do objective-track comparisons and act accordingly, we've got the RAM to do the comparing, and we've got the storage to enable a good number of possible futures to be held in memory during the comparison process..it's hardly rocket science..

..and no, you're still not seeing it right, the number of options open to a corps are very limited, less i suspect than the first placing on an iGo board, just as the options for a btn are limited. A corps has to look at the objectives, a btn only at the enemy in front, they shouldn't even use the same parts of the program..

..as to the unknown, isn't that what recon is for ?..

[a white rabbit]

ORIGINAL: Karri

ORIGINAL: golden delicious

ORIGINAL: a white rabbit

..you're looking at it wrong, on the right magnification, a formation, say a corps is one 'thing', with a limited number of options,

The options are finite, sure. But they number in the millions. Raise this to the power of the number of formations, and then add in the possible actions of the other side (bearing in mind sharply limited intelligence, whereas in Chess and Go intelligence is perfect).

..what toaw does now, is decide btn by btn, refering only to the pre-set objective track for that btn's formation,

This is more or less the problem. But the solution to this isn't a brute-force approach like you use for a Chess computer. You'd want a learning AI which tries to be more like a human player and less like an adding machine.

The idea I had would be for the player to design objective tracks independent of the formations. The AI would then judge how it was performing on each of these objective tracks relative to one another, and assign its formation to these tracks depending on the situation. So if the situation on one track is changing rapidly, that gets extra formations assigned to it.

IMO, the only solution if one wants to improve the Ai is to completely redo the OOB system of TOAW. Once you have a 'clear' OOB, ie this division is part of this corps, which is part of this army, which is part of that Army Group which is commanded by the Supreme Command, can you actually develope an AI that thinks in the grand scale.

Furthemore, the Supreme Command needs to 'know' how to give objectives(instead of designer implementing those objective tracks), then the army groups, corps, divisions, and battalions need to know what they can do and what they should do.

The key is information and how to use that information, and it should flow both ways. For example the 1st corps gives the 1st division the task of capturing the city of Kharkov. 1st division 'analyses' the situation and sends back a message that this is impossible without 2nd and 3rd division securing flanks. 1st corps then analyses the situation and decides if it can allow 2nd and 3rd division to do that. If not it will either cancel the attack or ask for more reinforcement...or if the situation is desperate it will force the order...and so on.

..sorry but we're stuck with objective tracks, but hopefully at a higher formation level..

..what you describe is , on the right magnification, a "tactical" matter, grand "tactical" maybe, but whatever you call it, is part of the 2nd level comparisons, which are an Elmer thing, as are the 3rd level, really tactical btn actions..

..sorry to repeat myself, but all of which takes enormous temp storage, which we have, and RAM, which we have. Elmer needs space and time, to 'think', in fact to do the sums and see which comes up with best numbers and act, then add up the results, recompare, and act and so on till turn end..

..computers are stupid, get the view point right, a human thing, and you can make them jump thru hoops if you have the necessary, see preceeding para. Toaw 1 was written in an age when 10GB storage and 128 RAM was huge, it's basic machinery is still good, one of the reasons it's still around, but these limits no longer apply, and it should expand to the new limits, in particular those of temp storage, RAM is less important as a good program should always use the min RAM possible, s'a programmer-thing, it shows just how good you really are...

[a white rabbit]

ORIGINAL: ralphtrick

ORIGINAL: berto
Where it makes sense, and where it is implementable in future versions of TOAW, please give the AI more time to "think" according to our, the players', choosing.

I'll do that, but the problem is fundamentally different from chess. In chess, the computer wins by figuring out moves 8+ moves ahead. In a game like TOAW, it isn't even possible to look at the next move in that kind of detail because the number of potential end positions in a typical turn is huge.

There are 2 options for a non-cheating Elmer.
1) Do like a human does, and try to remember where you've seen units, rely on your memory of past times playing the game and starting positions, and make some sound decisions about what your options are and what's likely to work, guided by hints from the designer.

2) It's possible to play Elmer with both sides so that he can estimate what you might have done, unfortunately because he play by the same rules you do, after the first couple of moves, that becomes very, very, very difficult.

#1 is much more practical, and is probably where I'm headed with Elmer, along with giving the designer greater control over Elmer's behavior. There are also things called influence maps that can help to analyze maps. I'm not sure what part of that will be in the initial release and what parts will come later.

Ralph

..apolgies to Ralph, but..

..please to look at the faulty human thinking there, starting with the fundamentallly flawed chess comparison., fine on a 56k Sinclair, but now ?!?..

..yes, if any map is taken btn by btn then the options are huge, that was always the excuse..

..now lets take our largest parent formation, say a corps, and just analise it's options, on a corps level/magnification map and compare them with our objective tracks, do it, it's around zoom-out 3/4, any scen, see how few choices there are ?

..now let's go to our divisions, that make up that formation, 2nd level, zoom 1/2, and look at the basically local decisions, all it needs to work on is the route to the Corps objective, so in reality, see how few choices there are ?..

..now down to zoom 0/1, btn level, on zoom 0, my options are very limited indeed, even on z1, after all the next combat phase is all that counts..

..3 levels, 3 levels of decision-making all of which end up at the parent formation as a refined number, how many parent formations, in most games very few, tops 20..

..i reckon Elmer can handle 20 pieces..

[golden delicious]

ORIGINAL: a white rabbit

..never the less, i can't see why it can't do objective-track comparisons and act accordingly, we've got the RAM to do the comparing,

That's the solution I proposed in the post you were quoting. But it can't make it's own priorities. Figuring out what you need to do to win is just too human a task.

..and no, you're still not seeing it right, the number of options open to a corps are very limited,

From a human point of view, yes. It can go here or here or here. But from a computer point of view it can put this unit in 145,100 and the other in 145,101, or they could swap round, or be in any of a thousand other combinations of hexes. All for one formation operating in a very small area. Then raise to the power of the number of formations.

Then add that you can't know what the result of any of these moves will be because your information will never be even close to being complete (even if you had perfect intelligence, combat is still random). So this brute force approach will never work no matter how much RAM you apply to the problem.

Not that formations are the problem. The PO can handle individual formations already.

[a white rabbit]

..i agree, a computer can't work outside of guidelines, but i don't believe Elmer has to be as rigid/stupid as he now is, on a strategic level, cos he's very good on the tac stuff.

.. Look at a CPA of a map, on the right zoom, let's try Europe 44. On zoom3/4, army level, Allies...

..the targets are few and relatively easy to give a numerical value to based on their relative, programmed importance.

..The ports first, no functioning port, immediate priority number, which port ? proximity, nearer the better; on rail net ? y/n; port size, bigger the better; nearness to own ports; known enemy units (Plus 25%), so he goes for the Contentin..

..Paris, pluses are river crossing point, rail hub, proximity, airfields, and a designer added French ego bonus..

..Brussels, pluses are rail net, proximity to a major port, aproaches the final objective Berlin, airports, river crossing point, and the route releases several minor portsl..

..he goes for Brussels

[a white rabbit]

ORIGINAL: golden delicious


From a human point of view, yes. It can go here or here or here. But from a computer point of view it can put this unit in 145,100 and the other in 145,101, or they could swap round, or be in any of a thousand other combinations of hexes. All for one formation operating in a very small area. Then raise to the power of the number of formations.

Then add that you can't know what the result of any of these moves will be because your information will never be even close to being complete (even if you had perfect intelligence, combat is still random). So this brute force approach will never work no matter how much RAM you apply to the problem.

Not that formations are the problem. The PO can handle individual formations already.

..just not so, what it handles are individual units. That these compose what we call a formation is irrelevant, it does not move the formation, just the bits..

..and what's the fascination of the phrase raise to the power of ? 20 formations or units or whatever is multiply by 20, not to the 20th power, which is a much smaller number, one that he can now handle ..

..as to lack of information, so ? it's a handicap we all play under, why should Elmer be any different ? He takes the best case as we all do, and suffers when he gets it wrong...mmm, maybe he could be given a board posting privilege and a "argghhhh i fucked up" message, then post the move in question..

..oh, one thing i tried on the Speccie was using the HQ unit as the formation reference point, so only one unit to 'think' about. It worked but i always got basically the same distribution pattern, and i didn't have the space to add optional formation patterns, not on 56K..

[Karri]

ORIGINAL: a white rabbit
..and what's the fascination of the phrase raise to the power of ? 20 formations or units or whatever is multiply by 20, not to the 20th power, which is a much smaller number, one that he can now handle ..

If it will be that simple, then the AI will be more idiotic than it is now.

[Karri]

ORIGINAL: golden delicious
How do you do this, though? How does the computer know what is important and what isn't? This is an incredibly human decision, which is why it is made by the designer
at the moment.

The bascis need to be of course done by the designer. But the computer, 'supreme command' needs a way to calculate the most important thing to do. like for example should Soviet Union delay and retreat instead of advance to Berlin...

This is how real armies work- but I think it's an inefficient and roundabout way for the computer to work. After all, I Corps, 1st division and everyone else are in fact all controlled by one staff. Further, the situation is much more complicated that deciding whether or not to attack one point and whether or not to assign support to that attack.

Well here you are wrong, why not simply make many AI's? Why does the basic grunt need to be controlled by the supreme command? We know what historically happened when a certain fuehrer though he was smarter than his generals and when he tried to order every single battalion personally.

So to take your basic concept, I Corps decides on a list of possible actions and sets them priority ratings. It then apportions troops to these tasks according to those ratings. Then it records the highest priority rating which could not be achieved due to lack of troops, and the lowest priority rating which was achieved. GHQ then reassigns troops from areas which were able to do all their priorities to areas which have lots to do.

All of this would be very difficult to make the computer do. The virtue of my proposition is that it fits the existing model where most of the problems have already been solved. It could also apply at least partially to existing scenarios as well as new ones.

I disagree, it's simple mathematichs. It's not difficult for computer to do. What is difficult is for the humans to program such a system.

[ralphtricky]

ORIGINAL: a white rabbit
..and what's the fascination of the phrase raise to the power of ? 20 formations or units or whatever is multiply by 20, not to the 20th power, which is a much smaller number, one that he can now handle ..

I'm sorry, but it is the power of. Let's say you have one piece you could move one hex. That's six possible locations. If you have two pieces, then since they'd move independently, but said the first one moves north, the second one can move any one of the six the first one moves northeast, the second one can still move anyone of the six, and so forth. That's six times six locations or six to the power of two locations.

Let's say a unit can move six hexes. The number of hexes that he can move to is six times six times PI or about a hundred hexes. Those two pieces have a possible 10,000 or so locations.

While it would be simple,keeping track in that way simply isn't possible.

Ralph

[ralphtricky]

ORIGINAL: Karri
I disagree, it's simple mathematichs. It's not difficult for computer to do. What is difficult is for the humans to program such a system.

So is cold fusion[:'(], we just need to figure out a couple of those pesky engineering details.

People are getting a lot better about programming AI. That's especially true now that PCs have enough power that they can devote some of that power into the AIs. Up until recently, especially for the real-time games, they were able to devote very little horsepower into the AI.

The big advantage to any hierarchical AI, which mimics the behavior of a regular army, is that it allows you to control the complexity of the picture that you need to look at at any one time. The General Staff AI needs to determine whether to attack or retreat, whether to head for the left or the right flank, and broad strategies like that. It can do this based upon a 3 x 3 or 4 x 4 representation of the map. It will also help the AI to respond realistically to feints, etc.

The main reason that you want objective tracks right now, is that determining the plan is an extremely complicated problem. A human can take a look at a map, read the briefing, and from this formulate a plan. While the AI can analyze the map, it can't read the briefing. You'd also need to have the AI understand events triggered by hex occupation, future reinforcements, etc..

It also helps for some scenarios in keeping the AI playing historically.

The AI does need to know how closely it should follow the objective tracks, and when to throw them out because things have gone off the rails, and the player or the scenario designer or both should be able to modify this behavior.

Ralph

[golden delicious]

ORIGINAL: Karri
Well here you are wrong, why not simply make many AI's? Why does the basic grunt need to be controlled by the supreme command?

Because the aim of designing AI is to produce a strong opponent- not one who acts like a human.

We know what historically happened when a certain fuehrer though he was smarter than his generals and when he tried to order every single battalion personally.

Hitler did not have an intel pentium processor and a gigabyte of RAM.

I disagree, it's simple mathematichs. It's not difficult for computer to do. What is difficult is for the humans to program such a system.

Semantics.

[Karri]

ORIGINAL: golden delicious
Because the aim of designing AI is to produce a strong opponent- not one who acts like a human.

On the contrary, we want one that can 'read' the game like a human. Not an AI that use this and that cheat to be 'strong', like in so many games so far.

Hitler did not have an intel pentium processor and a gigabyte of RAM.

...yeah...

Semantics.

Wow, you completely trashed my point. Your argument is pure gold.

ORIGINAL: ralphtrick
So is cold fusion[:'(], we just need to figure out a couple of those pesky engineering details.

We, or rather them scientists, still try. Still, isn't that a bit defeatist attitude?

People are getting a lot better about programming AI. That's especially true now that PCs have enough power that they can devote some of that power into the AIs. Up until recently, especially for the real-time games, they were able to devote very little horsepower into the AI.

I haven't honestly yet faced a single AI that would impress me in any way. real time games especially suck.

The big advantage to any hierarchical AI, which mimics the behavior of a regular army, is that it allows you to control the complexity of the picture that you need to look at at any one time. The General Staff AI needs to determine whether to attack or retreat, whether to head for the left or the right flank, and broad strategies like that. It can do this based upon a 3 x 3 or 4 x 4 representation of the map. It will also help the AI to respond realistically to feints, etc.

Well yeah. But why does the 'general staff' still need to guide every single unit? I mean let's look at the current system; it sucks. Honestly, the AI is bad, really bad. So why not try something different?

The main reason that you want objective tracks right now, is that determining the plan is an extremely complicated problem. A human can take a look at a map, read the briefing, and from this formulate a plan. While the AI can analyze the map, it can't read the briefing. You'd also need to have the AI understand events triggered by hex occupation, future reinforcements, etc..

Yeah, well the problem is that the objective tracks is one plan. And on top of that it is a different plan for each formation. It doesn't work. It's better than nothing, but it's really not that good. If yu want to improve it, then make it possible to make the formations take in effect each others 'tracks'.

That's not even the problem, the problem is that the objective track concentrates on capturing the map, which causes a problem since the objective should be to destroy the enemy forces, which the objective tracks cause to be a secondary objective.

[golden delicious]

ORIGINAL: Karri

On the contrary, we want one that can 'read' the game like a human. Not an AI that use this and that cheat to be 'strong', like in so many games so far.

It doesn't have to cheat- it has numerous advantages anyway, because it knows the code in a way the player never can.

This whole approach to computers and robotics infuriates me. Why has a Japanese company made a walking robot? Robots are rubbish at walking- and tracks are better anyway. A robot will never walk as much like a human as a human does, and an AI will never be as good at being human as a human is. So quit trying- it's not necessary.

Wow, you completely trashed my point. Your argument is pure gold.

Well, to be fair, you didn't really have a point in the first place. It wasn't too hard.

Well yeah. But why does the 'general staff' still need to guide every single unit?

It doesn't have to, but this is one of the advantages of AI. A human brain can never properly understand how one unit relates to the action of the other 1500. An AI can.

That's not even the problem, the problem is that the objective track concentrates on capturing the map, which causes a problem since the objective should be to destroy the enemy forces, which the objective tracks cause to be a secondary objective.

That's a good point. I suppose you should have the option just not to define any objective tracks at all. Then the AI locates the enemy centre of gravity and tries to neutralise it one way or another. It would probably be pretty good at doing the former through statistical analysis.

[Karri]

ORIGINAL: golden delicious
It doesn't have to cheat- it has numerous advantages anyway, because it knows the code in a way the player never can.

It doesn't know the code, at all. THAT would really require AI we've never seen.

This whole approach to computers and robotics infuriates me. Why has a Japanese company made a walking robot? Robots are rubbish at walking- and tracks are better anyway. A robot will never walk as much like a human as a human does, and an AI will never be as good at being human as a human is. So quit trying- it's not necessary.

...what?

Well, to be fair, you didn't really have a point in the first place. It wasn't too hard.

...or you didn't undrestand it, either way it doesn't mean you have a point.

It doesn't have to, but this is one of the advantages of AI. A human brain can never properly understand how one unit relates to the action of the other 1500. An AI can.

Nonsense. As it is right now, the AI is doing far worse job undrestanding the relations between the units. You encircle a division and the AI is happily sitting that other formation where it is, because that's it's objective.

That's a good point. I suppose you should have the option just not to define any objective tracks at all. Then the AI locates the enemy centre of gravity and tries to neutralise it one way or another. It would probably be pretty good at doing the former through statistical analysis.

The basic 'core' of actions always needs to be laid down by the designer. I still think the first step is to create a real 'OOB', instead of the system we have now, where each fromation is a separate entity.

[golden delicious]

ORIGINAL: Karri

It doesn't know the code, at all. THAT would really require AI we've never seen.

I mean it can calculate odds without having to use the attack planner- because it is the attack planner. It can- in theory- mentally put all those units together and estimate the outcome. Humans can try to do this, but they're not as good at it.

...or you didn't undrestand it,

I understood what you meant (but thanks for assuming I'm an idiot). You were picking a petty hole in my wording because you disagreed with other parts of my argument.

Nonsense. As it is right now, the AI is doing far worse job undrestanding the relations between the units. You encircle a division and the AI is happily sitting that other formation where it is, because that's it's objective.

You don't seem to see what my point is. The above is the behaviour of the current AI. We're discussing alternatives. In the basic objective-based alternative I proposed, if the player suddenly leapt up one objective track (as would happen in a flanking or encircling action), the PO would react by directing more formations to that track.

This approach isn't the best- but it's a step up from the existing system which is relatively easy to achieve.

The basic 'core' of actions always needs to be laid down by the designer. I still think the first step is to create a real 'OOB', instead of the system we have now, where each fromation is a separate entity.

I don't see this need. Since formations should be able to switch between higher HQs anyway, why tie them to those HQs for the purpose of the AI? It may be that it's best for the AI to chop the front up into sectors and assign its formations between them, but I don't see why this system should be based arround a rigid command structure.

[Karri]

ORIGINAL: golden delicious
I mean it can calculate odds without having to use the attack planner- because it is the attack planner. It can- in theory- mentally put all those units together and estimate the outcome. Humans can try to do this, but they're not as good at it.

In order to calculate the odds it has to cheat(see the enemy unit information), otherwise it canno't calculate any more than human can.

I understood what you meant (but thanks for assuming I'm an idiot). You were picking a petty hole in my wording because you disagreed with other parts of my argument.

Reap what you sow.

You don't seem to see what my point is. The above is the behaviour of the current AI. We're discussing alternatives. In the basic objective-based alternative I proposed, if the player suddenly leapt up one objective track (as would happen in a flanking or encircling action), the PO would react by directing more formations to that track.

yeah...which was a point I made aswell, so I guess neither of us see each others arguments...however I do not view this as the best possible AI, or even one that can offer much more 'resistance' than the current one.

I don't see this need. Since formations should be able to switch between higher HQs anyway, why tie them to those HQs for the purpose of the AI? It may be that it's best for the AI to chop the front up into sectors and assign its formations between them, but I don't see why this system should be based arround a rigid command structure.

Erm, because as it is formations have NO higher HQs. I don't really get what you are proposing, that there is a command structure or that there should be none?

Why would a proper OOB tie down the units to certain HQ? The point of a proper command system is just the opposite...as it is now, they are tied down, and have no higher HQs.

[golden delicious]

ORIGINAL: Karri


In order to calculate the odds it has to cheat(see the enemy unit information),

Is it a cheat when you use the attack planner?

The AI can make an estimate based on that same calculation (plus some bits which it currently ignores), only it doesn't have to move the units into place first.

yeah...which was a point I made aswell, so I guess neither of us see each others arguments...however I do not view this as the best possible AI, or even one that can offer much more 'resistance' than the current one.

I agree it's not the best possible- but I'm concerned with what is achievable, as there are numerous things that need doing and only very limited resources.

Erm, because as it is formations have NO higher HQs. I don't really get what you are proposing, that there is a command structure or that there should be none?

That there doesn't need to be. The reason for a command structure in a real army is that one human officer can only handle a certain number of subordinates. That's not the case for an AI.

Why would a proper OOB tie down the units to certain HQ? The point of a proper command system is just the opposite...as it is now, they are tied down, and have no higher HQs.

They're not tied down. Take FitE. You can move a division across the map and it will perform exactly the same way with no other actions. If you design a force structure, you also have to provide a mechanism to allow units to transfer.

[Karri]

ORIGINAL: golden delicious

Is it a cheat when you use the attack planner?

The AI can make an estimate based on that same calculation (plus some bits which it currently ignores), only it doesn't have to move the units into place first.

I ment that in order to calculate the attack it needs to see what kind of equipment the enemy unit has. Unless it can do that, it won't do any better than a human player. In fact, a human player can do far better because he knows the 'tricks' of the combat system. Ant unit attacks etc.

Simple odd calculations as in attack and defence strenght don't mean a thing, because they don't decide battles. There's been lot's of discussion of this before.

I agree it's not the best possible- but I'm concerned with what is achievable, as there are numerous things that need doing and only very limited resources.

Well yes, very true. Since I don't play against AI I prefer the other changes take priority.

That there doesn't need to be. The reason for a command structure in a real army is that one human officer can only handle a certain number of subordinates. That's not the case for an AI.

I'm not quite sure about that. It can handle a million units for sure, but it can't handle them well.

They're not tied down. Take FitE. You can move a division across the map and it will perform exactly the same way with no other actions. If you design a force structure, you also have to provide a mechanism to allow units to transfer.

No, not actually. Supply, artillery support, etc. is reduced if the unit belongs to another formation. Providing a mechanism to allow unit transfers should be no big deal.

[golden delicious]

ORIGINAL: Karri

I ment that in order to calculate the attack it needs to see what kind of equipment the enemy unit has. Unless it can do that, it won't do any better than a human player. In fact, a human player can do far better because he knows the 'tricks' of the combat system. Ant unit attacks etc.

The AI, though has other advantages. It can track counters from turn to turn and remember their approximate combat factors even if they're not "spotted" on a turn. It can analyse rear area deployments over several turns to estimate the total force in the rear even when it is never all visible at once.

Well yes, very true. Since I don't play against AI I prefer the other changes take priority.

Ditto- although this is a circular argument. If the AI were a real opponent more people would use it.

I'm not quite sure about that. It can handle a million units for sure, but it can't handle them well.

The point is that it can handle each one of those million units just as well as it could handle each one of a hundred units. In the case of a human player, he can handle a hundred brilliantly but will not be able to cope with a million- or even two thousand.

No, not actually. Supply, artillery support, etc. is reduced if the unit belongs to another formation.

You were talking about higher commands- not moving one part of a formation. Then the only consideration is co-operation levels, which are often unaffected anyway.