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Back in the days of the PSX I remember a friend who was never able to complete Warcraft II on the system because the later stages would fill up memory and slow down the game until it froze due to the number of units the A.I. was producing versus the system's capability.
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I imagine this was addressed in future games with unit capping respective of a designated system's resources.
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A month back I found myself in massive frustration when I discovered that Red Alert 3 was programmed to cheat by quickly manifesting as many units as possible.
Now, when RA3 first came out 'as many units as possible' may have been manageable but if EA set that unit cap
to adjust to a potentially upgradeable system......
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Have any of you tried playing twelve year old RTSs recently, which once offered a challenge within reason, only to discover that the A.I. has become a massive spam whore?

I haven't experienced this with RTSs, and I'm certainly not sure about your listed issue. RA3 should be new enough (and was multi-system enough) that it should likely have internal timing and not been written to expect real mode/speed up without bound.

But plenty of older classic games definitely have this problem.

* Lots of NES games counted on system slowdown when many things were on screen for a built-in handicap. This often vanishes emulated. (Though I think some emulators have built this in now.)
* Some older games definitely locked to CPU speed for their timing, and faster CPUs ruin them. Mechwarrior 2 was one of them that comes to mind that required slowdown to work. (On top of a few other issues...)

If you want to know why this latter one happens: https://superuser.com/a/631131

No, the RTS games I play typically have been recoded for the modern age, like Warzone2100.

Red Alert 3 is hard locked to 30 FPS. All the internal logic is also bound to it. If you attempt to unlock the framerate, it will just speed up the game.

As for CPU speed impacting gameplay, you will usually notice it. Either by, as mentioned, the game running faster than it should, or things breaking like AI not working, scripts breaking etc. But this is mostly a problem with very old games.

I can say that Red Alert 3 works perfectly fine on a Windows 10 PC.

As someone who plays a lot of old(er) RTSes, no, I can't say I've ever run across this kind of issue. There are, of course, games which are just designed poorly at their time and will behave oddly on newer OSes or hardware, but that has nothing to do with the genre they're part of :P. Freedom of multi-threaded speech, man :P...

Warcraft II's AI has always been spammy, nothing has changed in that regard.

I don't know much of such games but it's kinda interesting topic. I think The 7th guest (at least original release) has some vs. AI minigame that became close to impossible to win on newer hardware without using external programs to plan moves.

I think it's going to depend on the game. I still play Age of Empires 1-2 (1997-1999) that are 22-24 years old now without any issue or AI changes.

Edit: Games that have physics locked to frame-rates can easily break when non working VSync causes like +900fps on modern PC's. There are fixes to that though, eg, use a wrapper like dgVoodoo to upgrade the renderer so that VSync does work / and or cap the frame-rate externally.

Ultima 2 runs spectacularly poorly on non-period computers. Specifically, one of two things will happen:
* The game will run *way* too fast, resulting in you losing all your food before you have a chance to do much. (Note that the game is turn-based, except that your turn ends if you take too long (where "too long" can be way too short on a non-period computer).)
* The game tries to calibrate the game loop by measuring how long it takes for a loop to run a certain number of times, then uses the result of that as a denominator. (Or, at least, that's how I suspect the game is working.) However, if the CPU is fast enough, this loop could easily finish in zero (0) time, resulting in the game trying to divide by 0.

There's a reason that the GOG version of Ultima 2 has DOSBox running at a ridiculously low number of cycles (I heard something like 300); if it ran faster than that, the game would not be playable.

Ultima 3 seems to handle things better; the time to enter a command is 5 seconds even on modern computers. The only issue that you run into on a modern computer, then, is that the whirlpool, which moves in real time, moves *way* too fast, which can be a problem when it comes to ship life span, or when you're trying to avoid or seek it out.

(Note: These are assuming you're not using any fan made patches. Said patches exist, and they are meant to fix the issues I mention here, with some options for fixing other perceived flaws with the game.)