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In some 4Xs with no city cap or expansion penalty, exponential growth is the optimal solution.
Alas, this inevitably means that the player's cognitive load also grows quadratically in time, until each 1 turn takes >1.5 hours to grind out. Soon thereafter, you shrug and play something else. (I've never finished a game of Space Empires IV or V because of this. SE3 I did finish, only once, ever.)
In 4Xs with a city limit but no penalty, the optimal solution tends to be exponential growth up to the city limit, then stop
Amplitude's 4Xs (including Endless Space 1 & 2) introduce expansion disapproval as a braking mechanism. As an armchair designer, I approve of their attempt: it shows that they've taken the lessons learned from old 4Xs into account, and they've tried something to address it. Expansion disapproval slows down your optimal expansion rate, without entirely limiting it. Roughly speaking, the number of cities you can keep Fervent (90+ approval) depends on your techs, luxury boosters, some hero skills/accessories, and the size of your cities, and all of these things increase as you advance through tech Eras -- if you choose to go get them. You could emphasize +approval things instead of other productivity or military gains, and have many cities, or do the converse, or hunt for a sweet spot amidst those trade-offs. Trade-offs are good, and keep the game interesting.
To simplify, there is an "optimal number of cities" for each Era, and its growth isn't quite exponential. You're penalized for exceeding this curve too quickly, but you're penalized even more by lagging behind the curve. Around Era V-VI, you could have 20+ cities all Fervent, and that's enough for any 1 game. Even on a huge map, you need only 55-60 cities for Expansion victory condition, and so you cannot have more cities than that (because the game ends and you win). So as your conquering armies bring you close to 1/2 that amount, city approval becomes almost irrelevant. Just have your unstoppable armies keep doing what they're doing, steamroll the rest of the cities, ignore their unhappy status, and go win the game.
I get the need to mechanics that stop blobbing however I still dislike how endless legend does it. Because it stops expansion by putting a hard limit on it.
If they felt the need to prevent blobbing, I’d rather have some sort of strong temporary penalty to expansion, or have the expansion penalties only apply to new cities, so expanding just because less useful, but never negatively useful like in endless legend.
I mean they could at least maybe add a vassal/sack option, so you have a way to deal with people when you don't have the approval to absurd them.
Expansion disapproval doesn't prevent you from grabbing "more" cities than your optimal number. You just trade off some approval for having those extra cities. You lose some bonuses, but gain raw FIDS and growth rate. It's a trade-off. EL doesn't prevent you from doing it. (On the flip side, EL doesn't prevent its Endless AIs from doing it, either, and so this is exactly what they do to settle-spam their entire continents. Then they're all playing the midgame at the low-approval/few empire plan tiers/few luxury boosters end of the spectrum. You can join them down there and beat them at it, or choose a different point on that same spectrum and overtake them on efficiency.)
In fact, in the bigger picture, all of us play some stretches of the game "sub-optimally" on expansion disapproval, because it turns out it's actually "optimal" overall, considering that you usually need to land-grab some good regions before the AIs spam it all away. The economic trade-off is only part of the equation. Play dozens of games where you stick slavishly to the ideal economic curve, and you'll realize that in many of them, you got outraced to a region, and it actually hurt you more in the long run, because you either had to fight a war to take it later -- or, worse, that you couldn't even fight that war, and you lose that game without ever having had a chance. On post-mortem reflection, you realize that the chance you passed up was, indeed, to have won the race to that region, which would have totally changed the shape of the midgame. Correctly judging when it's beautiful to get ugly is also part of your EL mastery.
Case in point: I almost never go for a 3rd city in late Era I, because I know that having 3 cities so early sucks. Except ... if my sole neighbor is freaking Roving Clans, whom I know will settle the entire continent around me, then it's totally worth it to take a 3rd region early just to make a perfect north-to-south wall and cut the continent in half. This knowledge doesn't come from any analysis of cities, disapproval, or game mechanisms; you basically have to lose to Roving Clans peacefully engulfing you a few times before you realize that stopping that is the #1 priority.
As well, you can also just ignore penalties altogether (I think) and take the massive production hit. But Honestly that doesn't seem fun to me, even it if works. Running around in the game with 100, 50% productions regions just seems like a dull way to play. At that point you’re just ignoring the approval mechanic.
Imagine if negative upkeep didn't force disband units and destroy buildings. You could play the game on 0 gold, and pure production, running big deficits all the time. But ignoring a central game mechanic would just eventually make thing less fun.
As well people are saying you can deal with approval, which may be true, I haven’t played the game that much. But most techs give a flat bonus to approval, and expanding gives a flat penalty, so you can really just see any tech as providing that many more cities at current approval.
Sewer system give +20, but you could also just say it's 2/3/4 increased city cap.
I’m the end it's really just personally preference but I just really dislike penalties like the expansion penalty. It stacks infinity and it will often make expansion negatively useful. I feel like there are other ways a game can make blobbing suboptimal without infinity increasing penalties.
Out of curiosity, what other game design mechanisms have you seen to nerf the exponential growth strategy? Which ones did you think work well? Which ones did you actually enjoy? One thing's for sure: whatever the mechanism, some players will complain about it :) And when there's no restriction, they complain about that
I have zero experience with Civ* everything, Master of Orion, and some other classic 4Xs. I've seen these mechanisms:
0. No expansion restrictions. Walter Bright's Empire (and its many, many clones and knock-offs), Malfador's Space Empires III, IV, V; Warlock 1; numerous other skittles games. Solved by: exponential growth, a.k.a. city spam. Killed by: cognitive overload.
1. Hard cap, with increasing % penalty thereafter. Planar Conquest; Warlock 2. (Oh, how the Warlock community howled when they went from 1 to 2 :) Warlock 2 also introduced special cities, which you can't build up but don't count against your cap, and I immediately saw that special city spam is the uber-solution, after #0
2. No cap, but your population migrates among cities, so more cities doesn't (immediately) give more productivity. Pandora: First Contact.
3. Flat malus per city/region, reduced by research. Amplitude's Endless*.
4. Hard cap, and that's that. If we consider RPG party size to be analogous to cities, then most party RPGs fit here: you have six or eight slots in 1 party all game long, with no way to increase it. Some newer RPGs have evolved to be like FIFA Campaign Manager: you start with a small party, and through successful adventuring you eventually get a stable full of 20-30 guys, but a party is still only a few at a time. Battle Brothers; Darkest Dungeon. I guess the logical evolution of these games is that, some time in the 2030s, we'll have the multi-party RPG, where you have tactical control over 3-5 parties of 2-8 guys each, and you simultaneously assault a tough castle from 3-5 different directions at once. The turn-based RPG industry isn't quite there yet :(
I think #0 is awful without some serious UI/scripting support. Basically, the player's workload scales up linearly with empire size, until all fun is lost amidst a sea of un-fun details. To my konwledge, it hasn't been solved, even yet.
I don't mind #1, #2, or #3 (nor even #4). I don't think any of them are ideal solutions, but I'm willing to do each of them well to win those games. I think #1 is the most kludgy and artificial, basically ducking the #0 problem with least effort, with no deep evidence that it actually solves anything.
Overall, I think there should be something like a cost that prevents mindless spam from being the obvious optimal strategy. I appreciate many game designers for sticking their necks out and offering alternatives. I think EL is a particularly nice total package, in which you have dozens of game mechanisms all dovetailing in neat ways, and it remains fun and interesting. But I still shop every Steam sale for new 4Xs and RPGs, hoping to find another game with its own merits.
I think the primary issue is snowballing. You just get to big, and no one can stop you. So games go from being interesting challenging to being over, but you still might have 90% of the game left to mop things up. The scaling micro/cognitive load might make the game dull/slower, but snowballing makes it pointless.
To answer your question: I don't think I've ever seen a 4X game really solve the problem well. Just some are less bad than others. However, in fairness designing a good 4X game is hard. For me the games that stand out the most are the asymmetric ones. Things like XCOM, Darkest Dungeon and Slay the Spire. Since the human and the AI are playing different games at that point, it makes it easier to have a challenging game at all stages.
Also, Your multi party assault sounds interesting, but my experience with XCOM: long war makes me think it might have problems. For LW I always ended up with a team of 8 units, with a bunch of abilities each. Since I had so many unique units with unique abilities, I forgot which units had which abilities, and didn't use them half the time.
Back to 4X games, I do think the blobbing issue can be solved without hard limits(Hard limits being infinitely scaling penalties, or actual city caps).
A better AI would help. While this always applies, if you've ever seen CIV 6 AI, it's terrible combat wise. If doesn't build or use it's combat units very effectively. It also never seems to attack you after early game, despite massive production advantages in higher difficulties. The reason I am mentioning this is that a better AI would put up a better fight and not get runover. When the AI is trivial to defeat in combat, it makes snowballing easier. In fact, you could make an AI that Turtles when invaded, so even if you win the war, it takes so long you fall behind civ's that were playing tall.
Another solution would be giving more options to tall players. Make it so there is always something you can do, with that something actually being useful and interesting.
For many games, playing tall means you run out of things to do. For endless legend I've only played a little bit, but I've run into situation where I built all the buildings I could, so I just built units with the plan to sell them.
You could also just have substantial but temporary penalties to conquering. Like if fast game speed is 150 turns in EL, it takes 30 turns to make a conquered city productive, and you have to spend extra resources to subdue the populace. You could make conquering slow or expensive enough, that non agro players keep up by playing peacefully.
As well you might have to use several ideas to prevent blobbing, and not just 1. IE I think blobbing is a complicated problem but is solvable.