I've been fascinated with Wide play for a long time now, and I've finally gotten to a point where I believe that Wide empires are competitive with Tall empires for fast science/culture/diplo victory. I have yet to personally get a sub-200 science victory with a Wide game, but I believe it's only a matter of time. Somewhat recently, Acken achieved a sub-200 Deity science victory with an 8-city Korea game. So we know that it's possible. But "possible" doesn't automatically equal good. A better question is, "is going Wide desirable?" I think it is, for reasons outlined below.
Definitions: "Tall" = four or fewer self-founded cities, finishing Tradition. "Wide" = five or more self-founded cities, finishing Liberty.
There are a lot of nuances to Wide play that differ from Tall, but that's a whole discussion unto itself. Here, I just want to explain the important theoretical concepts that I think support Wide play as an idea. There are two main ones I want to talk about here.
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1. Food/Growth. Conventional wisdom has it that Tall play gets superior growth. After all, it's right there in the Tradition finisher: "+15% growth in all cities". Obvious. Liberty doesn't have anything like this. However, this only means that Tall has more growth PER CITY than Wide. An empire with more cities can actually overcome this bonus and generate more total growth.
Let's assume, for the sake of argument, that base growth is the same in all cities -- call this value x. An empire with six cities and the Tradition finisher would generate a total of (6x * 1.15) growth, or 6.9x total growth. An empire with seven cities and no Tradition finisher would generate 7x total growth. Here, the seven-city empire comes out slightly ahead. But this isn't a realistic comparison. A more realistic comparison is a four-city empire with Tradition and a six-city empire without. Here, the Tall empire generates (4x *1.15) = 4.6x total growth, while the Wide empire generates 6x total growth. Wide is way ahead now. It's really no comparison.
Furthermore, we have to account for the fact that food requirements for growth go up as population rises. Going from 10 to 11 pop costs a lot less food than going from 30 to 31. Compare a four-city empire with four 20-pop cities to a six-city empire with six 13-pop cities. The latter empire needs significantly less surplus food in a city to increase its population.
Take these two things together: 1. A Wide empire can have more total growth than a tall empire. 2. A Wide empire gains more population per unit of growth than a Tall empire. Combined, the outcome is this: A Wide Empire can gain population significantly faster than a Tall empire.
For an example, here's a screenshot of my most recent completed game, a seven-city science victory with Egypt. None of my cities are particularly large -- my capital is size 25, which is downright small for a science victory endgame. But my total population is 157. Across four cities, this would be equivalent to an average size of 39 population, which is actually pretty massive for this point in the game. I've been able to gain a ton of total population by making many cities.
2. Happiness. Again, we're fighting conventional wisdom here. Consensus says that the global happiness mechanic discourages wide play. But this isn't actually true, for the reason that per-city happiness sources more than offset extra unhappiness for founding more cities.
Consider: One point of population generates one point of unhappiness, and each city adds an additional three unhappiness on top of that. Let's take two hypothetical empires, Tall and Wide, each with 160 total population. The Tall four-city empire generates 160 unhappiness from population, plus 12 unhappiness from number of cities, for a total of 172 unhappiness. The Wide six-city empire generates 160 unhappiness from population, plus 18 unhappiness from number of cities, for a total of 178 unhappiness. Tall is indeed ahead.
But let's see what happens when we add in some local happiness sources. Let's say you have a Coliseum and a Pagoda in every city. The Tall empire above gets 16 total happiness from these buildings. The Wide empire gets 24 total happiness from these buildings. Add these to the numbers above, and the Tall empire has a total unhappiness deficit of 156, while the Wide empire has a total unhappiness deficit of 154. Wide is actually ahead! And this is only with Coliseums and Pagodas. Add in other sources of per-city happiness, and Wide pulls further and further ahead. Zoos, Circuses, and Stone Works all contribute, as can many other buildings via religious beliefs and social policies. And the more cities you add on to the Wide empire, the farther ahead Wide gets under this math.
So, why the common belief that happiness penalizes Wide play? There are two main reasons, I think. The first is fairly obvious -- without these happiness buildings, the Tall empire is ahead, and newly founded cities have no buildings. So Tall does start out ahead, and Wide doesn't catch up until it has its buildings. The second reason is more interesting.
As discussed above, Wide empires can gain population more quickly than Tall empires. This means that Wide empires spend their happiness more quickly, even with more happiness to work with. It's thus more common to encounter a visible happiness crunch with Wide play. But this is something that feels like a problem more than it actually is a problem. Happiness is first and foremost a limiter on population. It does contribute to Golden Age points, but that's a minor consideration. For the most part, it doesn't matter how much positive happiness you have -- you either have enough to keep growing, or you don't have happiness and need to stop growing.
Consider two scenarios: In Scenario A you have 10 happiness to spare. Scenario B is exactly the same, but you instantly have 10 more population, putting you at zero happiness and forcing you to stagnate/avoid growth. Scenario B is clearly better, but it feels like you have a problem. If you haven't carefully thought it through, being in Scenario B feels like something you should try to avoid. But it's actually perfectly ok. You have a stronger empire in Scenario B than in Scenario A, and you can simply focus on non-food tiles until you find more sources of happiness.
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There are a lot of other considerations that come into play for Tall versus Wide. Policy costs, national wonder costs, building maintenance costs, road maintenance costs, more efficient rush-buying, aggressive expansion penalties, defensibility, and faster early science may all tip the balance toward Tall play. On the other hand, faith, great person points, and more specialists provide additional edges to Wide play. It's a complicated system, and there's a lot to consider. But hopefully you can see that there is actually some theoretical basis in support of going Wide.
Definitions: "Tall" = four or fewer self-founded cities, finishing Tradition. "Wide" = five or more self-founded cities, finishing Liberty.
There are a lot of nuances to Wide play that differ from Tall, but that's a whole discussion unto itself. Here, I just want to explain the important theoretical concepts that I think support Wide play as an idea. There are two main ones I want to talk about here.
~~~~~~~~~~
1. Food/Growth. Conventional wisdom has it that Tall play gets superior growth. After all, it's right there in the Tradition finisher: "+15% growth in all cities". Obvious. Liberty doesn't have anything like this. However, this only means that Tall has more growth PER CITY than Wide. An empire with more cities can actually overcome this bonus and generate more total growth.
Let's assume, for the sake of argument, that base growth is the same in all cities -- call this value x. An empire with six cities and the Tradition finisher would generate a total of (6x * 1.15) growth, or 6.9x total growth. An empire with seven cities and no Tradition finisher would generate 7x total growth. Here, the seven-city empire comes out slightly ahead. But this isn't a realistic comparison. A more realistic comparison is a four-city empire with Tradition and a six-city empire without. Here, the Tall empire generates (4x *1.15) = 4.6x total growth, while the Wide empire generates 6x total growth. Wide is way ahead now. It's really no comparison.
Furthermore, we have to account for the fact that food requirements for growth go up as population rises. Going from 10 to 11 pop costs a lot less food than going from 30 to 31. Compare a four-city empire with four 20-pop cities to a six-city empire with six 13-pop cities. The latter empire needs significantly less surplus food in a city to increase its population.
Take these two things together: 1. A Wide empire can have more total growth than a tall empire. 2. A Wide empire gains more population per unit of growth than a Tall empire. Combined, the outcome is this: A Wide Empire can gain population significantly faster than a Tall empire.
For an example, here's a screenshot of my most recent completed game, a seven-city science victory with Egypt. None of my cities are particularly large -- my capital is size 25, which is downright small for a science victory endgame. But my total population is 157. Across four cities, this would be equivalent to an average size of 39 population, which is actually pretty massive for this point in the game. I've been able to gain a ton of total population by making many cities.
Spoiler :
2. Happiness. Again, we're fighting conventional wisdom here. Consensus says that the global happiness mechanic discourages wide play. But this isn't actually true, for the reason that per-city happiness sources more than offset extra unhappiness for founding more cities.
Consider: One point of population generates one point of unhappiness, and each city adds an additional three unhappiness on top of that. Let's take two hypothetical empires, Tall and Wide, each with 160 total population. The Tall four-city empire generates 160 unhappiness from population, plus 12 unhappiness from number of cities, for a total of 172 unhappiness. The Wide six-city empire generates 160 unhappiness from population, plus 18 unhappiness from number of cities, for a total of 178 unhappiness. Tall is indeed ahead.
But let's see what happens when we add in some local happiness sources. Let's say you have a Coliseum and a Pagoda in every city. The Tall empire above gets 16 total happiness from these buildings. The Wide empire gets 24 total happiness from these buildings. Add these to the numbers above, and the Tall empire has a total unhappiness deficit of 156, while the Wide empire has a total unhappiness deficit of 154. Wide is actually ahead! And this is only with Coliseums and Pagodas. Add in other sources of per-city happiness, and Wide pulls further and further ahead. Zoos, Circuses, and Stone Works all contribute, as can many other buildings via religious beliefs and social policies. And the more cities you add on to the Wide empire, the farther ahead Wide gets under this math.
So, why the common belief that happiness penalizes Wide play? There are two main reasons, I think. The first is fairly obvious -- without these happiness buildings, the Tall empire is ahead, and newly founded cities have no buildings. So Tall does start out ahead, and Wide doesn't catch up until it has its buildings. The second reason is more interesting.
As discussed above, Wide empires can gain population more quickly than Tall empires. This means that Wide empires spend their happiness more quickly, even with more happiness to work with. It's thus more common to encounter a visible happiness crunch with Wide play. But this is something that feels like a problem more than it actually is a problem. Happiness is first and foremost a limiter on population. It does contribute to Golden Age points, but that's a minor consideration. For the most part, it doesn't matter how much positive happiness you have -- you either have enough to keep growing, or you don't have happiness and need to stop growing.
Consider two scenarios: In Scenario A you have 10 happiness to spare. Scenario B is exactly the same, but you instantly have 10 more population, putting you at zero happiness and forcing you to stagnate/avoid growth. Scenario B is clearly better, but it feels like you have a problem. If you haven't carefully thought it through, being in Scenario B feels like something you should try to avoid. But it's actually perfectly ok. You have a stronger empire in Scenario B than in Scenario A, and you can simply focus on non-food tiles until you find more sources of happiness.
~~~~~~~~~~
There are a lot of other considerations that come into play for Tall versus Wide. Policy costs, national wonder costs, building maintenance costs, road maintenance costs, more efficient rush-buying, aggressive expansion penalties, defensibility, and faster early science may all tip the balance toward Tall play. On the other hand, faith, great person points, and more specialists provide additional edges to Wide play. It's a complicated system, and there's a lot to consider. But hopefully you can see that there is actually some theoretical basis in support of going Wide.