Why hate bananas?

This is absolutely the opposite of true. Civ4 was completely anti-environmentalist, any player who wasn't terrible at the game would have deforested most of their land by the midgame, and turned worthless 1-food jungles into 2-food grassland as quickly as possible. Not to mention jungles actually caused unhealth.

I like Civ4 much more than Civ5, but this is one of the things I don't mind from Civ5.

In civ 3, I remember losing units in Jungle tiles, can't remember reason why, but perhaps unhealthy?
 
OK, so I think I have this figured out. Supposing you have a granary, the difference between having an improved banana tile and an unimproved one is +2:c5food:, -2:c5science:.

1:c5citizen:= 1:c5science:, so if the extra 2:c5food: can net you 2:c5citizen: in the time it will take you to get from building the plantation to building the university, then the plantation pays for the loss of jungle pretty easily (slightly more than pays for itself, since that's +2:c5science: that you don't need to allocate a worker for).

This table is the amount of turns that +2:c5food: will save you, depending on how much you already have and how big your city is.

Code:
              1FD   2FD   3FD   4FD   5FD   6FD   7FD   8FD   9FD   10FD   11FD   12FD
1POP          10      4     2     1     0     1     1     0     0      0      0      0
2POP          16      6     3     2     1     1     1     0     0      1      1      0
3POP          22      8     5     3     2     1     1     1     0      1      1      0
4POP          30     11     6     4     2     2     2     1     0      1      1      0
5POP          36     14     8     4     3     3     1     1     2      1      0      1
6POP          44     17     9     5     4     3     2     2     1      1      1      1
7POP          52     19    10     7     4     3     3     2     1      1      2      1
8POP          60     22    12     8     5     3     3     3     1      1      2      1
9POP          68     25    13     9     6     4     3     2     2      2      2      1
10POP         76     28    15    10     6     4     4     3     2      2      2      1
11POP         84     32    17    10     7     6     4     3     3      2      2      1
12POP         93     35    19    11     8     6     4     4     3      2      2      2

So, to figure out whether improving bananas pays off in science, find your city's :c5citizen: on the left and your current :c5food: on the top. Add the number at that intersection to the number one down and to the right (since after 1 turn, you're going to get one more :c5citizen: who will presumably be working a tile producing one more :c5food:). If the sum of those two numbers is greater than the number of turns it will take you to get a university out, you should build the plantation.

This is incomplete, of course; this only states whether the extra :c5food: will give you +2:c5cscience: before the university is built. Even if it doesn't net your the extra :c5citizen: before that, it will still make up that difference at some point.

My conclusion: I'm probably going to convert my banana tiles to plantations a lot more often, especially if I get a sugar, spices or cotton start and end up researching Calendar earlier than I would normally.
 
Civ4 jungles were like marshes in 5, completely worthless and to be removed immediately. I like how 5 makes them have an actual yield like forests. I still generally prefer plantations over leaving the tile. Universities come way after I've put that food to use. Science is good but extra population leading to production or more science is better early imo.
 

Do keep in mind this is only true if there's no other tiles within city limits that are used and can be upgraded, cities that can be connected by making roads etc.

Why would I cut down a perfectly good jungle just because it's infested with bananas, if I can chose to upgrade the hill for that extra production that are severely limited in jungle areas, or make that farm on a grassland tile or xxxxx.

Banana improvement is so low in priority in my opinion that at the time you actually have a worker available to use time on it, you're getting close to education anyways :p
 
This is absolutely the opposite of true. Civ4 was completely anti-environmentalist, any player who wasn't terrible at the game would have deforested most of their land by the midgame, and turned worthless 1-food jungles into 2-food grassland as quickly as possible. Not to mention jungles actually caused unhealth.

I like Civ4 much more than Civ5, but this is one of the things I don't mind from Civ5.

First off, this is simply incorrect - keeping even jungles in areas you settled late could in some cases be a good idea due to the National Park wonder, or in areas where a jungle tile fell within the fat cross of multiple cities for the happiness boost. Second, I specifically mentioned playing post-industrial starts meaning there was the option of going ecologist right off the bat. Third, the whole climate aspect was much more fleshed out in IV, if perhaps overdone, whereas V has gone the opposite direction, completely ignoring it other than the jungle science bonus and leaves little reason not to completely deforestate an area already rich in production.

@ Polisurgist: Whether to plantation or not is simple: Early game, always plantation, but it isn't a high priority due to how many turns it takes to clear jungle and build one unless you happen to have a plantation pantheon. Around the time of universities, it's a matter of whether you want more science right now or more growth, which will mean more science and the other benefits of additional pop, but only in the much longer run and cost you more happiness. If it's your Monarcy capital and you already have a large tech lead, have National Epic and Garden in the city, then Plantation starts to look very good. In most other cases, the plain jungle probably wins out.
 
Do keep in mind this is only true if there's no other tiles within city limits that are used and can be upgraded, cities that can be connected by making roads etc.

Why would I cut down a perfectly good jungle just because it's infested with bananas, if I can chose to upgrade the hill for that extra production that are severely limited in jungle areas, or make that farm on a grassland tile or xxxxx.

Banana improvement is so low in priority in my opinion that at the time you actually have a worker available to use time on it, you're getting close to education anyways :p
Right, but when making a model like this is to hold all outside variables constant and equal. There's all kinds of other things that might be going on outside of the decision of whether to improve or not improve a particular banana tile. Civ is a game with a lot of variables, and we aren't going to account for all of them with pen and paper (or Excel). The purpose here is to determine whether it's cut and dried always going to be better to leave the jungle unimproved, and I think this is a good case that it's not clearly the better option, though it'll be the case both ways in some situations.

The other case I didn't mention here is whether you have 1. other banana tiles and 2. other plain jungle tiles in the range of your city. My guess is that building a plantation on the first banana tile is generally a good idea (assuming you do it as soon as you're able to chop the jungle and build the plantation), while the payoff gets less for each subsequent banana tile, especially if you're only using one worker (another factor not accounted for in my model). Though if I had other jungle tiles in my boundary, I'd probably chop all the bananas, knowing that I'll have plenty of science tiles to work in the future and that I'll have a bit of a rough time with food.
 
Brazilian bananas are the most annoying, because they render the jungle useless, what with preventing you from building your UI and all.
 
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