Worker chopping is amazing, but you need a level 2 tech for it.
If your plan is to go worker first, chop to help build a settler (and thus end up with an extra worker and down a couple forests), this will probably only work if you start with mining AND dont go for an early religion.
But is very strong.
Also, If your city is on a plains hill, it will give 2 food/2 hammer/1 trade instead of 2/1/1. This extra hammer is a big deal. I believe that all else equal, it is worth spending an extra game turn to get your initial settler onto a hill. (Other factors in the position could make it not worth it however).
With 2/2/1 from your city instead of 2/1/1, and working a tile that gives 2/1 or 1/2, You have 5 production a turn towards a settler instead of 4. That speeds settler 1 up to 20 turns. However, if you do the grow to size 3 plan, all you get from the bonus is an extra warrior/scout or so during this time.
Now, I think growing first would be good in circumstances where the area around your city is high in food, low in production. Like flood plains.
If your city is 2/1/1 and you work a flood plains for 3/0/1, you have 3 excess food to grow in 8 turns, or you have a 25 turn settler. If you have another flood plains square, then at size 2 thats a 20 turn settler.
So you can go: grow to size 2 and make a 20 turn settler, taking 28 turns and giving you an extra city size (and thus a faster 2nd settler!!).
So if you are in a heavy food/low production spot (pretty much, flood plains, to make this fast enough), I would grow a bit. Otherwise I think i would make a settler first.
Also, I would spend 1 game turn to position my capitol on a PLAINS hill (defense bonus too!), to get 2/2 instead of 2/1 out of the square! That spends 1 turn but speeds up the first settler by 5 turns.
If your plan is to go worker first, chop to help build a settler (and thus end up with an extra worker and down a couple forests), this will probably only work if you start with mining AND dont go for an early religion.
But is very strong.
Also, If your city is on a plains hill, it will give 2 food/2 hammer/1 trade instead of 2/1/1. This extra hammer is a big deal. I believe that all else equal, it is worth spending an extra game turn to get your initial settler onto a hill. (Other factors in the position could make it not worth it however).
With 2/2/1 from your city instead of 2/1/1, and working a tile that gives 2/1 or 1/2, You have 5 production a turn towards a settler instead of 4. That speeds settler 1 up to 20 turns. However, if you do the grow to size 3 plan, all you get from the bonus is an extra warrior/scout or so during this time.
Now, I think growing first would be good in circumstances where the area around your city is high in food, low in production. Like flood plains.
If your city is 2/1/1 and you work a flood plains for 3/0/1, you have 3 excess food to grow in 8 turns, or you have a 25 turn settler. If you have another flood plains square, then at size 2 thats a 20 turn settler.
So you can go: grow to size 2 and make a 20 turn settler, taking 28 turns and giving you an extra city size (and thus a faster 2nd settler!!).
So if you are in a heavy food/low production spot (pretty much, flood plains, to make this fast enough), I would grow a bit. Otherwise I think i would make a settler first.
Also, I would spend 1 game turn to position my capitol on a PLAINS hill (defense bonus too!), to get 2/2 instead of 2/1 out of the square! That spends 1 turn but speeds up the first settler by 5 turns.
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