I'm making a few assumptions here . The first is that Indians have a UU that is given an extra movement point . The second is , like in Civ 3 , even 1/3 of a movement point can be used to move to any place , or to initiate an action .
Taking that , on a terrain of type T ( which has movement cost 1 , i.e. , a unit with two movement point can cover two such terrain squares in one turn ) , it takes N workers to construct a road in one turn , then , given any number of workers higher than N , it will take any civilisation whose worker has one movement point a minimum of M ( and a maximum of 2*M , which is much more common ) turns to construct a road across M tiles of terrain type T ( assuming that no infrastrucutre existed in the first place , as is the case in the early game ) . The Indian worker can , however , do this job in M/3 turns ( or rather , M/(bonus granted by roads ) ) .
This is rather simple to show . Imagine six adjacent squares A , B , C , D , E , and F ( of terrain type T ) . Imagine we have put 3*N workers on A ( divided into three sets of N workers - X , Y , and Z ) . N workers use their movement points and construct a road on A ( X has used their movement points ) . Then another N workers ( the set Y ) move to the next tile ( which is B ) , and use the one remaining movement point to construct another road on B . The last remaining workers ( set Z ) use the already constructed roads on A and B to move to C , with only 2/3 movement point remaining , and construct a road on C . The turn ends . The position at end-of-turn is - X on A , Y on B , and Z on C , and roads on all A , B , and C .
On the next turn , X ( located now at A ) move across the roads on B and C ( which use up 2/3 movement points ) , and land on D . Having 1/3 movement point remaining , they construct a road on D . Y ( located at B ) move across the roads on C and D , and , like X , construct a road on E with only 1/3 movement point remaining . Z ( located now at C ) move across the roads on D and E and , like X and Y , construct a road on F with only 1/3 movement point remaining . The turn ends . The position is identical to the end of the first turn , with X , Y , and Z poised to construct roads on the next three squares in the next turn .
Let us see what the Indian workers have accomplished in two turns - all starting on the same tile , they have constructed a road on six tiles in one two . This means that it will be possible for the Indians , if you take the road route , to have workers build roads for your army units ( having one movement point ) as the army moves along plain terrain ( with the army always exactly one turn ahead of the workers , if it starts on the same tile ) . This is a fantastic advantage for a warmonger - your army becomes effectively a "treat all terrain as roads" on all plain terrain ( and also obviously so for a builder ) .
But this is only the tip of the iceberg - the effect mentioned here is scalable . It is obvious that , when railroads come out , it will be possible for 10*(k*N) workers to build railroads across 10 squares ( of terrain T ) in only one turn ( where k*N is the number of workers required to build road+railroad in one turn ) . Imagine an industrial army of artillery and infantry ( as currently that is the most powerful ) which can treat all plain terrain as railroad .
All this is , of course , assuming that the Indian worker is faster in that it has an extra movement point . If Firaxis says no , this elaborate model I've constructed will be shot to hell .
Note : This should really have been in "Strategy and Tips" , but as the game isn't released , there is no strategy and tips .
UPDATE : This strategy is no longer exclusive to the Indians , and can be used by all Civs . The Indians have an advantage only in that they can road six squares in place of the three others can , given enough workers .
Taking that , on a terrain of type T ( which has movement cost 1 , i.e. , a unit with two movement point can cover two such terrain squares in one turn ) , it takes N workers to construct a road in one turn , then , given any number of workers higher than N , it will take any civilisation whose worker has one movement point a minimum of M ( and a maximum of 2*M , which is much more common ) turns to construct a road across M tiles of terrain type T ( assuming that no infrastrucutre existed in the first place , as is the case in the early game ) . The Indian worker can , however , do this job in M/3 turns ( or rather , M/(bonus granted by roads ) ) .
This is rather simple to show . Imagine six adjacent squares A , B , C , D , E , and F ( of terrain type T ) . Imagine we have put 3*N workers on A ( divided into three sets of N workers - X , Y , and Z ) . N workers use their movement points and construct a road on A ( X has used their movement points ) . Then another N workers ( the set Y ) move to the next tile ( which is B ) , and use the one remaining movement point to construct another road on B . The last remaining workers ( set Z ) use the already constructed roads on A and B to move to C , with only 2/3 movement point remaining , and construct a road on C . The turn ends . The position at end-of-turn is - X on A , Y on B , and Z on C , and roads on all A , B , and C .
On the next turn , X ( located now at A ) move across the roads on B and C ( which use up 2/3 movement points ) , and land on D . Having 1/3 movement point remaining , they construct a road on D . Y ( located at B ) move across the roads on C and D , and , like X , construct a road on E with only 1/3 movement point remaining . Z ( located now at C ) move across the roads on D and E and , like X and Y , construct a road on F with only 1/3 movement point remaining . The turn ends . The position is identical to the end of the first turn , with X , Y , and Z poised to construct roads on the next three squares in the next turn .
Let us see what the Indian workers have accomplished in two turns - all starting on the same tile , they have constructed a road on six tiles in one two . This means that it will be possible for the Indians , if you take the road route , to have workers build roads for your army units ( having one movement point ) as the army moves along plain terrain ( with the army always exactly one turn ahead of the workers , if it starts on the same tile ) . This is a fantastic advantage for a warmonger - your army becomes effectively a "treat all terrain as roads" on all plain terrain ( and also obviously so for a builder ) .
But this is only the tip of the iceberg - the effect mentioned here is scalable . It is obvious that , when railroads come out , it will be possible for 10*(k*N) workers to build railroads across 10 squares ( of terrain T ) in only one turn ( where k*N is the number of workers required to build road+railroad in one turn ) . Imagine an industrial army of artillery and infantry ( as currently that is the most powerful ) which can treat all plain terrain as railroad .
All this is , of course , assuming that the Indian worker is faster in that it has an extra movement point . If Firaxis says no , this elaborate model I've constructed will be shot to hell .
Note : This should really have been in "Strategy and Tips" , but as the game isn't released , there is no strategy and tips .
UPDATE : This strategy is no longer exclusive to the Indians , and can be used by all Civs . The Indians have an advantage only in that they can road six squares in place of the three others can , given enough workers .
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