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While we’re discussing the relative values of food, hammers and commerce, I thought it might be useful to apply this theory to the question of worker actions. Here I’ll be looking only at those “basic” improvements that can be made in the early stages because these have far and away the biggest influences on the game. I’ll also be using figures based on Epic speed so you’ll need to make a few small adjustments to convert to Standard or Marathon – although the conclusions should be the same.
I’ll also be looking at “time value” of specific resources to take into account what will be gained from the worker actions over a long period. In very simple terms this says that 1 food now is worth more than 1 food in x turns.
In more general terms I can define three sets of values
F(t) = The value of 1 unit of food in turn t
H(t) = The value of 1 unit of production in turn t
C(t) = The value of 1 unit of commerce in turn t
So something simple like a farm can be expressed in the following way
F(1) + F(2) + F(3) + …… + F(N)
N is some arbitrary term limit that I have placed on measurements which is limited to the maximum number of turns in the game. We can also allow for the worker build time remove the first few terms and then value the worker time by dividing this total value by the number of worker turns required.
Something more complicated like a cottage will be equal to (allow for Epic speed build times and cottage growth times)
C(6) + C(7) + ….+ C(20) + 2 x [C(21) + C(22) +….+C(50)] + 3 x [C(51)+ ……]
We can also allow for other factors in the calculations here which reflect tech or civic effects on the different values generated by the improvements.
Now that I’ve complicated matters, I’ll simplify them a lot to first come up with some numbers. The first term I want to get is a single exchange rate for food, hammers and commerce. In fact here everything will be translated into gold at the following rates
1 food = 3 gold
1 hammer = 1.5 gold
1 commerce = 1 gold
For reference I will also calculate the figures using Blake’s exchange rates to see how they compare.
I will ignore any effect of multipliers.
Finally, I will assume a fixed interest rate of 2% per turn. The 2% is a very arbitrary number so there’s really no basis for it except to say that we should easily be able to generate these sorts of growth rates on our Civ investments at Epic speed. For comparison, the rate used for Marathon speed would be 1% and that used for standard would be 3%.
So for those interested in the detailed formulae, some examples of the terms above, expressed in turns of gold, would be C(1) = 1/1.02 and F(3) = 3 / [1.02*1.02*1.02]
I’m probably losing a lot of you here so I’ll cut to the chase and value improvements now. Let’s start with the seeing what would happen if we farmed a river plain right next to our capital.
F(8) + F(9) + …….
= 130.6g
Since it takes 8 turns to complete this, the “value” added by each worker turn is 130.6g/8 = 16.3g.
Let’s look at that again!!!! We’ve just finished a worker and all it does is put down a pathetic little farm next to our capital. Every turn spent on this mediocre improvement is generating 16.3g for us and this cost us a mere 90 hammer/food combo. If the worker can just manage this for another 100 turns, it will have been worth something in the region of 800 gold!!! With figures like these you can see why many people might play worker first strategies.
Next it’s the cottage and I will assume that the +1c from Printing Press and +2c from Free Speech does get added after 250 turns and 350 turns respectively. In fact this assumption adds almost no extra value to the cottage build because it is so far distant.
The cottage still works out to be valued at 118.8g and at 6 turns the worker is adding value at a rate of 19.8g per turn. Our first worker’s value has just shot up to the region of 1000 gold!! Not only do you want to build one quickly but it’s worth declaring war just to steal a worker from your nearest neighbour.
Third, the mine although here I want to make a small adjustment. Although the worker action generates 2h, this is not a tile that we would normally be working. I’ll be generous and assume that we would otherwise work a 2/0/0 tile so the added value of the mine is actually –1/+3/0 which converts at my rate to 1.5gpt. Also the mine actually takes 7 turns to build since one turn is expended in moving to the hill. The value of the mine comes to 66.6g and the worker generates value at 9.5gpt. Once again I think this confirms what we already know that our worker action to build a mine is going to be some way down our list of priorities.
Moving through the main resource improvements we might see at this stage the values created for each turn spent working on the improvement are as follows
Pigs: 67.9gpt
Wheat/Corm 32.6gpt (49.0gpt if irrigated)
Rice 15.3gpt (32.6gpt if irrigated)
Gold (Plains Hill) 34.9gpt
Gems (Grassland Hill) 38.1gpt
Cows 45.3gpt
Horses: 30.2gpt
Sheep(Plains): 52.8gpt
Copper(Plains Hill) : 19.0gpt
Ivory (Plains) : 18.9gpt
I did say that I would show the values using Blake’s exchange rates but now I think that this would just be throwing more obscure numbers into the mix. Given that the only variation we have is in the rate of conversion to commerce, it obvious that the only changes will be that all expressions of food and hammers will fall when expressed in these terms.
When it comes to the actually ranking of these improvements most of the resources stay more or less in the same place although grassland hills gems moves just above cows while ivory becomes more worthwhile to improve the copper (if the copper tile produces less food). Probably more noticeable is the relative value of cottages and farms with the latter being around two-thirds as valuable an improvement as the former.
To close, let’s now try to value that worker or ours and assume we have pigs, gold, horse to improve. After that the worker spends all its time building cottages. Using the numbers from Blake’s figures, this worker is worth, at the time it is built, 2,082 gold. In my book that’s more than you’d probably get from a GP!!
I’ll also be looking at “time value” of specific resources to take into account what will be gained from the worker actions over a long period. In very simple terms this says that 1 food now is worth more than 1 food in x turns.
In more general terms I can define three sets of values
F(t) = The value of 1 unit of food in turn t
H(t) = The value of 1 unit of production in turn t
C(t) = The value of 1 unit of commerce in turn t
So something simple like a farm can be expressed in the following way
F(1) + F(2) + F(3) + …… + F(N)
N is some arbitrary term limit that I have placed on measurements which is limited to the maximum number of turns in the game. We can also allow for the worker build time remove the first few terms and then value the worker time by dividing this total value by the number of worker turns required.
Something more complicated like a cottage will be equal to (allow for Epic speed build times and cottage growth times)
C(6) + C(7) + ….+ C(20) + 2 x [C(21) + C(22) +….+C(50)] + 3 x [C(51)+ ……]
We can also allow for other factors in the calculations here which reflect tech or civic effects on the different values generated by the improvements.
Now that I’ve complicated matters, I’ll simplify them a lot to first come up with some numbers. The first term I want to get is a single exchange rate for food, hammers and commerce. In fact here everything will be translated into gold at the following rates
1 food = 3 gold
1 hammer = 1.5 gold
1 commerce = 1 gold
For reference I will also calculate the figures using Blake’s exchange rates to see how they compare.
I will ignore any effect of multipliers.
Finally, I will assume a fixed interest rate of 2% per turn. The 2% is a very arbitrary number so there’s really no basis for it except to say that we should easily be able to generate these sorts of growth rates on our Civ investments at Epic speed. For comparison, the rate used for Marathon speed would be 1% and that used for standard would be 3%.
So for those interested in the detailed formulae, some examples of the terms above, expressed in turns of gold, would be C(1) = 1/1.02 and F(3) = 3 / [1.02*1.02*1.02]
I’m probably losing a lot of you here so I’ll cut to the chase and value improvements now. Let’s start with the seeing what would happen if we farmed a river plain right next to our capital.
F(8) + F(9) + …….
= 130.6g
Since it takes 8 turns to complete this, the “value” added by each worker turn is 130.6g/8 = 16.3g.
Let’s look at that again!!!! We’ve just finished a worker and all it does is put down a pathetic little farm next to our capital. Every turn spent on this mediocre improvement is generating 16.3g for us and this cost us a mere 90 hammer/food combo. If the worker can just manage this for another 100 turns, it will have been worth something in the region of 800 gold!!! With figures like these you can see why many people might play worker first strategies.
Next it’s the cottage and I will assume that the +1c from Printing Press and +2c from Free Speech does get added after 250 turns and 350 turns respectively. In fact this assumption adds almost no extra value to the cottage build because it is so far distant.
The cottage still works out to be valued at 118.8g and at 6 turns the worker is adding value at a rate of 19.8g per turn. Our first worker’s value has just shot up to the region of 1000 gold!! Not only do you want to build one quickly but it’s worth declaring war just to steal a worker from your nearest neighbour.
Third, the mine although here I want to make a small adjustment. Although the worker action generates 2h, this is not a tile that we would normally be working. I’ll be generous and assume that we would otherwise work a 2/0/0 tile so the added value of the mine is actually –1/+3/0 which converts at my rate to 1.5gpt. Also the mine actually takes 7 turns to build since one turn is expended in moving to the hill. The value of the mine comes to 66.6g and the worker generates value at 9.5gpt. Once again I think this confirms what we already know that our worker action to build a mine is going to be some way down our list of priorities.
Moving through the main resource improvements we might see at this stage the values created for each turn spent working on the improvement are as follows
Pigs: 67.9gpt
Wheat/Corm 32.6gpt (49.0gpt if irrigated)
Rice 15.3gpt (32.6gpt if irrigated)
Gold (Plains Hill) 34.9gpt
Gems (Grassland Hill) 38.1gpt
Cows 45.3gpt
Horses: 30.2gpt
Sheep(Plains): 52.8gpt
Copper(Plains Hill) : 19.0gpt
Ivory (Plains) : 18.9gpt
I did say that I would show the values using Blake’s exchange rates but now I think that this would just be throwing more obscure numbers into the mix. Given that the only variation we have is in the rate of conversion to commerce, it obvious that the only changes will be that all expressions of food and hammers will fall when expressed in these terms.
When it comes to the actually ranking of these improvements most of the resources stay more or less in the same place although grassland hills gems moves just above cows while ivory becomes more worthwhile to improve the copper (if the copper tile produces less food). Probably more noticeable is the relative value of cottages and farms with the latter being around two-thirds as valuable an improvement as the former.
To close, let’s now try to value that worker or ours and assume we have pigs, gold, horse to improve. After that the worker spends all its time building cottages. Using the numbers from Blake’s figures, this worker is worth, at the time it is built, 2,082 gold. In my book that’s more than you’d probably get from a GP!!
- I think I've invoked this one quite a lot.
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