[GS] Rethinking Lumber Mills

[Lily_Lancer]

If you have a piece of forest, chop it or place lumber mill?

Before I tend to think this as no problem, you shall always chop. However after calculation I start to challenge this conclusion on online speed.

Build Lumbermill: +2 production, +1 from trees, so actually +3 production per turn altogether. In late game you can still remove and chop. +1 from Steel and +1 from cybernetics. +1 appeal and becomes +2 after Conservation.
Chop: +production right now. Also clear a tile for your district/wonder/other improvements.

Suppose you get X production from chopping now, and Y net prod(consider the builder charge cost ) from chopping in late game. There's T turns between now and late game. Suppose value inflates at t% per turn.


Simpliest Model:

Your profit from chopping now: X (suppose you don't build other things thereafter)
Profit from late-game chopping: 3*(1-t%)/t%+Y*(1-t%)^T (ignore bonus from appeal or steel)

On online speed suppose X=40, Y=60 and t=7%, T=50, then you get 41.45 from building lumber mill but only 40 from chopping now. So you shall build lumber mill if your citizens do not have a better place to work on.

On standard speed suppose X=80, Y=120 and t=5%, T=75, then you get 80 from chopping now but only 59.56 from lumber mill. So you shall chop now.


Conclusion:
On online speed, if your citizens do not have a better place to work on, you shall build lumber mill instead of chopping right now. Surprisingly this yields a little more than chopping. If they do have better tiles to work then you shall chop. Keep (rain)forests for district adj or Earth Goddess is not always inefficient.

On standard speed you shall always chop.

 

[leandrombraz]

It took you 3 months and a math formula to figure that out? I been doing this since the June patch.

The improved lumber mills also made it viable to use woods adjacency, mostly for Civs that benefit from it like Norway, or that benefit from the appeal like Australia. Same for Rainforest but not as good since you can't chop and replant later.

 

[Builderphile]

It took you 3 months and a math formula to figure that out? I been doing this since the June patch.

Good for you?

But how could you possibly know whether what you are doing is optimal if you didn't do the math (and it sounds like you didn't)?

 

[Melliores]

If you do the math you should also take into account adjacency boni for woods and lumbermils - those can provide with extra science/faith/production, apart from the pop working the tile. Keeping the woods is generally the better option unless you need the tile for a wonder or district.

 

[Victoria]

Chop bonuses.
Immediate requirement is also a thing as is chopping later to avoid chop loss due to wonder loss or card gain and similar.
Still good to see the figures.

 

[leandrombraz]

Good for you?

But how could you possibly know whether what you are doing is optimal if you didn't do the math (and it sounds like you didn't)?

I was walking a day on the beach when I saw something shiny coming out of the sea. I went to see what it was and I was amazed to see a Crab, a Golden Crab! If that wasn't weird enough, the Crab spoke. "Come closer", he said. I approached with reverence and bend my knee, recognizing that I was in the presence of something divine. The Crab came close to my ears and whispered: "Lumbers Mills are viable now".

That's how I know you it. That's how I know everything I know. Praised be the Crab God.


I'm just teasing him since he likes to answer to other people this same way. Answering your question though, you don't always need to do the math to know something is good, sometimes it's just obvious. For me that one was obvious and honestly, it's more fun to play that way than chopping everything that dare to feature in one of my tiles. It's nice to see the math, even though it doesn't take everything into account, but it's hardly necessary, unless you're obsessed with reaching perfection and can't risk wasting a bit of production here and there.

 

[lotrmith]

Conclusion:
On online speed, if your citizens do not have a better place to work on, you shall build lumber mill instead of chopping right now. Surprisingly this yields a little more than chopping. If they do have better tiles to work then you shall chop. Keep (rain)forests for district adj or Earth Goddess is not always inefficient.

On standard speed you shall always chop.

But

So never overvalue anything that gives you bonus a couple of turns later, and never underestimate anything that gives you immediate bonus.

 

[Lily_Lancer]

It took you 3 months and a math formula to figure that out? I been doing this since the June patch.

The improved lumber mills also made it viable to use woods adjacency, mostly for Civs that benefit from it like Norway, or that benefit from the appeal like Australia. Same for Rainforest but not as good since you can't chop and replant later.

But

If you don't play online speed but play on any other speed, according to the math you shall always chop right now. Only wait for Magnus or card if this city is to welcoming Magnus/card within 10 turns, otherwise chop right now.

It took you 3 months and a math formula to figure that out? I been doing this since the June patch.

The improved lumber mills also made it viable to use woods adjacency, mostly for Civs that benefit from it like Norway, or that benefit from the appeal like Australia. Same for Rainforest but not as good since you can't chop and replant later.

You shall always chop if you don't play online speed.

Before September patch the value t shall be 8~9%, this means you shall always chop on online speed.

Only post September patch building lumber mills become viable in some but not most situations. The requirement is still strict, you need to have no better tile to work on than that tile even if that tile is chopped.

So if you been doing this since June patch, I'm sure you don't play efficiently. Yes you can claim you don't care about efficiency, but that brings the discussion back to the chaos "I'm a casual player so I don't play efficiently and only win victory at T219 standard speed. However I think this is a quick finishing time so what I'm going to say is all correct, and you're all wrong if you finish earlier than me since if you finish earlier you're no longer casual player"

Such discussions are outside the topic this thread is talking about.

 

[leandrombraz]

You shall always chop if you don't play online speed.

Before September patch the value t shall be 8~9%, this means you shall always chop on online speed.

Only post September patch building lumber mills become viable in some but not most situations. The requirement is still strict, you need to have no better tile to work on than that tile even if that tile is chopped.

So if you been doing this since June patch, I'm sure you don't play efficiently. Yes you can claim you don't care about efficiency, but that brings the discussion back to the chaos "I'm a casual player so I don't play efficiently and only win victory at T219 standard speed. However I think this is a quick finishing time so what I'm going to say is all correct, and you're all wrong if you finish earlier than me since if you finish earlier you're no longer casual player"

Such discussions are outside the topic this thread is talking about.

I'll wait for the "Rethinking lumber mills on standard" thread 3 months from now to answer that.

 

[Lily_Lancer]

I'll wait for the "Rethinking lumber mills on standard" thread 3 months from now to answer that.

Unfortunately due to math calculation this may never happen, unless they strengthen mills or nerf chopping again.

You're saying this just because you don't know math or scientific way of dealing things, you tend to play by belief. With maths If I make a mistake I instantly deny and correct it, however you follow your religion on mills so you always stand still even if you realized that may be incorrect.

Yes you can stand still and continue to think T219 is a good record or sth. like that. You can do that all day, I know.

 

[Ownsya]

I'm wondering how you chose the values for X, Y, t, and T?
I guess X is production from chopping, but the others are not clear to me

 

[lotrmith]

If you don't play online speed but play on any other speed, according to the math you shall always chop right now. Only wait for Magnus if this city is to welcoming Magnus within 10 turns, otherwise chop right now.

Depends on what you're producing when you're chopping, what cards you have active or might have discovered or change in ensuing turns, etc.

It's almost like every game you play might have a general strategy to employ with ideal play to aim for, but also presents thousands of variables along the way that you'd do well to prepare to adapt to. With this in mind I'd say it's best to avoid sweeping, absolute generalizations.

 

[Lily_Lancer]

I'm wondering how you chose the values for X, Y, t, and T?
I guess X is production from chopping, but the others are not clear to me

Y is net prod gain from late game chop, suppose you chop and get 95 prod in late game but the builder charge cost 35 then Y=60.
t is the inflation rate. 1 production this turn generally worth 1+t% production the next turn, and (1+t%)^n production n turns later.
T is the number of turns between now and late game when you plan to remove and chop. Suppose now is T60 and you plan to remove and chop around T110, then T=50.

 

[Ownsya]

Y is net prod gain from late game chop, suppose you chop and get 95 prod in late game but the builder charge cost 35 then Y=60.
t is the inflation rate. 1 production this turn generally worth 1+t% production the next turn, and (1+t%)^n production n turns later.
T is the number of turns between now and late game when you plan to remove and chop. Suppose now is T60 and you plan to remove and chop around T110, then T=50.

I understood how you defined them. Okay so these are example values, I guess based on some sample games you've played? What about the inflation value, is that something you simply guess or did you use some method to conclude inflation is 5% and that before September patch it was 8-9%?

 

[Lily_Lancer]

I understood how you defined them. Okay so these are example values, I guess based on some sample games you've played? What about the inflation value, is that something you simply guess or did you use some method to conclude inflation is 5% and that before September patch it was 8-9%?

Before September it was 6~7% on standard speed and 8~9% on online speed. Since there is city defense bug that allows you to capture cities really quick(also pillage yield large number of science and culture so you develop on trees is also too quick) so investment on troops get much better paid off. Now these bugs are fixed so not that profitable.

 

[Nefelia]

If you don't play online speed but play on any other speed, according to the math you shall always chop right now. Only wait for Magnus or card if this city is to welcoming Magnus/card within 10 turns, otherwise chop right now.

No.

Your analysis suffers from one massive flaw: the arbitrary start point (X) and end point (Y) for your analysis.

Beyond that, you also ignore that the decision to chop or not will depend on a large variety of contextual considerations such as:
- is the tile needed for a district or wonder
- is the tile needed for a farm or unique improvement (great wall, etc)
- is the forest needed for long term production (in a city lacking hills or resources that can be mined)
- is the increased appeal from the forest significant to one's future goals
- is the adjacency bonus from the forest worth preserving
- does the forest provide strategic value (line of sight, movement penalty, defense bonus)

Perhaps considering these factors is implied, but from reading your initial post your conclusion seems pretty absolute.

A final consideration is the sheer joy of not having crap production in cities surrounded by flat lands. Those lumber mills are crucial to those cities not being utter trash at production.

 

[The googles do nothing]

Suppose value inflates at t% per turn.

Please explain.. Is this because your building something with that production which returns interest?

I would like to know how much of the civ player base would shink if chopping was seriously lowered or removed. With chopping I can avoid the AI 'stealing' wonders i'm building, can get a new city up to a size I will not loose from loyalty, rush an attack or defense, spam settlers. On the other hand if chopping went away it might force fir axis to address why chopping is so beneficial.

 

[Ownsya]

Before September it was 6~7% on standard speed and 8~9% on online speed. Since there is city defense bug that allows you to capture cities really quick(also pillage yield large number of science and culture so you develop on trees is also too quick) so investment on troops get much better paid off. Now these bugs are fixed so not that profitable.

I'm trying to make sense of this, your explanations sometimes skip some steps or assume background knowledge, but I'm trying to spell it out. My understanding is that chopping yields increase as you unlock more civics/techs. So you're translating # of civics/techs unlocked to # of turns based on your games (how many turns it takes you to unlock them) and then backing out your inflation rate from there?

Also I'm not an economist so I'm not quite understanding your formula. It doesn't looks like a net present value formula based on a periodic inflation rate, as I might've expected. Also I don't understand how your first term, 3*(1-t%)/t% doesn't include number of turns T, unless your t% here is non-periodic and based on the inflation over a given period. Then in the same equation you use Y*(1-t%)^T where t% here is presumably periodic (per turn). To my knowledge, NPV would be Y / (1-t%)^T, anyway, not multiplied... Again, I'm not an economist and I could simply be ignorant of what you're actually doing here, in which case please explain.

In my mind the calculation should be:
3 production per turn for T= 50 turns, inflation is 7%. I would use the equation for "present value of an annuity"
present value of 50 turns of production = 3 * { 1 - [1 / (1.07)^50] } / 0.07 = 41.4.
This means that if we consider inflation to be 7%, then 3 production for 50 turns is worth 41.4 production right now.

Then we add the value of chopping after 50 turns. For this I'd use the formula for present value in terms of future value adjust for inflation, PV = FV / (1+t%)^T.
Present Value of chopping after 50 turns = 60 / (1.07)^50 = 2.04.
This means that if chopping after 50 turns yields a net of 60 production, that 60 is worth only 2 production right now.

Finally we add the two to get 43.4 production for waiting 50 turns vs 40 production for chopping right now. Result based on your assumed values.

If I use your values for Standard Speed of Y=120, t%=5, T=75, then the total Present Value is 61, which is less than X=80.

I think your formulas are slightly off but get very close values. Then again, I think it depends a lot on how you chose your inflation rate, and of course there can be other things to consider as some people have commented. In my current game, I have a coastal city with a single forest and no hills. Chopping now may be theoretically the better thing to do, but then I have 0 production almost forever until I can get the harbor which will take almost forever to build. Just an example

 

[Lily_Lancer]

I'm trying to make sense of this, your explanations sometimes skip some steps or assume background knowledge, but I'm trying to spell it out. My understanding is that chopping yields increase as you unlock more civics/techs. So you're translating # of civics/techs unlocked to # of turns based on your games (how many turns it takes you to unlock them) and then backing out your inflation rate from there?

Also I'm not an economist so I'm not quite understanding your formula. It doesn't looks like a net present value formula based on a periodic inflation rate, as I might've expected. Also I don't understand how your first term, 3*(1-t%)/t% doesn't include number of turns T, unless your t% here is non-periodic and based on the inflation over a given period. Then in the same equation you use Y*(1-t%)^T where t% here is presumably periodic (per turn). To my knowledge, NPV would be Y / (1-t%)^T, anyway, not multiplied... Again, I'm not an economist and I could simply be ignorant of what you're actually doing here, in which case please explain.

In my mind the calculation should be:
3 production per turn for T= 50 turns, inflation is 7%. I would use the equation for "present value of an annuity"
present value of 50 turns of production = 3 * { 1 - [1 / (1.07)^50] } / 0.07 = 41.4.
This means that if we consider inflation to be 7%, then 3 production for 50 turns is worth 41.4 production right now.

Then we add the value of chopping after 50 turns. For this I'd use the formula for present value in terms of future value adjust for inflation, PV = FV / (1+t%)^T.
Present Value of chopping after 50 turns = 60 / (1.07)^50 = 2.04.
This means that if chopping after 50 turns yields a net of 60 production, that 60 is worth only 2 production right now.

Finally we add the two to get 43.4 production for waiting 50 turns vs 40 production for chopping right now. Result based on your assumed values.

If I use your values for Standard Speed of Y=120, t%=5, T=75, then the total Present Value is 61, which is less than X=80.

I think your formulas are slightly off but get very close values. Then again, I think it depends a lot on how you chose your inflation rate, and of course there can be other things to consider as some people have commented. In my current game, I have a coastal city with a single forest and no hills. Chopping now may be theoretically the better thing to do, but then I have 0 production almost forever until I can get the harbor which will take almost forever to build. Just an example

Yes your version is more accurate. I'm just using some estimation techniques to simplify my calculation, such as 1-t~=1/(1+t), 1+t~=1/(1-t) when t<<1.

The inflation rate is based on the assumption that the value of time, or more accurately, 1 turn, is always the same. So I just look at my yields per turn and it seems that this grows ~7% per turn on online speed and ~5% per turn on standard speed. Of course not accurate but an estimation.

No.

Your analysis suffers from one massive flaw: the arbitrary start point (X) and end point (Y) for your analysis.

Beyond that, you also ignore that the decision to chop or not will depend on a large variety of contextual considerations such as:
- is the tile needed for a district or wonder
- is the tile needed for a farm or unique improvement (great wall, etc)
- is the forest needed for long term production (in a city lacking hills or resources that can be mined)
- is the increased appeal from the forest significant to one's future goals
- is the adjacency bonus from the forest worth preserving
- does the forest provide strategic value (line of sight, movement penalty, defense bonus)

Perhaps considering these factors is implied, but from reading your initial post your conclusion seems pretty absolute.

A final consideration is the sheer joy of not having crap production in cities surrounded by flat lands. Those lumber mills are crucial to those cities not being utter trash at production.

When the numbers are close, like the 43 and 40 on online speed, these factors may influence your desicion and are worth discussion.

When numbers are far-away ,like the 61 and 80 on standard speed, it is easy to conclude that in at least 99% of situations you shall chop immediately.

It seems that I'm using Newton's law to conclude that you cannot run faster than a car. However you begin to cry

"Hey, you don't consider the effect of general relativity. The running of earth and moon and sun, or a nearby nuclear power plant, or whatsoever, may influence my speed and the speed of car a little bit, under strict constraints I may be running faster than that car.

However you only use the outdated Newton's law, how dare you to be so absolute?"


You don't use general relativity to compute the speed of a car, do you?

 

[lotrmith]

When the numbers are close, like the 43 and 40 on online speed, these factors may influence your desicion and are worth discussion.

When numbers are far-away ,like the 61 and 80 on standard speed, it is easy to conclude that in at least 99% of situations you shall chop immediately.

It seems that I'm using Newton's law to conclude that you cannot run faster than a car. However you begin to cry

"Hey, you don't consider the effect of general relativity. The running of earth and moon and sun, or a nearby nuclear power plant, or whatsoever, may influence my speed and the speed of car a little bit, under strict constraints I may be running faster than that car.

However you only use the outdated Newton's law, how dare you to be so absolute?"


You don't use general relativity to compute the speed of a car, do you?

It seems more like you have such a narrow focus on the game that you only ever consider, for example, producing one of five things and never anything else in your pursuit of 'ideal' or even 'perfect' play. This among other things ignores the myriad factors that influence a player as the game progresses fluidly, every turn, such that you lead us all to believe that if any situation ever arose that would cause you to divert from 'perfect' play you would likely smash that Restart button and begin again.

 

[Nefelia]

When the numbers are close, like the 43 and 40 on online speed, these factors may influence your desicion and are worth discussion.

When numbers are far-away ,like the 61 and 80 on standard speed, it is easy to conclude that in at least 99% of situations you shall chop immediately.

Again, nope.

You did not acknowledge the glaring flaw in your analysis: the arbitrary start and end point of your examples. Why is turn 120 the end point? How would adding another 20 turns effect the analysis. Another 40 turns?

You have the potential to present this formula as a general rule of thumb for informing players seeking maximal efficiency, but you are misusing this tool. Rather than making a blanket assessment of "always chop immediately on Standard speed", you should be suggesting that chopping is most efficient if they anticipate the game ending in less than X turns, and lumber mills are a better investment if they anticipate the game ending in more than X turns.

It seems that I'm using Newton's law to conclude that you cannot run faster than a car. However you begin to cry

Well, that was a constructive rebuttal. I think I'll leave off here.