Micromanagement is alive and well in Civ 4!

[Zombie69]

You're still doing the whip very inefficiently in your example. I don't know how many times i need to say this before you finally understand, but :
ALWAYS WORK THE FOOD RESOURCE

On turn 10, you should have worked the food resource and gained 5 food to be applied to your next whip. You go up to level 7, but whip on the very turn where you get there, so there's no unhappiness penalty. Besides, on the turn you go back up to level 7, you lose the whip penalty, so even if you didn't want to whip immediately (though not doing so would be a bad move), going up to level 7 would be the thing to do.

NEVER WASTE FOOD (it's far too valuable), AND NEVER LET A FOOD RESOURCE LIE IDLE.

In an real game, i would actually work the food resource on turn 9 also, let my city grow, and whip again the next turn. YOU DON'T HAVE TO WAIT UNTIL THE WHIP UNHAPPINESS GOES BACK DOWN TO ZERO BEFORE YOU WHIP AGAIN. Sure, doing this 4 or 5 times in a row, with all the food you're making, you'll eventually get to a point where you whip with still 10 turns left to go to the whip unhappiness. So be it. Better than not whipping to your max potential. In a real game, after all this time, you max happiness should be going up due to new resources or new buildings.

Just one extra happiness will then let you do the following :
- grow to max granary at size 6, with one turn left to whip unhappiness
- grow to size 7, now happy
- waste 1 or 2 turns of not whipping to grow to level 8
- whip 4 pop instead of 3, putting to good use the extra food that you should ALWAYS, ALWAYS have been working

Two more happiness makes it even better, because you don't have to waste happy turns not whipping :
- grow to level 7, full granary (or near full)
- grow to level 8
- whip 4 pop right after you got to level 8 (do this even if there's still unhappiness left due to whipping, NEVER WASTE FOOD)

I hope i made it clear enough, what with all the uppercase. It seems like repeating something over and over will be the only way to make you understand the principle.


As for your example without whipping, please redo it in a more comprehensible manner. Just tell us how many turns you work each type of tile, and your total FPC so that we can compare it to the whip scenario. None of that "turns lost" thing, which just makes everything more confusing. Don't count the city center production and commerce in either scenario, since they just cancel each other out and are therefore irrelevant to the discussion.

 

[Compromise]

In the posts I've made over the last couple of days, here's what I believe I've shown to my satisfaction (I do not claim originality for many of these points):

1) The more citizens you whip at a time, the more efficiently they are converted to hammers. (Very far from original.)

2) If your city's citizens are working unimproved tiles, it's better to whip them, no matter how many you whip at a time. (not original, but proved here)

3) If you are happiness limited, your food surplus is +2F while working MaxHappy-1 tiles and your last citizen can either be whipped or put to work on a mined hill:
. . a) grassland hill mine: you can get 30H (or 48H max with the bugged whip) for him now plus 1H/turn for 10 turns, or 4H/turn for 10 turns
. . b) plains hill mine: you can get 30H/48H now plus 1H/turn for 10 turns, or 4H/turn for 10 turns
. . (these conclusions are, I think, original)

4) If you are happiness limited, the best time to whip is likely to be the very turn you grow to MaxHappy. I only outline the 1-pop whip case, but I think it's at least often, if not always, the case for 2+-pop whipping too. (original)

5) If you whip 3-pop from a happiness-limited city that has really high-productivity marginal tiles, the whip gives you a 5-10% return bugged or fair. (the idea is far from original, the quantification might be)

So what to make of this? Here are my bottom line, take-home, easy-to-follow results. Note how little they differ from Zombie69's original position that he has been strongly suggesting I don't understand or agree with.


1) Always work bonus food resources while under your happiness cap
2) Whip as many citizens at a time as you can
3) a) At HappyCap, whip just after you grow.
. . b) Below HappyCap, whip just before you grow.


Whoa! Those first two and half the third are exactly what Zombie69's said all along! I know. He's right. I have never once disagreed with him about any of them (except 3a). His replies to my posts indicates that he thinks I've disagreed with him, but he is mistaken.

The calculations I've made on these cases indicate something else that might be of interest to people glancing through this thread.

If you're not interested in micromanaging whipping for best production results, you're probably losing about 10% in production and/or commerce compared to those who do. This compares whipping to standard means of production.

The previous italicized statement is also one way to help evaluate the benefit of running the Slavery civic.

I think it might be of interest to some non-micromanagers to know what they're missing by not following all of Zombie69's excellent micromanagement techniques. This quantifies the cost for not using the whip optimally.

All I've shown is that there are a couple cases--e.g. when you have a spare high-production resource that you'd otherwise not be working and you're at your happiness limit--when you can squeak a little more (more, but delayed) production out of a city by working the resource by whipping one citizen. (Unless you exploit the bug. Then it's *always* better to whip.) Whipping three at once gives you a better return. I don't know about whipping two (probably close to even if a fair whip. I'm sure for 4 or more at a time it's an even better idea to whip. Because these special cases are not common enough, and because the benefit is small enough, the easier rule of thumb to remember and apply is just grow and whip.

I've also shown that in the happiness-limited case, it's better to whip just before you grow than just after.

Finally, I've quantified the benefit you get from the whip when you whip 3-pop at once. Think of it as about 10% over normal production methods.

What I've presented is only interesting to those interested in extreme micromanagement, which is why I've presented it here. It will have little affect on your gameplay if you ignore every single word.

Except these: Happy CIVing!

 

[Compromise]

...As for your example without whipping, please redo it in a more comprehensible manner....

No. I simply can't devote any more time to this. I think my last post indicates how much our thinking overlaps. I can see that I haven't been able to make you understand the conditions under which your strategy is just a little suboptimal. Actually, your strategy is *never* suboptimal if you can exploit the pop-to-hammer calculation bug.

I have presented my city totals in three ways: my original way, a modification of malekithe's way, and another way involving opportunity cost on missed tile-turns. You have glanced through or ignored the first two and not taken the time to understand the third. I believe I've been clear and complete. I can't think of more ways to show my calculations that won't take an inordinate amount of my time.

Again, I hope that my last post indicates to you that I completely understand your position, your calculations, and your conclusions. If you are not interested in taking the time to understand mine, that's fine. My thoughts are documented here for anyone with the time and interest to verify the calculations and conclusions for themselves.

 

[malekithe]

If you're not interested in micromanaging whipping for best production results, you're probably losing about 10% in production and/or commerce compared to those who do.

...

I think it might be of interest to some non-micromanagers to know what they're missing by not following all of Zombie69's excellent micromanagement techniques. This quantifies the cost for not using the whip optimally.

While you are correct, it's worth pointing out that in order to get similar results to whipping (in your last trial), you still had to perform a fair amount of micromanagement. Namely, you had to purposely go into a food deficit for a couple of turns so that you could benefit from the food resource to recover from that deficit. I'm not sure this is something most people do on a regular basis. It was really only a fall-out of the mathematical model used to simulate the management of the city. I use(d) it on occasion in real games, but, since I discovered the efficiency of whipping, I devote the same amount of micromanagement (possibly less, actually) and get better results.

 

[Zombie69]

1) The more citizens you whip at a time, the more efficiently they are converted to hammers. (Very far from original.)

I disagree. Because of the exploit, it's the exact opposite. Whipping 1 is more efficient than whipping 2, which is more efficient than whipping 3. Even without the exploit, the is the case (not taking into account happiness), because you're left working fewer tiles for a shorter period of time.

2) If your city's citizens are working unimproved tiles, it's better to whip them, no matter how many you whip at a time. (not original, but proved here)

Even if your city's citizens are working improved tiles, it's better to whip them. As long as there's no whip unhappiness in your city, and the city is at max pop, you should always whip. Improved tile or not.

3) If you are happiness limited, your food surplus is +2F while working MaxHappy-1 tiles and your last citizen can either be whipped or put to work on a mined hill:
. . a) grassland hill mine: you can get 30H (or 48H max with the bugged whip) for him now plus 1H/turn for 10 turns, or 4H/turn for 10 turns
. . b) plains hill mine: you can get 30H/48H now plus 1H/turn for 10 turns, or 4H/turn for 10 turns
. . (these conclusions are, I think, original)

I disagree with your results, because your methodology was faulty. Besides, the numbers depend on starting pop level, so you can't just blurt out numbers like that and expect them to be true for any case.

4) If you are happiness limited, the best time to whip is likely to be the very turn you grow to MaxHappy. I only outline the 1-pop whip case, but I think it's at least often, if not always, the case for 2+-pop whipping too. (original)

I disagree. It's often (if not always, i need to work on this one) better to whip just before going up in level, not after.

5) If you whip 3-pop from a happiness-limited city that has really high-productivity marginal tiles, the whip gives you a 5-10% return bugged or fair. (the idea is far from original, the quantification might be)

No, it gives more than that. It's just that you never used the whip properly (as can be shown by the fact that you actually left a high food tile idle for 2 out of 10 turns).

Note how little they differ from Zombie69's original position that he has been strongly suggesting I don't understand or agree with.

Still very different.

1) Always work bonus food resources while under your happiness cap

Always work bonus food resource no matter where you stand. If happiness becomes a problem, whip now rather than later, but always, ALWAYS work the food resource.

2) Whip as many citizens at a time as you can

Completely wrong. Cities with high food should whip as many as they can to maximize production while minimizing unhappiness. Cities with low food should whip as few as they can to maximize the bonus from while still being able to grow.

3) a) At HappyCap, whip just after you grow.

Wrong. Again, i must tell you, it's often (if not always) the case that you should whip before growth, not after.

. . b) Below HappyCap, whip just before you grow.

Whether you're at or below happy cap has nothing to do with whether you should whip before or after growth. The factors involved seem to be much more complex.

Whoa! Those first two and half the third are exactly what Zombie69's said all along! I know. He's right.

If you think that, then you still don't understand what i'm saying. It looks to me like we don't agree on any of your points.

I have never once disagreed with him about any of them (except 3a).[/u] His replies to my posts indicates that he thinks I've disagreed with him, but he is mistaken.

Your post indicates that you still don't know what i'm talking about, which explains why you don't understand why i say that you disagree with me.

The calculations I've made on these cases indicate something else that might be of interest to people glancing through this thread.

Be careful about trying to draw any conclusion from your calculations, since they still haven't been done correctly.

If you're not interested in micromanaging whipping for best production results, you're probably losing about 10% in production and/or commerce compared to those who do. This compares whipping to standard means of production.

You're losing more than that (your calculations still haven't been done properly even for one single scenario), and the actual numbers depend on circumstance, chief on which being your the amount of excees food you can manage.

The previous italicized statement is also one way to help evaluate the benefit of running the Slavery civic.

It would be a good way if your numbers were correct, but unfortunately you haven't reached that point yet. Either way, the numbers differ greatly for every city, depending on its size and its amount of excess food, so trying to decide whether to adopt slavery based on those numbers would be impossible without making a list for all different scenarios, finding in which scenario each if your cities stands, and adding those up, which would be ridiculously time consuming. Either way, it's not needed, because i can already tell you that slavery is always the best option. All the other options in this civics group frankly suck. The only time it's worth it to get out of slavery is when you're starting to get too much unhappiness from other civs switching to emancipation.

I think it might be of interest to some non-micromanagers to know what they're missing by not following all of Zombie69's excellent micromanagement techniques. This quantifies the cost for not using the whip optimally.

I agree it would be of interest, unfortunately you've provided no such info as of yet.

All I've shown is that there are a couple cases--e.g. when you have a spare high-production resource that you'd otherwise not be working and you're at your happiness limit--when you can squeak a little more (more, but delayed) production out of a city by working the resource by whipping one citizen. (Unless you exploit the bug. Then it's *always* better to whip.)

Even without the exploit, it's always better to whip, provided you have enough food surplus to afford it (except at very high city sizes). But since you've yet to shown appropriate use of the whip, you couldn't show this.

Whipping three at once gives you a better return. I don't know about whipping two (probably close to even if a fair whip. I'm sure for 4 or more at a time it's an even better idea to whip. Because these special cases are not common enough, and because the benefit is small enough, the easier rule of thumb to remember and apply is just grow and whip.

Actually, the return doesn't get better as you whip more, it gets worse (as shown by Malekithe in his excellent post. But if you whip more, it means you're using more food, so even though the return per food is less, the total hammers are more.

The last sentence in the paragraph above is the only thing i agree with in this entire post. It is indeed a good rule of thumb to remember to just grow and whip. Never refuse a food bonus, work all the food you can without building any non-resource farms, and whip all this great food into lots of hammers. A good rule of thumb for how many points you should whip at a time is how many you can regrow with the food surplus that you have, in the 10 turns it takes for unhappiness to subside.

I've also shown that in the happiness-limited case, it's better to whip just before you grow than just after.

Again, happiness has nothing to do with whether of these is better. The factors involved are totally different and much more complex.

Finally, I've quantified the benefit you get from the whip when you whip 3-pop at once. Think of it as about 10% over normal production methods.

No, you haven't. You've provided flawed calculations giving false results for one case (size 6, +5F), and didn't even attempt to provide the numbers for different sizes and different food surplus. Those numbers are completely different.

What I've presented is only interesting to those interested in extreme micromanagement, which is why I've presented it here. It will have little affect on your gameplay if you ignore every single word.

It would be interesting for those who like micromanagement, if the numbers were right. As it stands, it's not only uninteresting, but downright hurtful if someone bases his game on numbers he expects to be right, unaware that the numbers provided are completely wrong.

 

[Zombie69]

I think my last post indicates how much our thinking overlaps.

I think your last post indicates how our thinking is completely opposite.

I have presented my city totals in three ways: my original way, a modification of malekithe's way, and another way involving opportunity cost on missed tile-turns. You have glanced through or ignored the first two and not taken the time to understand the third. I believe I've been clear and complete. I can't think of more ways to show my calculations that won't take an inordinate amount of my time.

Again, I hope that my last post indicates to you that I completely understand your position, your calculations, and your conclusions. If you are not interested in taking the time to understand mine, that's fine. My thoughts are documented here for anyone with the time and interest to verify the calculations and conclusions for themselves.

Actually, i've made a huge amount of effort to understand your results above. I managed to understand the first part, even though it wasn't as well formatted as Malekithe's. The second part, i really tried, but it's hard to understand what you're talking about. I know that in the first part, which i understand for sure, you made big mistakes near the end, which totally disquilify any numbers you could come up with. You didn't use the whip properly, and so it will surely show up as less efficient than it truly is.

 

[Compromise]

While you are correct, it's worth pointing out that in order to get similar results to whipping (in your last trial), you still had to perform a fair amount of micromanagement. Namely, you had to purposely go into a food deficit for a couple of turns so that you could benefit from the food resource to recover from that deficit. I'm not sure this is something most people do on a regular basis. It was really only a fall-out of the mathematical model used to simulate the management of the city. I use(d) it on occasion in real games, but, since I discovered the efficiency of whipping, I devote the same amount of micromanagement (possibly less, actually) and get better results.

You're right about the micromanaging I did in that case. I was specifically trying to get back to the same point the city started at within 10 turns so that the two cases could be compared on an equal--or near-equal--basis. In real life, under those circumstances, you'd just have to work your food bonus and production tiles so as not to lose a population point or grow above your happy cap.

Thanks for pointing this out.

 

[Compromise]

Actually, i've made a huge amount of effort to understand your results above.

Thank you, I appreciate that.

Also, I apologize. I overstepped my bounds when I attempted to put words in your mouth about what we would agree or disagree about. It looks like we disagree on many points.

Your reply to my summary chastises me for not accepting as absolute truth that I must always work bonus food tiles and whip the resulting citizens efficiently into hammers.

I am aware of no errors in my examples, and will correct any that are pointed out to me. Telling me that I'm wrong doesn't make me wrong.

My conclusions are extrapolations based on my understanding and interpretation of my examples. That extrapolation is an error-prone process.

 

[Zombie69]

You're right about the micromanaging I did in that case. I was specifically trying to get back to the same point the city started at within 10 turns so that the two cases could be compared on an equal--or near-equal--basis. In real life, under those circumstances, you'd just have to work your food bonus and production tiles so as not to lose a population point or grow above your happy cap.

Thanks for pointing this out.

No, like i said, in real life, you still wouldn't work the production tiles (which are inferior tiles, remember?) What you'd do, like i said, is keep growing and just make the next whip one turn sooner.

If you wanted comparisons that both finish where they started, you should have simply taken Malekithe's example, which was at pop 7 (with whipping) and 8 (no whipping).

 

[Zombie69]

Your reply to my summary chastises me for not accepting as absolute truth that I must always work bonus food tiles and whip the resulting citizens efficiently into hammers.

I am aware of no errors in my examples, and will correct any that are pointed out to me. Telling me that I'm wrong doesn't make me wrong.

Look a few posts before (#242), where i clearly explained where you went wrong. On turns 9 and 10 in the whip scenario, you used inferior tiles, making this option seem less attractive than it really is.

Again, if you absolutely must use an example where both cases end where they started, use Malekithe's example at pop 7 and 8.

 

[malekithe]

I wanted to redo the example I did earlier because, as was pointed out, I had a couple numbers wrong and I'd like to better manage the no-whip case to target a similar hammer output to whipping (to see what it truly sacrifices).

First the whipping case:

Turn	Pop	Basket	Surplus	Comm.	Hammers
1	4	34/28	5	12	96
2	5	25/30	5	16	0
3	6	15/32	5	20	0
4	6	20/32	5	20	0
5	6	25/32	5	20	0
6	6	30/32	5	20	0
7	7	19/34	5	24	0
8	7	24/34	5	24	0
9	7	29/34	5	24	0
10	7	34/34	5	24	0

I've taken 10 turns to return to my previous state. At this point I'd whip again.

In the no-whip city, I'm going to allow them to make use of 2 grassland hills tiles and 2 plains hills tiles. The goal is to convert the excess food from the food resource into hammers as efficiently as possible. To do this, I'm going to work all four mines for all but two turns. During those last two turns, I'm going to, first, work nothing but the food resource and some hamlets in order to grow back most of what was spent working the mines and then I'm going to stop working the plains hills to leave the net food change at 0. The simulation looks like this:

Turn	Pop	Basket	Surplus	Comm.	Hammers
1	8	17/36	-1	12	14
2	8	16/36	-1	12	14
3	8	15/36	-1	12	14
4	8	14/36	-1	12	14
5	8	13/36	-1	12	14
6	8	12/36	-1	12	14
7	8	11/36	-1	12	14
8	8	10/36	-1	12	14
9	8	9/36	5	28	0
10	8	14/36	3	20	6

So after summing the output columns of both simulations, it looks like this:
Whip: 204C, 96H
No-Whip: 144C, 118H

You'll note that the mining city converted food to hammers more efficiently (1:2.33 vs. 1:1.92). However in order to achieve those results, it had to spend population turns performing the conversion. Those population turns were turns not spent generating commerce. Total population turns available in both cases are 61 for the whip and 80 for the no-whip. However, the no-whip had to use 34 of those pop-turns working hills, converting food into hammers. The whip city, essentially, only sacrificed 19 pop-turns performing the conversion. Notice that the difference in non-sacrificed pop turns (15) multiplied by the commerce output of those pop-turns (4) is exactly the difference in commerce output between the two trials.

If you had substituted grassland hills for the plains hills in the no-whip scenario, you would have gotten a higher food-to-hammer conversion efficiency, but you would have sacrificed even more pop-turns, leading to an even larger drop in commerce. The advantage of slavery is that it allows you to convert your excess food in to hammers at a competitive rate while not sacrificing nearly as many pop-turns and therefore commerce.

Edit: Also of note... Pop-turns spent converting food to hammers by working mines cost more (in civic and city maintenance) than pop-turns lost to slavery.

Edit 2: Changed everything to use 7/8 pop. The food totals in the two trials are more in-line in this scenario.

 

[Zombie69]

Malekithe, thanks for the great analysis which perfectly highlights one of the most important aspects of whipping, which is that it allows one to work (and grow) more cottages, because we don't need to work any tiles that produce hammers. This was already mentioned before, but all too briefly, and this is a perfect demonstration of that principle.

There's just one thing that's not truly fair between the two examples though. At the end, both have the same food, but one has -1 happiness for one turn. To be fair, you should let both cities work the food and al cottages for one turn to make it fair. This will give +4C to the non-whip case, since it currently has one more tile it can use.

Edit : i just saw a typo in your table, that doesn't change anything to the results. At turn 6, you're at 15/32, not 30/32.

Edit : i found another mistake that's much more important. All your turns are the situations at the beginning of turns. This means that you're only actually showing 8 turns, not 9. Again, we go back to the same situation that Compromise presented in his own table, where he didn't know what to do with the food anymore. I suggest that your previous example, which was really one pop higher than stated, was an easier point for discussion, since both versions really did finish equal both in food and happiness. And i want to make it clear that i'm not pushing for that version because it helps my cause. Indeed it hurts it, because the bigger the size of the city, the less efficient whipping becomes.

 

[malekithe]

Thanks for the feedback Zombie. I changed around the above post to use the 7/8 pop scenario. Results are similar, of course.

 

[Compromise]

Well done, malekithe! You've found a presentation format we can all agree on.

I'll submit the following 10-turn 8-pop tile-usage cycle for comparison to the 3-pop whip case.

Instead of trying to maximize the pop->hammer conversion rate (a good comparison, and Zombie69 is right about the commerce cost associated with doing so), I'll try to get between 90 and 96 hammers. Since 5-tiles are better than 4-tiles, I'll also try to maximize use of food resource. I'll then compare to your 3-pop whip case which I haven't checked and will take as reported.

Ham = Hamlet
GHM = Grassland Hills Mine
PHM = Plains Hills Mine
Foo = 5F food resource

Turn 1: Ham Ham Ham Ham Ham GHM PHM PHM
Turn 2: Ham Ham Ham Ham Ham GHM PHM PHM
Turn 3: Ham Ham Ham Ham Foo GHM PHM PHM
Turn 4: Ham Ham Ham Ham Foo GHM PHM PHM
Turn 5: Ham Ham Ham Ham Ham Foo PHM PHM
Turn 6: Ham Ham Ham Ham Ham Foo PHM PHM
Turn 7: Ham Ham Ham Ham Ham Foo PHM PHM
Turn 8: Ham Ham Ham Ham Ham Foo PHM PHM
Turn 9: Ham Ham Ham Ham Ham Foo PHM PHM
Turn 10: Ham Ham Ham Ham Ham Foo PHM PHM

Out of 80 citizen-turns, that's 4 on GHM, 8 on Foo and 20 on PHM. That leaves 48 citizen-turns working hamlets.

Using malekithe's presentation:

Turn    Pop     Basket  Surplus Comm    Hammers
1       8       17/36   -3      20      11
2       8       14/36   -3      20      11
3       8       11/36   0       16      11
4       8       11/36   0       16      11
5       8       11/36   +1      20      8
6       8       12/36   +1      20      8
7       8       13/36   +1      20      8
8       8       14/36   +1      20      8
9       8       15/36   +1      20      8
10      8       16/36   +1      20      8

No-whip return: 92H, 192C

The 3-pop whip return: 96H (90H if the bug is fixed), 204C

My conclusion was that in the 3-pop whip case, whipping was 5-10% better in hammers and commerce. I believe this example supports that conclusion.

Also, in an actual game, if I wasn't interested in micromanaging and was running a civic other than slavery (or just didn't care to maximize my production by whipping), and I wanted production out of this city...I'd work the food resource, 2PHM, and 1GHM. This is food-neutral and if you add the 1H from the city center, gives 12H/turn which will suffer no roundoff error from any 25%xn production bonus. (Another good issue raised early in this thread!)

It would be about 5% better to whip, and you'd get the hammers earlier.

 

[Zombie69]

Correct me if i'm wrong, but i just noticed that it seems you and Malekithe are still showing only the state after 9 turns, rather than 10. If this is the case, then again, the comparison isn't fair, because after 10 turns, the whipping case will be at 5 extra food compared to where it started, while the non-whipping case in both your examples is at equal food to where it started. It looks like even at 7 and 8 pop, we're still not getting a fair point of comparison. Or am i just not interpreting those tables correctly? Looks to me like you're showing the state at the beginning of each turn, and the production and commerce obtained from each turn, but to be fair, the food situation at the end of 10 turns should be shown, which right now will give 5 more food with the whip.

Then unless we can make an example that actually fits perfectly, i suggest we force the non-whip case to finish with 5 extra food as well, to be fair. We could say that both cities are trying to grow slowly to adjust to new happiness resources that are coming online at a very slow rate. Actually, this seems very realistic to me, since it's safe to assume that cities, on average, will grow at least 5 food per 10 turns to adjust to new happiness.

Also, the gold saved from maintenance, as pointed out by Malekithe earlier, should be added to the commerce for the whip case. Then i think we'd have as fair a comparison as we can get.

Of course, the comparison will still only be valid for size 8 with +5F. Any attempt to carry it over to any other situation without running the numbers again would be pointless, because the numbers will vary greatly. The higher the size, the less effective slavery will be. The higher the food surplus, the more effective slavery will be. Both of these factors will have a great impact on the final results.

 

[malekithe]

I think you're right Zombie, the whipped case is producing 5 extra food over ten turns. How would you recomend that 5 food be put to use? Normally, I'd just rush another building or unit one turn early. Simply trading it in at 2 for 1 seems somewhat reasonable, but I'm not 100% sure.

If I did the 2 for 1 trade, we'd have 106H/204C output from the whip and 92H/192C non-whip. Maintenance costs would amount to about 8 extra gold, which I'll subtract from the non-whipped case, giving 92H/184C.

If we then value 1 hammer at 2 commerce as well (fairly common), we have a total output from the two scenarios of:

Whip: 416C
No Whip: 368C

That gives whipping a total efficiency of 113%.

I could also add in some calculation to factor in the extra value of hammers now vs. hammers later. But, I don't know a good depreciation rate. If we were to assume hammers next turn are worth 99% (chosen without much analysis) of hammers this turn, then the output for non-whip drop to 88.3 hammers. Whipping efficiency climbs to 115%.

So 13-15% better to whip than not. I could live with those numbers. Plus, I'd imagine it only gets better if fewer hills are available or the population is smaller.

Also, as an aside, if we value 1 hammer at 2 commerce, my trial run at the no-whip was actually better than Compromise's.

 

[Zombie69]

Out of curiosity, here's what happens in this case if, as suggested by Compromise, we start whipping just after growing, rather than just before.

Here i show the state of the food supply after 10 turns. I expect it to be only at +2 compared to where we started rather than +5, because as stated in my article, waiting until after the growth costs 1 food per point pop whipped, which means in this case that it costs 3 points. However, as i started thinking a few posts up, the fact that we can maybe grow faster might make a difference. I'm still not sure about this last bit though, so this comparison with Malekithe's table should be interesting.

It is assumed that 2 turns before whipping, the granary was filled to the max using avoid growth. Then one turn before the whip, the city was allowed to grow to size 8 with the 5 food surplus, bringing the city up from 34/34 to 22/36.

Turn	Pop	Basket	Surplus	Comm.	Hammers
1	5	22/30	5	16	96
2	5	27/30	5	16	0
3	6	17/32	5	20	0
4	6	22/32	5	20	0
5	6	27/32	5	20	0
6	7	16/34	5	24	0
7	7	21/34	5	24	0
8	7	26/34	5	24	0
9	7	31/34	5	24	0
10	8	19/36	3	24	0
11	8	22/36	3	24	0

In this case, we can see that we got to size 5 one turn earlier (this will always be the case when waiting after growth to whip, we'll always start one size bigger but without a more-than-full granary). We also happen to get to size 7 one turn earlier (this won't always be the case that another level will come earlier, but in this case it does, given us another another 4 extra commerce).

In this case, whipping after the increase makes us get to level 8 one turn too soon. We'll have to whip again before the 10 turns are over. The 11th turn here would not happen as portrayed above, because i'd actually whip on turn 10, i.e. 9 turns only after the original whip. But just for the sake of argument, let's pretend that i don't have a happiness problem on turn 10, and i'm still at size 7 at 36/34 (i know this isn't possible, but this is to represent cases where we don't get back to the top level too soon). Then i could still make 5 food. I'd end up on turn 11 (i.e. after 10 turns) at 24/36. Compare that to the 22/36 where Malekithe ends up in his example. However, i started one turn after he did, so with 5 more food. He ended up with 5 more food than he started with, while i ended up with 26 - 24 = 2 more food. As i expected initially, waiting after the growth to whip cost me precisely 3 food.

What i gained in exchange for the 3 food are 8 commerce (4 for being at size 5 one turn sooner, and 4 from being at size 7 one turn sooner). Is 8 commerce worth more than 3 food? I'd say it depends. Considering that i also get two more turns of cottage growth (which i personally value at 2 commerce per turns of growth, for a total of 4 commerce), then i'd say that yes, it was worth it. However, this assumes that i didn't run into happiness problems at the end, which i did. In this case, whipping later allowed me to work at size 7 for one more turn, which made all the difference. Not all cases would provide this opportunity.

So you see Compromise what i was talking about when i said that whipping before growth is better food wise, that happiness before the whip was not what made it better or worse, and that the evaluation would be different everytime, and involve knowing how many turns are needed for each pop growth if whipping before growth and if whipping after growth, and the value of the tiles that can be worked?

By whipping before growth, you always save 1 food per pop point whipped. By whipping after growth, you always get at least one more turn of production from one tile, and sometimes more than one turn. Whether or not it's more than one depends on when the pop growths occur in each scenario. How much the extra tiles worked are worth depends on the value of the tiles. you're working before the whip. Do you understand now what i was talking about? And why i said lately that it might be too complicated to give any kind of definitive statement, since it differed too much from case to case, without any noticeable pattern?

 

[Zombie69]

I think you're right Zombie, the whipped case is producing 5 extra food over ten turns. How would you recomend that 5 food be put to use? Normally, I'd just rush another building or unit one turn early. Simply trading it in at 2 for 1 seems somewhat reasonable, but I'm not 100% sure.

I changed my post after you started typing yours (didn't know you were still here, you must live in Europe because it's awfully late here). Check it out again for my new suggestion. I think it's the fairest way to do it at this point.

Also, as an aside, if we value 1 hammer at 2 commerce, my trial run at the no-whip was actually better than Compromise's.

That's about the relative value i give them as well.

 

[Zombie69]

I think i've gained a good enough grasp now of when (in general, no specifics could be given without providing a huge, mostly useless, 3- or 4-dimensional table) it may be better to whip after growth rather than before it.

I've added 2 paragraphs to the article to discuss this. Credit goes to Compromise to make me realize that this was even a possibility. As you can see by reading the article, the situations are rather rare, but they do occur and so i thought it was worth mentioning.

 

[malekithe]

I changed my post after you started typing yours (didn't know you were still here, you must live in Europe because it's awfully late here). Check it out again for my new suggestion. I think it's the fairest way to do it at this point.

Nope, not in Europe. Seattle. It's pretty late, but I go into work pretty late most of the time.

I've produced another table for a no-whip trial. This time targeting a 5 food gain at the end. I'm, again, attempting to convert food to hammers as efficiently as possible. Anyway, here goes...

Turn	Pop	Basket	Surplus	Comm.	Hammers
1	8	17/36	0	16	11
2	8	17/36	-1	12	14
3	8	16/36	-1	12	14
4	8	15/36	1	16	10
5	8	16/36	1	16	10
6	8	17/36	1	16	10
7	8	18/36	1	16	10
8	8	19/36	1	16	10
9	8	20/36	1	16	10
10	8	21/36	1	16	10
Total		22/36	[B]+5[/B]	[B]152[/B]	[B]109[/B]

So 109H/152C vs. 96H/204C.

Applying the 8 commerce penalty for population maintenance: 109H/144C.

Convert at 2 commerce per hammer:
Whip: 396C
No Whip: 363C

That's only an 8% improvement (mostly because I made sure to use the most efficient conversion rate available).

However, if we look at the numbers another way, whipping gets 88% as many hammers, but 142% as much commerce. Multiply those together and the effect of whipping, for this scenario, is an extra 25%.

And, of course, all of this ignores the fact that hammers now are worth more than hammers later. That is just too situational to take into account so I'll assume a steady-state value for now.