# Whipping cycles

Discussion in 'Civ4 - Strategy & Tips' started by Quechua, Nov 14, 2007.

1. ### QuechuaUnique Unit

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I've seen it repeated on here that slavery converts surplus food to hammers in about a 1:2 ratio. The logic is that it takes roughly 15 to grow a pop point with a granary in the early game, and you get 30 per point from whipping.

After thinking about it, I think the ratio is much closer to 1:1, being only a little better than simply using the surplus to work hills and plains. I'll explain my reasoning, which very well may be flawed.

There's two problems with the 15 per 30 argument:

- No matter how many citizens you whip, you still decrease your happy cap by 1 for 10 turns. Even if you can only work a forest, you're still giving up 10 every cycle.

- You must spend some time with an unhappy citizen, which cuts into your surplus food for no gain.

So let's consider a simple example. Your happy cap is stuck at 5. You have a grassland pigs tile, and as many forests of any terrain type as you want to work. I'd love to provide a screenshot, but I'm clueless with worldbuilder.

Without whipping you get 5 from the city center and 4 forests, and you get 6 surplus from the city center and the pigs. If you spend the surplus on switching grassland forests to plains or hill forests, you get 11 per turn.

Now what we get from whipping obviously depends on how we do it. The conventional wisdom is to 2-pop whip once every 10 turns, just before we'll grow into unhappiness. I'll try to end the cycle with just as much food as I started. I also believe the unhappy citizen will hurt our production, so I'll try to minimize the time we're unhappy.

We'll start with 26/30 at pop 5, and 2-pop whip for 60 going to size 3 for one turn. I'll configure the food surplus to 3

1) 26/26, 6

Now we grow to size 4, and are at happy cap. I'll configure surplus to 2

2) 16/28 8
3) 18/28 ''
4) 20/28 ''
5) 22/28 ''
6) 24/28 ''
7) 26/28 ''

Now we're back to 5 pop, but have an unhappy citizen. I'll go to max growth of 6, but we lose 2 by being unhappy.

8) 14/30 4
9) 18/30 ''
10) 22/30 ''

And now finally we're back where we started. We've made 60 + 6 + 6*8 + 3*4 = 128

Remember 5 hammers per turn have nothing to do with surplus food, so this is 78 over 10 turns from a 6 surplus. That's a 1:1.3 ratio. We only get 18 extra hammers every 10 turns by using whipping, and we don't even have any mines?!

Ok, that's an extra axeman every 20 turns, but that doesn't sound quite right. Are my whipping tactics or my math wrong? (or both?)

2. ### oyzarHave quit civ/forums

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here is a save you can use...

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3. ### UncleJJDeity

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I think the problem is that your example is happiness constrained. Using Slavery in those circumstances is less effective than it can be. That is why you are getting less than the theoretical food to hammer ratio. Slavery can be difficult to apply in the early game and is used mainly to rush build when having a building or unit a few turns earlier is more important than maximising hammer production.

You should take another example if you want to see a case where whipping is at its most effective. For instance in the middle game when HR is available a city can have any happiness limit (by adding soldiers) and grow until it hits the health cap. Under these conditions you would find working high food tiles and whipping to be much more efficient than working weak tiles like forests or plains hills up to city sizes of about 10.

In fact once you can chain irrigate you would be much better off chopping at least some of the forests down and working grassland farms instead of grassland woods. At size 5 we have a theoretical food to hammer exchange rate of 2 hammers for 1 food (since it we get 30 hammers and it takes 15 food to grow to size 6). Consider just the last citizen; working a farm for 10 turns would give us +10 food which we can turn into 20 hammers if we whip once we reach size 6, meanwhile working a grassland forest instead gives 10 hammers. Of course I have avoided considering happiness problems which you are getting tied up in with all the micromanagement considerations, but this is the true power of Slavery as a way to convert food to hammers.

4. ### QuechuaUnique Unit

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But my entire point is it's the unhappiness problems that decreases the theoretical 2:1 ratio. That's why I went into micromanagement detail. If you can can show me how to do better with grassland farms at a 5 happy cap in detail, I'd be interested.

I'll think about your post more, but I think with higher happiness caps you're actually doing worse, since it takes a little more food to regrow per pop. You're still losing a potential productive citizen for 10 turns every time you whip.

And thanks Oyzar for providing a save!

5. ### dutchfireModeratorModerator

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At happy cap 5, you shouldn't grow your city to size 5, but you should be whipping at lower pop thus avoiding unhappy citizens.

6. ### DiamondeyeSo Happy I Could Die

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I follow a general rule of thumb that cities should never grow into unhappiness - if I whip from happycap 5 to pop 3, I'll have it grow to 4 and stay there until unhapiness is gone. Also, whips from pop 4 to 2 are more effective than the 5-3 you mention as far as I remember, the food required to grow (with granary) is 10-11-12-13-14? At size 5, you whip away 25 for 60 - how's that for a ratio? 1:2,4.
Ofcourse, whipping is situational, but I find it useful in most cases earlygame.
The prime reason I ain't usin it anymore is that I mainly play LAN with friend who hates to wait for me sitting and calculating if it pays to whip, and also due to the random event made possible by the Slavery Civic.

7. ### QuechuaUnique Unit

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Ok, if we're going to be persistently whipping, never actually growing to size 5 makes sense. I think this will do better than my example slightly. But if my 6 is turning to 12 per turn or better, and I get 4 from the city square and my 3 forests, I should get 160 after ten turns.

Can anyone come up with a whipping strategy that actually makes near this amount after a ten turn cycle?

8. ### IndiansmokeDeity

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Whipping is situational, that is why spiriual is so powerfull. Plan your whips Switch to slavery and switch out after 5 turns. Especially now with the slave revolt events it is a must for spiritual civs

The benefit from whipping is mostly to get something earlier or when you need it than to convert food to hammer more efficiently....unless you are Montezuma....

9. ### UncleJJDeity

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I did say Slavery is very hard to use in the very early game. If your happiness limit is 5 then the -1 from whipping is a serious loss of production. At that size about the only use of whip I make is to grow the city to size 6 and whip a library in for 3 pop (90 hammers). I then use the 2 scientists to limit grow to size 4 until the unhappiness is recovered. That gets a good head start towards the first GP while I research towards Monarchy. Adopting HR and if lucky having a wine available gives unlimited happiness and it essentially unleashes the power of food; allowing growth (to work more tiles), conversion of food to GPPs through specialists and food to hammers through Slavery. If you want to use Slavery effectively then beeline Monarchy and solve happiness problems.

In several places you make the assumption that Slavery gives a conversion rate of 1 food to 2 hammers. Strictly speaking this is only correct at a city size of 5 (and specifically for a whip from size 6 down to 5). I use a rule of thumb to decide whether Slavery is worthwhile at other city sizes.

City size 5 has a hammer from food rate of 2:1
City size 10 has a hammer from food rate of 1.5:1
City size 15 has a hammer from food rate of 1.2:1
City size 20 has a hammer from food rate of 1:1

With these conversion rates in mind it is easy to estimate the rates for intermediate city sizes. Using those conversion rates it is possible to decide which tiles to work to maximise hammer production. A grassland farm (pre Biology), for instance, is equivalent to a grassland hill at size 10 (both produces a net 1.5 hammers per turn) and inferior at size 15 where the hill produces a net 1.75 hammers and the farm only 1.20 hammers per turn. Not until size 20 is a grassland forest equivalent to a grassland farm and it is this that informs why forests should be cleared in the early game (since Lumbermills and Railways are a long way off and Biology will restore the balance anyway). My basic idea is that the vaue of food tiles changes as the city grows and Slavery becomes less efficient. However in the late game if you have many farms Biology re-energises Slavery and a similar effect can be had from corporations that give a lot of food.

10. ### dutchfireModeratorModerator

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DaveMCW has a post somewhere in this sub-forum with a list of when it becomes bad to whip away a citizen working a specific tile IIRC.

edit: found it here

11. ### MyOtherNameEmperor

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Okay; let's see what I can do with a city with a granary, happiness cap of 5, 6 food tile, and all types of forests.

Non-whipping strategy: work 3 plains hills forests and 1 grassland forest. Net production is +0/11 (0 food, 11 hammers) per turn.

Here's one whipping strategy:

Starting at size 5 with 20 food stored:

(1) Spend 2 turns to produce +12/10, then whip 3 pop points.
(Granary added 15 food, 5 overflow, growth at 30)

(2) At size 3, spend 2 turns to produce +12/6
(Granary added 15 food, 2 overflow, growth at 26)

(3) At size 4, carefully spend 8 turns to produce +15/65
(Granary added 15 food, 3 overflow, growth at 28)

Repeat.

Over 12 turns, this consumes 3 pop points and produces 81 raw hammers. At 30 hammers per pop point, this works out to 14.25 hammers per turn.

12. ### oyzarHave quit civ/forums

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Not often you are able to whip 3 pop points that often that early in the game though.. For something more feasible like whipping axemen(which actually require you to micromanage so you never actually get too much overflow into an axe. How would you go to produce the most axemen the fastest. Obviously static at size 5 still gives 11 hammers per turn. you can max give 4 hammers to an axe before you have to whip or you'll only whip 1 point. Is there any way to optimalize this? what about if you have some grassland(non-farms) in adition? what about farms?

13. ### KrikkitTwoImmortal

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I think the key to slavery is when you have excess food. and nowhere to spend it

If slavery can only get ~ 1:1 hammer to food, that is still better than the citizen which gives 1 hammer per 2 food.

The other purpose of slavery is converting Population to emergency/speed production ie units, Wonders, granaries, courthouses, etc. (rather than converting food to hammers)

14. ### QuechuaUnique Unit

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Ok, this is the kind of thing I'm looking for. Unfortunately, I think your numbers are a little off, the granary doesn't always give 15, it gives half of level you are growing from (e.g. 13 growing from 3 to 4). And also you're going to have to deal with an unhappy citizen growing back to 20/30 at the end of the cycle.

For others, I'll clarify what I was getting at in my first post. How do we evaluate the production of a city if we are going to persistently whip a food surplus? The common wisdom is we consider how much food it takes to grow back our population from whipping. This is why I was talking abut 1:2 ratios, but yes I'm aware the actual numbers depend on pop size.

So in my example of a 6surplus, and as many forests we want, the naive estimate is 17 per turn. If I allow you grassland farms instead, the naive estimate is 20 per turn.

But there are a few factors that cut this way down. Just trying a few things, I can't seem to break 14 per turn. For comparison, we get 11 never touching a whip.

The factors are:
-Whipping cuts your max productive population by at least one. In our example, every lost citizen counts for 1 per turn. If you intentionally stay well below the cap, you are losing even more hammers this way.

-Unhappy citizens cut into your surplus food, which increases the food per population point. You can avoid unhappy citizens if you slow your growth but...

-Slowing your growth by spending your food surplus on normal production dilutes your efficiency. In our example we can slow growth by converting surplus at a 1:1 ratio. In many cases this would be even worse.

So, can you find a way to persistently whip that even breaks a 1:1.5 ratio at low population caps? I'll give you grassland farms as well as the forests if you want...

15. ### OTAKUjbskiTK421

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Even when the ratio is exactly 1:1, and you gain no extra production through whipping, I think it's important to whip anyway, because during the turns you're regrowing your city, you're likely to be working 2F Grassland tiles. Even though it's just a few turns per whipping cycle, those 2F tiles can be Cottages -- making your Production city just as effective but with a small added bonus of a few Commerce.

QFT

Spoiler math showing why DaveMcW is right :
I made a chart recently comparing the food cost of each population point (with a granary on Epic speed) to how many hammers they generate when whipped, and the values are almost exactly the values UncleJJ posted:

Code:
```Values along the left indicate the population of the city whipped.
Values along the top indicate the number of population points whipped.
Values in the center represent the hammers per food given the city and whip size.

POP	1	2	3	4	5	6	7	8	9	10	11	12	13
1
2	2.81
3	2.5
4	2.36	2.43
5	2.14	2.25
6	2.04	2.09	2.17
7	1.87	1.95	2.01
8	1.8	1.83	1.9	1.95
9	1.66	1.73	1.77	1.83
10	1.6	1.63	1.68	1.73	1.78
11	1.5	1.55	1.58	1.63	1.67
12	1.45	1.47	1.51	1.55	1.59	1.63
13	1.36	1.4	1.43	1.47	1.51	1.55
14	1.32	1.34	1.37	1.4	1.44	1.47	1.51
15	1.25	1.28	1.31	1.34	1.37	1.4	1.43
16	1.21	1.23	1.26	1.28	1.31	1.34	1.37	1.4
17	1.15	1.18	1.2	1.23	1.25	1.28	1.31	1.34
18	1.12	1.13	1.16	1.18	1.2	1.23	1.26	1.28	1.31
19	1.07	1.09	1.11	1.13	1.15	1.18	1.2	1.23	1.25
20	1.04	1.05	1.08	1.09	1.11	1.13	1.16	1.18	1.2	1.23
21	1	1.02	1.03	1.05	1.07	1.09	1.11	1.13	1.16	1.18
22	0.97	0.98	1	1.02	1.04	1.05	1.07	1.09	1.11	1.13	1.16
23	0.93	0.95	0.97	0.98	1	1.02	1.03	1.05	1.07	1.09	1.11
24	0.91	0.92	0.94	0.95	0.97	0.98	1	1.02	1.04	1.05	1.07	1.09
25	0.88	0.9	0.91	0.92	0.94	0.95	0.97	0.98	1	1.02	1.03	1.05
26	0.86	0.87	0.88	0.9	0.91	0.92	0.94	0.95	0.97	0.98	1	1.02	1.04
27	0.83	0.84	0.85	0.87	0.88	0.9	0.91	0.92	0.94	0.95	0.97	0.98	1
```
Using the chart is actually easier than it looks.

If you're at pop 4 and want to continuously whip for pop 2, then the target ratio is ~2.43. A Grassland Hill Mine has a better ratio of 1:3 (3.00), so you shouldn't kill a Grassland Hill Miner. A Plains Hill Mine has a worse ratio of 2:4 (2.00), so killing a Plains Hill Miner is ok.

It works the same way all over the chart. These are the ratios of some other production tiles for comparison:

Grassland Hill Mine: 1:3 (3.00)
Plains Hill Mine: 2:4 (2.00)
Grassland Hill Forest: 1:2 (2.00)
Plains Forest: 1:2 (2.00)
Plains Hill Forest: 2:3 (1.50)
Plains: 1:1 (1.00)
Grassland: 0:1 (???)​

Grassland Forests are an odd beast, because they grant production without affecting growth. Since I can't divide by zero, there's no way to fit them into this equation. I just know in practice Grassland Forests are great to work when re-growing from a whip.

-- my 2

16. ### QuechuaUnique Unit

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I don't think Dave's advice applies to what I'm getting at. He's using the food to regrow pop estimate, which is an overestimate of slavery's efficiency (that's what I'm arguing anyway). I also question if he's thinking about the conversion of food by normal tiles in the right way.

17. ### OTAKUjbskiTK421

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It's me again.

Because of the "Whipping Cycle" of 10 turns, whipping by itself (working food tiles exclusively) can't compete with even an okay production city working Plains Forests.

Is that what you're getting at? Because, I'm not sure many people will argue whipping can stand alone against 'normal' production.

Whipping isn't "watered down" by also utilizing normal production. Normal production is boosted by also utilizing whipping.

An okay production center with excess food after working its production tiles (or one using a lot of Plains Hill Mines) can use whipping to "augment" its production to make use of the extra food for production.

I think in a good production city, whipping can be used to augment the city even when there is no gain in production!

Take this city for example:

City Center: +2F 1P
Clams: +2F 0P
Corn: +4F 0P
Plains Hill x3: -2F 4P (ea.)
Grass Hill x2: -1F 3P (ea.)
Grassland x3: 0F 0P (ea.)

At Population 5, we can work Corn, 2 PHills & 2 GHills for 0F 15P.
At Population 4, we can work Corn, Clams & 2 Grasslands for +8F 1P.
At Population 4, we can work Corn, 3 PHills for 0F 13P.​

Starting from Population 5 with a Granary on Normal Speed: whip 2 population (5 to 3 for +60 hammers), grow to within 1 turn of population 5, switch to 0F 13P until 1 turn before unhappiness wears off, grow to 5 on the same turn the unhappiness wears off then rinse, repeat:

Code:
```Cycle1 = relative to the whipping cycle turn (whip at 0, 10, 20, etc.)
POP1 = city population
+FPT1 = food per turn for growth
HAVE1 = amount of food on the bar
NEED1 = amount of food needed to grow
HPT1 = hammers per turn (growth & whipping focused)
PROD1 = total production accrued (growth & whipping focused)
HPT2 = hammers per turn (working production at pop5: 0F 15P)
PROD2 = total production accrued (working production at Pop5: 0F 15P)

Cycle1	POP1	+FPT1	HAVE1	NEED1	HPT1	PROD1		HPT2	PROD2
0	3	8	14	26	61	0		15	0
1	3	8	22	26	1	61		15	15
2	4	8	17	28	1	62		15	30
3	4	0	25	28	13	63		15	45
4	4	0	25	28	13	76		15	60
5	4	0	25	28	13	89		15	75
6	4	0	25	28	13	102		15	90
7	4	0	25	28	13	115		15	105
8	4	0	25	28	13	128		15	120
9	4	8	25	28	1	141		15	135
10	3	8	19	26	61	142		15	150
11	4	8	14	28	1	203		15	165
12	4	0	22	28	13	204		15	180
13	4	0	22	28	13	217		15	195
14	4	0	22	28	13	230		15	210
15	4	0	22	28	13	243		15	225
16	4	0	22	28	13	256		15	240
17	4	0	22	28	13	269		15	255
18	4	0	22	28	13	282		15	270
19	4	8	22	28	1	295		15	285
20	3	8	16	26	61	296		15	300
21	3	8	24	26	1	357		15	315
22	4	8	19	28	1	358		15	330
23	4	0	27	28	13	359		15	345
24	4	0	27	28	13	372		15	360
25	4	0	27	28	13	385		15	375
26	4	0	27	28	13	398		15	390
27	4	0	27	28	13	411		15	405
28	4	0	27	28	13	424		15	420
29	4	8	27	28	1	437		15	435
30	3	8	21	26	61	438		15	450
31	4	8	16	28	1	499		15	465
32	4	0	24	28	13	500		15	480
33	4	0	24	28	13	513		15	495
34	4	0	24	28	13	526		15	510
35	4	0	24	28	13	539		15	525
36	4	0	24	28	13	552		15	540
37	4	0	24	28	13	565		15	555
38	4	0	24	28	13	578		15	570
39	4	8	24	28	1	591		15	585
40	3	8	18	26	61	592		15	600
41	4	8	13	28	1	653		15	615
42	4	0	21	28	13	654		15	630
43	4	0	21	28	13	667		15	645
44	4	0	21	28	13	680		15	660
45	4	0	21	28	13	693		15	675
46	4	0	21	28	13	706		15	690
47	4	0	21	28	13	719		15	705
48	4	0	21	28	13	732		15	720
49	4	8	21	28	1	745		15	735
50	5	6	15	30	13	746		15	750```
Compare the total amount of hammers at each Cycle turn 0 ... at the end of 5 cycles, the difference is only -4 hammers when whipping is used to augment this city (averages -8 hammers since it fluctuates depending on how many whipping cycles you observe).

So what do you get in exchange for those 4 hammers? 28 total turns worth of Grassland [Cottage] working: 36 commerce (avg +0.72 per turn) -- 64 if riverside (avg +1.28 per turn) -- 92 if riverside/financial (avg +1.84 per turn)).

Given there are 2 Grassland Hills in this city (the most efficient early non-resource production tiles), any larger happiness cap results in a substantial difference and is hurt by whipping.

EDIT: If you focus on always working the Grassland Hills (Corn, 2 GHills, 1 PHill for +2F 11H) and only stagnating right before hitting population 5 then whipping every 10 turns, you're able to augment production and slightly increase the total hammers generated:

EDIT2: It's probably not much, but smaller populations cost less in maintenance, so in both cases, you probably also gain a couple gold over the long term by whipping. (BTW, trade routes don't get population boosts until pop 10, IIRC, so there's no commerce lost in that respect from whipping.)

Code:
```Cycle1	POP1	+FPT1	HAVE1	NEED1	HPT1	PROD1		HPT2	PROD2
0	3	8	14	26	61	0		15	0
1	3	8	22	26	1	61		15	15
2	4	2	17	28	11	62		15	30
3	4	2	19	28	11	73		15	45
4	4	2	21	28	11	84		15	60
5	4	2	23	28	11	95		15	75
6	4	2	25	28	11	106		15	90
7	4	0	27	28	13	117		15	105
8	4	0	27	28	13	130		15	120
9	4	8	27	28	1	143		15	135
10	3	8	21	26	61	144		15	150
11	4	2	16	28	11	205		15	165
12	4	2	18	28	11	216		15	180
13	4	2	20	28	11	227		15	195
14	4	2	22	28	11	238		15	210
15	4	2	24	28	11	249		15	225
16	4	0	26	28	13	260		15	240
17	4	0	26	28	13	273		15	255
18	4	0	26	28	13	286		15	270
19	4	8	26	28	1	299		15	285
20	3	8	20	26	61	300		15	300
21	4	2	15	28	11	361		15	315
22	4	2	17	28	11	372		15	330
23	4	2	19	28	11	383		15	345
24	4	2	21	28	11	394		15	360
25	4	2	23	28	11	405		15	375
26	4	2	25	28	11	416		15	390
27	4	0	27	28	13	427		15	405
28	4	0	27	28	13	440		15	420
29	4	8	27	28	1	453		15	435
30	3	8	21	26	61	454		15	450
31	4	2	16	28	11	515		15	465
32	4	2	18	28	11	526		15	480
33	4	2	20	28	11	537		15	495
34	4	2	22	28	11	548		15	510
35	4	2	24	28	11	559		15	525
36	4	0	26	28	13	570		15	540
37	4	0	26	28	13	583		15	555
38	4	0	26	28	13	596		15	570
39	4	8	26	28	1	609		15	585
40	3	8	20	26	61	610		15	600
41	4	2	15	28	11	671		15	615
42	4	2	17	28	11	682		15	630
43	4	2	19	28	11	693		15	645
44	4	2	21	28	11	704		15	660
45	4	2	23	28	11	715		15	675
46	4	2	25	28	11	726		15	690
47	4	0	27	28	13	737		15	705
48	4	0	27	28	13	750		15	720
49	4	2	27	28	11	763		15	735
50	5		15	30		774		15	750```
(I hope that makes any sense.)

-- my 2

18. ### QuechuaUnique Unit

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Messages:
356
Uh-oh more long posts I have to carefully search through, and then still probably overlook something.

I've already provided an example in my first post of whipping beating a forest production city. I was surprised it didn't beat it by more. Since then, a couple people pointed out there was no need to ever grow to 5 in the cycle, and I was able to squeeze out a few more hammers.

Your example of getting the same production out of whipping while also working cottages is interesting, and I don't see any problems with it. But I am trying to find a way to maximize the production from a food surplus.

Think a city continually 2-pop whipping axemen for a rush. My point is the surplus isn't worth the naive estimate. Using the surplus to change grassland forests or farms to plains/hill forests converts the surplus to hammers in a 1:1 ratio and does indeed dilute the theoretical ~1:2 ratio. But if you don't slow your growth you run into happiness problems which also eat into your efficiency. You get further loss by losing some productive population during the cycle.

So my question for anyone is, what is the best way to optimize your production from the food surplus? Can you beat 14 per turn?

19. ### MrFelonyPrince

Joined:
Jun 11, 2006
Messages:
553
Location:
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what do you guys think about whipping an army early on? i remember one game i constantly had 2 or 3 angry citizens in some of my cities in order to whip an army of horses to take over native america? is it more important to get that army ASAP or would it be better to take the extra time to get the same army?

edit: btw i had cities that had both pigs and many hills to work. so if you had a high amount of food AND grass hills to work at max pop, which would you use? sounds like i should have just manually built out the HA's from the thread and whipped a lot less of them. I think (if i remember correctly), I would whip 1 for 3, build 1-2 two, then whip another for either 2 or 3 (i used it less liberally in my capital)

20. ### OTAKUjbskiTK421

Joined:
Mar 4, 2007
Messages:
1,511
Location:
not at my post
I think if you're rushing before building a Worker and improving tiles (i.e. Quecha or Dog Soldier rush), then whipping is crucial.

Grassland Hill Mines are awesome and should always be worked when available, imo.

I'm still trying to wrap my head around the most efficient and effective use of the whip, but it seems to me whipping should be considered icing -- not the cake.