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Okay then, a very simple test of the utility of whipping is for rushing settlers. It's a very simple comparison, because settlers use food, and growing uses food. So basically the question becomes:
Q) Starting at a given population level, say 3 or 4, is it better to hold at that population and train the settler, or to grow and then whip the settler out, returning to the original population?
Just to give some quick info: each population level costs 20 + 2*pop food, at size 1 it's 22 food, at size 10 it's 42 food. Granary halves that number.
All examples are considered to be using a granary, as they are essential for whipping.
So lets try a few different examples:
CASE STUDY 1: Grassland with pigs:
Food surplus = 6.
There are abundant grassland forests.
Cracking the whip:
Size 3 to 4 = 2 turns
Size 4 to 5 = 2 turns
Size 5 to 6 = 3 turns
Total turns = 7
On turn 8, the city is size 6 and a turn of production is devoted to the settler, bringing it to a level where it can be whipped with the loss of 3 population.
On turn 9, the whip cracks.
On turn 10, the settler pops out.
In this time, 30 extra hammers are produced, assuming working all grassland forest and the pasture pig. Some hammers might be commerce instead if working cottages or whatever.
Over the 9 turns, 130 hammers were generated. That's 14.4 hammers/turn.
The Old Fashioned Way:
The city produces 3 hammers and 6 food per turn, a total of 9 stuff that builds settler. In 11 turns, it will produce 99 food. We will generously assume it starts with 1 carryover and will thus complete the 100 hammer settler in 11 turns.
On turn 12, the settler pops out. During this time the entire production of the city was devoted to the settler.
Train or Whip?
Whipping requires 2 less turns, and generates 30 more hammers. We may not need that rocket scientist to figure out which is the superior option.
CASE STUDY 2: The city on the floodplains:
The city has an unlimited quantity of floodplains to work. This time we'll grow to size 8 and lash 4 population to death, exploiting the carryover to convert food to hammers. Thus the comparison starts at size 4.
However, the city will have a happy cap of only 6.
I love the sound of sobbing in the morning:
Size 4 to 5 = 2 turns
Size 5 to 6 = 3 turns
Size 6 to 7 = 2 turns
Size 7 to 8 = 3 turns (1 unhappy citizen)
Total turns = 10
On turn 11 the city is size 8 and tweaked to add not more than 9 food/hammers to the settler, such that it still requires 4 population to rush. Due to a bizarre quirk, angry people don't eat while training a settler/worker - the 2 unhappy people don't matter for this turn. So 9 is added (6 food from floodplains, 2 food + 1 hammer from city)
On turn 12, the city feels the sting of the whip.
On turn 13, the settler pops out. There is 35+ hammers overflow which instantly completes anything up to an axeman.
The city has generated 12 additional commerce and 10 additional hammers.
Total hammer value = ~142 in 12 turns, or 12 hammers/turn.
I'm a wussy humanitarian:
At size 4, the city works 4 floodplains and has the 2 food from the city tile; this gives it 6 food to work with, plus 1 hammer from the city tile. At 7 stuff/turn (and some carryover from previous build) it will take 14 turns to generate the settler, which will pop out on turn 15. During this time it will generate nothing extra, except ~4 hammers carryover.
Wait! I think there's a third option:
Imagine you found time to improve 2 mines to work.
The city now generates 9 stuff/turn, it will take 11 turns to generate the settler, with him popping out on the 12th turn.
Train or Whip?:
Whipping gets the settler out 2 turns faster, with 40 extra hammers generated and 12 free commerce.
Alternatively, if you make a couple mines you could generate the settler a turn quicker than whipping. But can you generate 30 hammers and 9 commerce in that one extra turn? I don't think so. Additionally you could create cottages on the floodplains instead of wasting time with mines, which gives a massive amount of extra commerce while growing-2-whip.
To summarize and ramble on:
If you can get somewhere around a +6 food surplus, it'll nearly always be quicker to grow and whip, rather than to build normally, especially with limited terrain improvement. When you're on floodplains, growing actually almost accelerates growth, since each population level costs 1 extra food to grow, but you get 1 extra food form working another floodplain. So you can continue to grow every 2 or 3 turns.
Growing above the happy cap isn't lethal, each pop above happy is -2 food and above health is -1 food. It is okay to exceed the happy/health caps as long as you still have a +5 or higher food surplus (+4 is borderline), once the surplus gets low, then is the time to whip. A city with 2 food specials can easily go 2-3 population above happy cap.
Generally to make maximum use of the whip you want to whip as much population as possible every 10 or 11 turns. Stacking anger is less than ideal and should only be done in emergency.
To avoid whipping anger building up, you can grow even larger and whip out extra population, so that whips come not more frequently than every 10 turns. To make full use of this you need to remember that each pop is turned into 30 hammers, and to make sure you don't add too many hammers to the build. A settler costs 100 hammers, so as long as you whip at above 91 hammers (remaining) you'll kill off 4 population and get up to 29 carryover in pure hammers - it's a 2-for-1 whip deal.
There aren't many other things the carryover/overwhip trick works well with, for a start any "accelerated" building (ie temples for spiritual) do not work - the carryover gets doubly nerfed down; NEVER over-whip such builds. Axemen, Spearmen and Jaguars cost 35 hammers, they are a good 2-for-1 deal. Swordsmen, catapults, missionaries and explorers cost 40 and are okay, although the 20 carryover isn't even enough for a whole archer. Macemen cost 70, but by then stuff costs so much that the maximum of 29 overwhip isn't much.
A rule of thumb:
Basically all population working marginal tiles like forest, coast or unimproved floodplain should be periodically killed off. Generally speaking, killing population working resources or floodplain cottages is a bad idea. Try not to whip more often than every 10 turns. Maximize food is your friend, always have maximize food on when running slavery and just whip away excess population.
Remember:
When you're about to train a settler, ask yourself: If I let this city grow 3 population larger, then whip it, will I get the settler out in fewer turns? If it has a decent food surplus, a granary, and isn't already at the happy cap, the answer will usually be "whip!". And in the meantime you'll get a lot of extra hammers towards another build.
Now get crackin'
Q) Starting at a given population level, say 3 or 4, is it better to hold at that population and train the settler, or to grow and then whip the settler out, returning to the original population?
Just to give some quick info: each population level costs 20 + 2*pop food, at size 1 it's 22 food, at size 10 it's 42 food. Granary halves that number.
All examples are considered to be using a granary, as they are essential for whipping.
So lets try a few different examples:
CASE STUDY 1: Grassland with pigs:
Food surplus = 6.
There are abundant grassland forests.
Cracking the whip:
Size 3 to 4 = 2 turns
Size 4 to 5 = 2 turns
Size 5 to 6 = 3 turns
Total turns = 7
On turn 8, the city is size 6 and a turn of production is devoted to the settler, bringing it to a level where it can be whipped with the loss of 3 population.
On turn 9, the whip cracks.
On turn 10, the settler pops out.
In this time, 30 extra hammers are produced, assuming working all grassland forest and the pasture pig. Some hammers might be commerce instead if working cottages or whatever.
Over the 9 turns, 130 hammers were generated. That's 14.4 hammers/turn.
The Old Fashioned Way:
The city produces 3 hammers and 6 food per turn, a total of 9 stuff that builds settler. In 11 turns, it will produce 99 food. We will generously assume it starts with 1 carryover and will thus complete the 100 hammer settler in 11 turns.
On turn 12, the settler pops out. During this time the entire production of the city was devoted to the settler.
Train or Whip?
Whipping requires 2 less turns, and generates 30 more hammers. We may not need that rocket scientist to figure out which is the superior option.
CASE STUDY 2: The city on the floodplains:
The city has an unlimited quantity of floodplains to work. This time we'll grow to size 8 and lash 4 population to death, exploiting the carryover to convert food to hammers. Thus the comparison starts at size 4.
However, the city will have a happy cap of only 6.
I love the sound of sobbing in the morning:
Size 4 to 5 = 2 turns
Size 5 to 6 = 3 turns
Size 6 to 7 = 2 turns
Size 7 to 8 = 3 turns (1 unhappy citizen)
Total turns = 10
On turn 11 the city is size 8 and tweaked to add not more than 9 food/hammers to the settler, such that it still requires 4 population to rush. Due to a bizarre quirk, angry people don't eat while training a settler/worker - the 2 unhappy people don't matter for this turn. So 9 is added (6 food from floodplains, 2 food + 1 hammer from city)
On turn 12, the city feels the sting of the whip.
On turn 13, the settler pops out. There is 35+ hammers overflow which instantly completes anything up to an axeman.
The city has generated 12 additional commerce and 10 additional hammers.
Total hammer value = ~142 in 12 turns, or 12 hammers/turn.
I'm a wussy humanitarian:
At size 4, the city works 4 floodplains and has the 2 food from the city tile; this gives it 6 food to work with, plus 1 hammer from the city tile. At 7 stuff/turn (and some carryover from previous build) it will take 14 turns to generate the settler, which will pop out on turn 15. During this time it will generate nothing extra, except ~4 hammers carryover.
Wait! I think there's a third option:
Imagine you found time to improve 2 mines to work.
The city now generates 9 stuff/turn, it will take 11 turns to generate the settler, with him popping out on the 12th turn.
Train or Whip?:
Whipping gets the settler out 2 turns faster, with 40 extra hammers generated and 12 free commerce.
Alternatively, if you make a couple mines you could generate the settler a turn quicker than whipping. But can you generate 30 hammers and 9 commerce in that one extra turn? I don't think so. Additionally you could create cottages on the floodplains instead of wasting time with mines, which gives a massive amount of extra commerce while growing-2-whip.
To summarize and ramble on:
If you can get somewhere around a +6 food surplus, it'll nearly always be quicker to grow and whip, rather than to build normally, especially with limited terrain improvement. When you're on floodplains, growing actually almost accelerates growth, since each population level costs 1 extra food to grow, but you get 1 extra food form working another floodplain. So you can continue to grow every 2 or 3 turns.
Growing above the happy cap isn't lethal, each pop above happy is -2 food and above health is -1 food. It is okay to exceed the happy/health caps as long as you still have a +5 or higher food surplus (+4 is borderline), once the surplus gets low, then is the time to whip. A city with 2 food specials can easily go 2-3 population above happy cap.
Generally to make maximum use of the whip you want to whip as much population as possible every 10 or 11 turns. Stacking anger is less than ideal and should only be done in emergency.
To avoid whipping anger building up, you can grow even larger and whip out extra population, so that whips come not more frequently than every 10 turns. To make full use of this you need to remember that each pop is turned into 30 hammers, and to make sure you don't add too many hammers to the build. A settler costs 100 hammers, so as long as you whip at above 91 hammers (remaining) you'll kill off 4 population and get up to 29 carryover in pure hammers - it's a 2-for-1 whip deal.
There aren't many other things the carryover/overwhip trick works well with, for a start any "accelerated" building (ie temples for spiritual) do not work - the carryover gets doubly nerfed down; NEVER over-whip such builds. Axemen, Spearmen and Jaguars cost 35 hammers, they are a good 2-for-1 deal. Swordsmen, catapults, missionaries and explorers cost 40 and are okay, although the 20 carryover isn't even enough for a whole archer. Macemen cost 70, but by then stuff costs so much that the maximum of 29 overwhip isn't much.
A rule of thumb:
Basically all population working marginal tiles like forest, coast or unimproved floodplain should be periodically killed off. Generally speaking, killing population working resources or floodplain cottages is a bad idea. Try not to whip more often than every 10 turns. Maximize food is your friend, always have maximize food on when running slavery and just whip away excess population.
Remember:
When you're about to train a settler, ask yourself: If I let this city grow 3 population larger, then whip it, will I get the settler out in fewer turns? If it has a decent food surplus, a granary, and isn't already at the happy cap, the answer will usually be "whip!". And in the meantime you'll get a lot of extra hammers towards another build.
Now get crackin'
, usually you'll work forests (if you have cottages you should be working them full time rather than whipping, most of the time). But for a fishing village it'll be commerce. Actually a fishing village is an ideal place to grow to 8 then whip 4, you get a "free" archer. This allows a city working pure food to create both the settler and garrison - a very nice little trick.
. I do think that's the more important question.
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