Hi Zombie69,
Thanks for the replies; I appreciate the attention. But I hope you'll bear with me a little longer, because I think I'm still not seeing the whip as the super deal you have described it as, at least not without a good amount of micromanaging.
I've set up a little experiment on paper. (Away from the game at the moment.) nF means n food. nH means n hammers. Size 6(30) means size 6 with 30 food in the food bar. +nF or -nF means the extra/deficit food, so a farmed grassland is 3F because it produces 3 food, but +1F because it takes 2 food to feed the citizen who's working that tile. Here's the setup:
Look at one city and concentrate only on food an production (we're trying to maximize production. Your only building is a granary. Playing at normal speed. Your happiness limit is 7. Your health limit is at least that, say 10.
You have just grown your city from size 6 to size 7, so all your people are happy and working. More people would be unhappy. It took (20 + 6x2 =) 32 food to grow so you have 16 food in the bank from the granary: size 7(16).
The tiles surrounding your city are 1 grassland pigs with a pasture (6F), and as many mined grassland hills (1F3H) and irrigated pre-biology farms (3F) as you want. Your city is located on a normal square and is 2F1H.
To maximize production and not grow, you would set your 7 citizens to work the pigs and 6 grassland hill mines. Per turn, and including the city center, that's:
Center(+2F1H), Pigs (+4F), 6 GHMines (6 x -1F3H): Total 0F 19H
If you work that setup for 10 turns, you get no growth and 190 hammers.
Below, I've separated the Turn numbers (what you see when you look at your cities during your turn), from the calculation (where the game runs the update and the AI's turns.
In the whip case you have:
Turn 0: (whip) 7(16) --> 6(16) + Whip Hammers
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 1: 6(17)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 2: 6(18)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 3: 6(19)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 4: 6(20)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 5: 6(21)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 6: 6(22)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 7: 6(23)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 8: 6(24)
. . City(+2F1H), pig(+4F), 5 grass hill mines (5x-1F+3H): +1F +16H
Turn 9: 6(25)
. . Work City(+2F1H), pig(+4F), 3 farms(3x+1F), 2 GH mines(2x-1F3H): +7F +7H
Turn 10 6(32) --> 7(16) pop growth
. . This is back to where we started, so we can whip again (or not!)
After ten turns...
Non-whip total: 0F +190H
Whip total: 0F +(16x9 + 1x7 + Whip = 151+Whip)H
So, you get 190 hammers over 10 turns from not whipping and 151+whip hammers from whipping and working as many production tiles as you can. You need to get 39 un-bonused hammers per whip to get the same total number of hammers as the no-whip case.
This implies that it hurts not to be working improved tiles. And unhappy citizens, such as those incurred by cracking the whip, can't work improved tiles.
There are many things neglected in this analysis:
1) Exactly what tiles you have--and whether or not you've improved them--makes a difference.
2) When you get those hammers can make a (big?) difference. (Aaahh...sneak attack!)
3) What your population size is and what your happy/health limits are make a difference.
4) Whether or not there is a production bonus makes a difference, and when you have a production bonus, you're also looking at the possibility of roundoff losses.
But unless I made some error--definitely possible!--I think you have to be exploiting an error in the pop-to-hammers calculation to get more total hammers over the total turns. I think the absolute best you can do is 48H/pop. Here, that would be a total of 211 compared to 190 hammers over 10 turns, or about 2H per turn (and you get many of them up front). But you have to get more than 39 hammers per whip to get a better-than-not-whip total number of hammers. [Edit: I had originall used 60H/pop, but Zombie69 points out that it is 48H+25% bonus. So to be fair you compare to 48 base hammers. This particular example doesn't use a production bonus, but the issue is discussed below.]
I realize that you need to have a production bonus of some kind to exploit the pop->hammers bug, but here I think I'm showing that without a production bonus, whipping will actually net you fewer hammers than you'd otherwise get. (Though again, you do get them sooner!)
For the example above, if you added a forge for a 25% production bonus, you'd lose 0.75H per turn in the no-whip case because of roundoff, but this is just an example. In real-life, you would have different tiles and might be able to micromanage to get most of that back, so maybe 6 or 7 extra hammers over 10 turns for the no-whip case. That's about the bonus (7) that you'd be getting from the population point too if it were calculated correctly.
It seems to me that unless there's an error in my analysis (and somebody please check it to find out!) that it is possible to use the whip to get more hammers than you otherwise would, but:
1) you need lots of micromanagement,
2) you need to exploit the pop-to-hammers calculation error
3) the max benefit is around 2H/turn which is less appealing the bigger your city is.
If that analysis is correct, then the take-home lesson is, Whip when:
1) you need/want it finished right now
2) the last tile your city is working is unimproved
3) you really like optimizing and are willing to extremely micromanage and take advantage of the bug for a max 2H/turn/city increase in hammers.
If I made an error, let me know by post or PM, and I'll correct the analysis so that readers don't have to flip between posts to find out the truth.