Rules of thumb for booming

[causative]

Not specific build orders, but some general rules of thumb I've been puzzling out.

• You need 3.5 farms (food income of 500 per minute) to support 5-batch women production from the CC
• You need 2 farms (food income of 300 per minute) to support constant production of men from a barracks in batches of 1. If you have four barracks and the CC all producing men in 1-batches, that means ten farms.
• 1-batching from a barracks in theory is the most efficient batch size for a big boom to 200 pop. In practice sometimes larger batches will be necessary to use up excess food.  But batches should be kept as close to 1 as possible.
• With no barracks you need 1 house builder if you can keep him going all the time. 1 barracks, 2 house builders. 2 barracks, 3 house builders. 3 barracks, 5 house builders. 4 barracks, 6 house builders. In theory - walk time may mean you need one more than this. Or if not all your house builders work on the same house at once you can use fewer.
• Roughly the process is: first spend any excess wood on farms to support your current barracks number plus 1, keeping wood as close to 0 as possible. Then wait until you have enough wood for another barracks without interrupting production, and make it. Repeat. (Process is more complicated if your barracks also costs stone.)
• If you have extra food from berries or hunting or Ptolemy teambonus, the same applies that you want 300 food income for every barracks (or CC producing men) plus 500 food income if you're batch producing women. There's little purpose in gathering more food than that, and the rest should go on wood and make barracks whenever there is excess wood. Food income from such sources can be measured with my show resource income mod.

The "1-batching is the most efficient batch size" may be the most controversial part of this. Here's my reasoning. What you want is to get the maximum production rate for the minimum upfront investment. If you have a large batch size, the batch should be counted as part of the upfront investment. So the efficiency is (production rate of men) / (300 + size of batch * 100). It turns out this is minimized for 1-batches.

Edited May 10, 2023 by causative

[Stockfish]

Thanks for you job @causative.

To be honest I disagree on you in some parts of your text, not in others. But I am curious in how did you develop that ''eficiency formula''.

Could you explain to me please?

Greetings

[Yekaterina]

@causative You may find this interesting 

 

 

[causative]

3 hours ago, Stockfish said:

Thanks for you job @causative.

To be honest I disagree on you in some parts of your text, not in others. But I am curious in how did you develop that ''eficiency formula''.

Could you explain to me please?

Greetings

You want to maximize your rate of production for a given upfront cost. The upfront cost is the cost that you have to pay in order to build the barracks, plus the cost that you  have to pay in order to "get production started," which is the total cost of the batch. Both of these can be considered fixed, sunk costs. Even though the batch cost is from one perspective recurring, it should be treated as a fixed cost plus a continuous per-second recurring cost.

For example, if you want to 10-batch, then you need 300 wood for the barracks if it's Mauryas (plus, actually, about 100 more opportunity cost for the time building the barracks, depending on number of builders and walk time), and you also need 500 wood and 500 food to get your 10 batch started. As long as you keep producing 10-batches, that 500 wood and 500 food is always tied up in the barracks. You also need to continuously harvest a recurring cost of 938 total resources per minute so that you will have enough when it's time for the next batch of 10, but this recurring cost is in addition to the upfront batch cost.

The production rate per minute for an N-batch is 60 * N / (10 * ceil(N**0.8)). The batch cost is 100 * N. The barracks cost (including build time) is maybe 400 equivalent. So the efficiency is 60 * N / (10 * ceil(N**0.8)) / (400 + N * 100). This reaches a maximum for N=1.

N       startup cost efficiency
1       0.012
2       0.011
3       0.010
4       0.0097
5       0.0090

For non-Mauryas the barracks cost will be different - lower, if you don't count the stone cost for the first three barracks, which only favors a batch size of 1 even more.

Edited May 10, 2023 by causative