So I noticed that there seems to be a lot of debate on what to value bonuses that are four territories large. Some strategic maps make them worth 3 armies, and some maps make them worth 2. There are even people who like to value them as 1. What's your opinion on this?

I might start. Since these four-territory bonuses are likely to be able to be conquered first turn, I tend to value them as 2 as I do not want to map to be capture-this-bonus you-win type of map.

All depends on the context really. If it’s a standard looking map with a bunch of groupings of 2, 3, and 4 territories then I’d value a 4 territory bonus as 3. Sure someone could get it first turn, but there’s enough other groupings for someone else to also do the same.

Four factors in the "strength" of a bonus"
position on the map
how quickly it can be captured, as an average considering all entry points
territory/bonus value ratio
defensibility (how many territories border other bonuses?)

While is it desirable to maintain a formula for all bonuses (usually t-1 or t-2), you can break the formula for the sake of balance, considering factors 1, 2, and 4.

If you are doing a t-2 scheme, I would suggest avoiding 3-territory and lower bonuses, because a 3 for 1 is worthless. The best range for t-2 scheme is from four to eight territories; for a t-1 scheme it's from three to seven territories.

Edited 1/22/2021 00:39:08

I like to value it based on how easy the bonus is to capture/defend. I'll value riskier 4 bonuses in the middle of the map as 3 income, and less exposed bonuses around the edges of the map as 2.

Interesting discussion. I agree with Orannis.

Middle of the map is stronger than edge by definition, therefore it should rather be the other way around.
That being said, I think it's not possible to generalize this argument since templates and maps are very different. On some option A is better and on some optiion B