Hi.

I have been working on a formula to determine the number of armies each bonus should have, and I wanted to know your opinion on it and if you know a more precise formula than the one I made.

Mine is:
(√t² + c² + b²) / 2,2

•t = Number of territories on the bonus (territories)
•c = Number of territories outside the bonus that connect to at least one territory of the bonus (connections)
•b = Number of territories inside the bonus that connect to at least one territory outside the bonus (border)

When you get to the result you just have to round the number to the closest integer.

Seems to work quite well for me. I'd appreciate any feedback, comments or suggestions.

Edited 8/28/2017 00:54:56

Do you take the root of the entire formula, or just the t,c and b (i.e., do you root before or after dividing by 2,2?). The way it's written makes that unclear.

Either way, as all formulas, I feel there are some subtleties it doesn't take into account.

First, this one seems to value connectivity over size. That's a decision I think works best for small, crowded maps. A bonus with, say, 8 territories and just 1 connection will have a relatively low value, while a bonus with 1 territory and 8 connections will have a pretty big value.
While this works for small maps, where every bonus can make the difference, it's a bit weird on big maps: the single territory with lots of connections will be a massively powerful starting spot.

Second, the formula doesn't take interconnectivity in the bonus into account, which does say a lot about how easy it is to conquer/defend a bonus. A bonus that is a long string of ten territories, where each territory only connects to two others (say, a passage through mountains or a bridge) is both more valuable for map control, but harder to take in the expansion phase of a game. How do you think that is reflected in the formula?

Third, and this is a tricky one for all formulas, is that it only takes direct connections into account. Bonuses near the corners of the map, or on islands (even if they share that island with other bonuses) are often seen as more powerful or strategic than bonuses in the middle of the map - simply because it's a safer position. Imagine a bonus on the middle of an island, surrounded by ten territories on that same island. Its value would be the same as a similar bonus surrounded by ten territories in the middle of the map - yet it is a better spot (and as such should probably be worth less).

All three probably boil down to the larger picture of the map. Is it a big map or not? Does it have a lot of weirdly shaped forms? Does it have closed off corners?
But also the type of game that will be played. With easy expansion (neutrals of 0), the defensive position of a bonus is much less important than its expansion possibilities (the mentioned string of territories would be a liability rather than a good bottleneck).

Of course a single formula would never be able to catch all nuances of a huge map, so, uhm, maybe everything I just wrote is nitpicking. Feel free to disregard it, of course. These were just the main problems I could see.

Edited 8/27/2017 09:14:49

I'm not sure why you add 'c' instead of subtracting it? Connections are an advantage, so if you want to balance things out, having many of them should lower the bonus value.

I'm not sure why you add 'c' instead of subtracting it? Connections are an advantage, so if you want to balance things out, having many of them should lower the bonus value.

Connections are an advantage when expanding, but they are a disadvantage when defending: a bonus with lots of connections is much more vulnerable.
So there is something to say for both: they can be worth less because they are easier to take, but they can also be worth more because they're harder to keep.
I feel it depends on the rest of the map. If it's a big map where most bonuses won't be on the front lines, more connections should lower bonus value. If it's a small map where most bonuses are under direct threat, more connections should increase bonus value.

You could just check your formula on a map like MME, which is pretty balanced.
If your formula is 1 army away from at least 5 bonuses, then - imo - your formula is bad.

I would be interested in the result.

Yes Murk, and the way I see it, the 'harder to keep' part is covered by b (number of borders). Lots of borders should make the bonus more valuable, so you add b. Lots of connections make it easier to threaten the rest of the map, so to balance it you substract c.

As you said yourself, 'a bonus with 1 territory and 8 connections will have a pretty big value. ' which is super imbalanced.

Ah, fair enough. I think that might be interesting to try out, yes. Especially since, in most cases, b and c will mostly cancel each other out.
The /2,2 would have to be lowered, but otherwise it would be fine, I think.

it's a good idea if you like to overcomplicate things.. I guess it is much easier or balanced in the end when you you use a simple formula and estimate deviations due to your gut feeling. However you probably forgot some brackets within your formula

"Connections are an advantage when expanding, but they are a disadvantage when defending: a bonus with lots of connections is much more vulnerable."

It's not a lot more vulnerable.

In a 1v1 you can attack it from multiple directions, sure, but the benefit of doing so is minimal.

In a team game or FFA, sure, you can be attacked by more players on a single turn, but you can also be supported by more players.

If a territory borders 5 other territories, they are very vulnerable to it, but it isn't very vulnerable to them.

Edited 8/27/2017 13:55:40

I think we mean the same thing. I can't post images, sadly.
Imagine two bonuses, both of five territories. Bonus A has all five territories on a horizontal row. Bonus B has all five territories on a vertical row and its lowest territory borders all five territories of bonus A.
Bonus B obviously has a better defensive position - the player only needs to stack armies in one territory, while the other player needs to defend all five territories.
On the other hand, bonus A can be taken in one turn, while taking bonus B takes five turns, so bonus A is better at the start.

You could just check your formula on a map like MME, which is pretty balanced.
...
I would be interested in the result.

Same.