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2*HP + power was something I used before (when playing on a board game, when you have to do all the math on your own!)
Even then, you really need to factor what units die, if one side is losing more power than the other (a, its a big deal. Occasionally on World War 2 Revised, Germany attacking Russia looks like an even fight, but its heavily German favored (Germany loses low value 1 attack units, while Russia is losing 2 defense units).If you want another interesting case, look at TWW. Its not uncommon for a heavily fortified Russian city to have fewer hitpoints and lower defense than an attacking German army, but still win the battle 90 to 100% of the time., due to a combination of targeted attacks and 'Skewness'. Even without targeted attacks, less complex abilities such as units supporting each other or having two hitpoints make a big difference.
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So to add to this, even if you came up with some function that could handle strength and HP to say 99% of the time. Most of the newer maps actually have things like targeted rolls, multi-HP units, positive/negative support, suicide units, etc. These make things much more complex to the point that its very difficult to even find the optimal casualties to select each round let alone have some function of the armies strength that predicts the winner. They also make it so A > B > C > A will always exist because I can have an AT gun army, a tank army, and an infantry army which form counters to each other with targeted attacks (AA like rolls).
Given all that, this is why the battle calc is very important and that we generally just use a strength estimate of 2*HP+power to give a very high level estimate of army strength as that is a fairly good yet simple formula.
The biggest issue with the A&A combat system tends to be that 1 or 2 additional units changes a battle from 50/50 to 95% win chance (especially true for LL). The ways to address this drawback is:
Have more of a ranged suicide unit type map where armies are mostly firing units at each other rather than entire stack vs stack Have limited combat rounds so that you can only inflict so many casualties per turn to avoid the first round of battle deciding the fate of the entire stack of units. This allows more tactics around retreating, counterattacking, reinforcing, etc. -
I'm still trying to figure out whether he's opened up a can of worms or not yet (I'm guessing no because CrazyG said this doesn't involve the game engine)
this thread is typically why I still read this forum though ... math, ai , strategy etc. etc! so interesting!
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@prastle Not sure about the downvotes. I can see them No Problem. (On a phone btw)
About the topic: Not an expert on maths, but I don't think there's a way to calculate some sort of strength of an army without knowing the opponents, there are just too many factors involved.
Because of this the hard AI at least simply uses the BattleCalculator to determine whether or not it's a good idea to attack a certain territory.
Also the reason the AI is relatively CPU-Heavy.
