Roland Johansen
Deity
It will have a bigger power advantage if power is calculated as strength^2. This larger power advantage is more accurate. This makes a difference when a warmonger is trying to decide whether to attack a small civilisation with good tech, or a large civilisation with bad tech. As a player, I will often choose the large civilisation, as I know that I can stomp over it, gaining experience, while taking few casualties. The power graph and AI decisions should reflect that reality.
This has far more to do with the human players abilities versus the AI. As a player, I can even get 5 to 1 ratio's against an AI with equal technology units. What does that mean? Are the AI units of a certain strength worth only 1/5th of the power of my units? We can't go that road because not all human players are equal and some even have problems with basically capturing cities.
Basically, you can't base a power to strength formula on your ingame experience fighting the AI's units of equal and lower technology because you're a far more capable tactician than the AI. The power to strength ratio should however work for every player versus AI and for AI versus AI conflicts.
The ideal exponent is presumably somewhere between 1.3 and 4, as I think we both agree. However, I think 1.5 is too low. I might go for something like 1.8, based on strength alone. When we add factors such as experience, war weariness, and upkeep, I still think strength^2 is fair.
There was a reason that I asked you to calculate the power ratio between strength 3 attackers and strength 3 defenders in your example. In your example, the strength 3 attackers only lose half the units of the strength 3 defenders which should lead to a different power valuation which is of course ridiculous. The reason that this illogical result occurs is because in your calculations, you completely ignored damage to units which weakens them. If 11 strength 3 units attackers attack 10 strength 2 units defenders and average results occur, then the result will be close to 10 wounded strength 3 units and 0 defenders. However that wounded aspect is very important. A counterattack against those wounded units will be far more effective. A strength 3 unit at 50% hitpoints is easily beaten by a strength 2 unit because of the large effect of hitpoints on the combat formula. The value of the exponent of 4 is therefore not reasonable, even in this matchup.
I do agree that 1.3 it a bit low, but not that 1.5 is a bit low.
Using goal seeking on making the average of 100% to 5% in 5% increments as close in ratio to a power curve, I get 1.32. Dividing the naive curve of ^2 by 1.32 gives us a 1.52 power curve once we take into account the fact that damaged units are weaker than the naive approximation assumed.
This last part wasn't clear to me.
Another thing to take into account is the power flux of each side. You could calculate this based on, say, X years of imperial production producing the highest power efficiency unit, where X varies based on game speed. This misses, however, being close to a new technology that will allow massive upgrades...
I suggested a similar approach to approximating the 'power' of producing units during the war.
It's a bit hard to estimate the power of upgrading due to a new technology. You could calculate the power of the army when it would be fully upgraded with the new technology and multiply that value by 1.5^-t where t is the number of turns until the technology is available (as long as t<=10). Then you take a weighted average of the current power and the future power (weights 1 and 1.5^-t).
In the case that upgrades are available with current technologies this leads to an average of the current power and the power while fully upgraded.
The final formula becomes a bit more complicated as an army can easily not be fully upgraded and be close to a new breakthrough military technology for even more upgrades.
The AI at some point decides your getting way to advanced and knows that it can't keep up, so it decides it needs to invade and at least destroy some cities and try to get as many other AI's to declare on you. Orginal BTS AI would do the same thing, but instead of 150 units it would send 20 and get maybe one far off AI to declare on you that meant nothing. That's the difference in Better AI.
This is to me, where Blake and others started down a road many others disagreed with. The ai in this case, isn't even playing "to win" it's basically just playing in a spoiler role. I still have problems, understanding why anyone would want the ai to do this. By mindlessly attacking the strongest player (and ok they might temporarily get a city or two, at the cost of their entire army), and thus almost guaranteing their own ultimate destruction, they are basically giving up there and then.
The AI has no tendencies to attack the strongest player or the player who is going to win. It will let your spaceship peacefully fly to Alpha Centauri even if it has a huge stack of units next to your undefended capital as long as you have friendly relations or your army is large enough to scare them from declaring war.
If you however have a small army and relations aren't good, then it might attack but it is unrelated to how close you are to any of the victory conditions or how many points you have on the scoreboard.
There has been some discussion however to maybe change this so that the AI is more aware of the victory conditions and how close someone is to them. This divides players into two groups: those who see it as a game with one goal 'victory' and those who want the AI to behave only according to diplomatic relations.
In the real world, there are actually two responses of countries towards strong countries:
A) Kiss their but and become friends
B) Create another group of nations that can compete with the strong country and its friends.
I would enjoy similar behaviour in civ4.