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Concentration of force

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  • Concentration of force

    Most of us know that one of they keys to winning battles is to concentrate your forces on the important objectives. There is an interesting side effect to this that crops up when you have a large advantage over the people you are attacking.

    Consider a scenario where a medieval infantry (attack 4) attacks a 2 defense unit (pick another med inf for this example) on a mountain. The defending med inf is unfortified, and so has an effective defense of 4.

    First case: 1 MI attacks 1 MI - and surprise surprise, there is a 50% chance of each MI winning the battle.

    Second case: 2 MI attack 1 MI - if the defender is not militaristic, the attackers have an 83.3% chance of winning, while if the defender is militaristic, they have an 81.1% chance of winning. No big surprise here either.

    The surprise comes in the average number of units lost. In case 1, each side lost 0.5 units on average in the battle. In case 2, the attackers lose 0.67 (0.69) while the defender loses 0.83 (0.81) units on average. Actually, this is pretty obvious - the first fight has a 50% chance of going either way, and if the first attacker loses, the second gets a chance to attack a wounded defender.

    Now consider a huge number of attackers (formally, an infinite number). The defender is certain to lose his unit eventually. While the attacker loses on average 0.76 (0.80) units, more or less (if the defender was restored to full health for each battle and was never promoted, the attacker would lose exactly 1 unit on average).

    The point is that for one on one battles with a 50% chance of winning, you will on average lose one unit for every enemy unit you kill. If you can attack with more than one unit against the same enemy, you lose less than one unit per enemy unit killed.

    Consider two small armies of 4 MI attacking 4 MI, with the defenders always being on mountains, so all fights are 50-50. A lot of one on one fights will lose both sides equal numbers of troops on average. At the other extreme, ganging your four up against each enemy troop individually, and then the survivors (if any) moving on to the next target gives you an average loss on 2.6 units, compared to the enemy's average loss of 3.3 units, giving you a 65% chance of wiping out your opponent (vs 50% in a series of 1 on 1 battles).

    The obvious conclusion: concentrate forces where possible. Most of the time it is better two have two units attack a single defender, leaving another one to go free for a while, compared with fighting two 1 on 1 battles. This is probably fairly obvious to most people though.

    The other conclusion: the civ that can field the biggest army starts off with an advantage, but that advantage grows as more battles are fought. If you start off with 20 MI, vs your opponents 10, after ten 2 on 1 battles, you end up with 14 MI, and your opponent has 2 (compared to the situation of fighting one on one battles where you have 15 and your opponent 5). The big army's advantage grows since it can take advantage of the stack effect to suffer fewer losses than it's enemy, even in (apparently) equal battles.

    This also generalises to some extent to unequal battles. You suffer fewer losses by stacking your troops and attacking small numbers of enemies in one go, than by taking on more equal battles. This hurts the AI in particular in pre-industrial wars, where their units tend to arrive in dribs and drabs to attack you, so you can mass your fast defense units and take them out with small losses compared to what you would suffer if those same units were stacked together.

    This also means that the civ with the larger army needs to devote less of its resources to replacing losses than the civ with the smaller army, meaning that it can either do more useful thing while fighting the war, or expand its army faster than the other civ is capable of (assuming equal manufacturing capacities).

  • #2
    Interesting. I could never have done all that math. I'm going to have to start building more units early on. Thanks. You taught me something.


    • #3
      Great explanation!

      The only thing to watch out for is over-concentration of force. If you wipe out all enemies with 10% of the attack force, your remaining attackers will have to waste time walking to other key positions before they can attack.

      To balance sufficient force and efficient deployment, try to send stacks that have a 95% chance of capturing your target. You can either guess from warmongering experience or plug the numbers into a battle calculator.


      • #4
        This is a very good suggestion. It is very important to send enough troops to actually seize the target. If you send one less unit than you need, and just end up fighting even battles, you haven't gained anything.

        But victory usually comes a different way for me. The AI has units it flags to go out and fight outside of cities. At the start of a war it will send these out to fight. I make it my first priority simply to destroy these AI troops as soon as they step into a disadvantagous spot, with my own offensive army.

        Otherwise if I conencrate my force and go off fighting somewhere, and the AI comes another direction, there's a chance the AI will actually take some of my cities. I'd rather destroy the AIs mobile army, then pick off helpless city defenders with my unchallenged army.

        A smart human player can always see the AI's stack and its next move. Its a simple matter to use your own force to counter theirs. That's why the AI cheats. ^_^


        • #5
          What do you means "cheats"? It has only one advantage and the boost it gets at the higher levels.
          Cheating is reloading when things did not go your way and the like. The Ai can't do that.


          • #6
            There's a reason you play against 5, or 10, or 15 AIs and not 1. ^_^ It'll take all of them gangbanging you and tech whorring to beat you. That's all I mean.


            • #7
              Originally posted by Frank Johnson
              This is a very good suggestion. It is very important to send enough troops to actually seize the target. If you send one less unit than you need, and just end up fighting even battles, you haven't gained anything.
              Even worse: Maybe you created a GL for AI.

              But, what is sure: the next turn will be even more difficult: the AI now has promoted units, and they can be healed in the city. Your sigeing units are weaker and weaker every turn.

              If I want to "enter" in a city and I am not sure, I always wait outside (al least 1 tile away from the city) until all the (planed) units are there. When I am sure, that all my units can attack in the same turn, I go for the city.


              • #8
                On numerous occasions I have seen the AI 'flee' his cities. Typically this happens when I have moved a large force close to one of his heavily defended cities and killed some citizens either by bombarding or starving. I don't know why he do it, maybe he is scared Or maybe he values the city less after I have pounded it a bit(why do I have 7 pikemen in my capitol, it's only worth 4 now?)
                Don't eat the yellow snow.


                • #9
                  What do you mean by flee? Do you mean no troops left to defend? Or did they just happen to send a unit ot so off to some other task?
                  The reason I ask is I just had to invasions. One where I dropped 64 units on a city in Japan and the other where I dropped 72 units on a hill next to a Chinese city. They did not flee in either case. In the first case they sent attackers by the dozens. In the second they did not attack as I dropped the troops on a hill. That would have been deadly for them as I had MI and Tanks, they had Infantry and Riders.


                  • #10
                    Using spies I saw that their cities were very heavy defended (7+ pikemen) by that eras standard but after a while they send troops out of the city. Not to fight, it actually looks like they tried to escape. This occured only when I had killed many citizens by either bombarding or starving(pillaging)
                    Don't eat the yellow snow.


                    • #11
                      I can't say for sure, probably a coincidence. The AI is not too bright you know. They will sit there with 50 units as you attack a city and not send anyone up to defend the city and have only a token force on hand.
                      They will do this city after city until they are out of units.
                      The doggedly try to get their min number of defenders in a city.


                      • #12
                        The best explanation I can think of is that the AI values the city less after I have pounded it a bit and then decides it is over-defended
                        Don't eat the yellow snow.


                        • #13
                          The Fleeing AI

                          I also thought I saw AI troops leaving a city after intensive bombardment. I had a couple different attacking forces at the time and just figured they were moving to counter the larger force, but perhaps it was a valuation that the AI performed saying in effect: "This city isn't worth 7 defenders, only four. I'm moving out some of these units." I'm definitely going to watch for this because I think you may be right!


                          • #14
                            They probably programed the AI to leave more defenders in bigger cities, where there would be a larger defensive bonus.


                            • #15
                              Very likely they redeployed based on city size and culture. It makes a little sense, but of course the fleeing defenders are killed as soon as the leave the city.

                              Of couse I have sent out defenders so as to divert the AI's forces. That is: If there is a big AI stack, you can send out weak units. The hope is that the AI will attack these weak units and not your city. This draws a portion of the AI force away from your city. This could buy you time to rush a defender, get strong reinforcements, and/or counter attack. For example if you have some archers left over (acting as MPs) during the industrial age. These archers are useless as defenders or attackers.

                              In any case (back to the subject at hand), I don't think the AI is using this elaborate strategy.