Costs of units/Combat Sequence

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Costs of units/Combat Sequence

Post by Griffey » Fri Feb 25, 2005 12:43 pm

Most combat sequences let units fire "simultaneously." The only exceptions are AAA, bombarding battleships, and submarines.

This "simultaneous" design of the combat sequence causes a serious imbalance in the design of most versions of A&A, which is related to the cost of units.

When units fire simultaneously, the bang-for-the buck you get out of a unit is not COMBAT STRENGTH DIVIDED BY COST.


Thus, e.g., the real cost effectiveness of d6 (1-2) infantry as an attacker is not 1/3, it is more like 1/9, or 0.1111. The real cost effectiveness of d6 (3-3) tanks is not 3/5, but 3/25, or 0.12. Thus tanks, in the simultaneous fire system of combat, or only a little better than infantry as an attack investment. It's no wonder that smart players buy infantry, is it?

The reason for this problem is simple. As the cost of a unit goes up, not only can you afford to buy less of the unit, but the cost to you each time the enemy scores a hit also increases.

For examle, suppose equal IPC cost value of infantry attack an equal IPC cost value of tanks.

30 infantry (= 90 IPC) attack 18 tanks (=90 IPC).

On the first round, the infantry will score about 5 hits, destroying 25 IPC worth of tanks. The tanks will score about 9 hits, destroying 27 IPC worth of infantry. Not much difference, really. Also, the infantry will have a radical, huge advantage on the defense, destroying 50 IPC worth of tanks, to a loss of only 27 IPC of infantry.

So the real combat worth of infantry as an investment, when we use simultaneous fire for these two types of units, is about the same on the offensive. And infantry is double the worth of tanks on the defensive.

As the cost of units increases, their value as an investment goes down radically, by the square of the cost of the unit. Is it any wonder that expensive units swiftly disappear with this system? Only a novice buys them.

The best solution is to adopt a Blitzkrieg Combat Sequence, in which the more expensive units fire earlier. This evens up the math nicely, by reducing the inverse square problem, by reducing the number of cheap units getting a chance ot fire.

1. AAA, submarines fire.
2. Land Bombardment by artillery and ships.
3. Aircraft and aircraft carriers fire.
4. Battleships, tanks fire.
5. Cruisers, artillery fire.
6. Destroyers, infantry fire.
7. Transports, forts fire.

For example, in the above example, the infantry will suffer nine hits before they fire, reducing the number of hits they score on the tanks they are attacking from 5 to 3.5. If the tanks were attacking, they would stand a much better chance, suffering only 7 hits on the first round, instead of 10.

The other solution, keeping simultaneous fire, is to make the costs of units much more nearly equal to one another. For example, if infantry cost 4 and tanks cost 5, the real investment value of a (1-2) infantry would be 0.067 (1/16) on the attack, and 0.125 (2/16) on the defense. The real nvestment value of tanks would be 0.12 (3/25) on both the attack and the defense.

This is much closer to what we want in the game design, yes?

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Post by Imperious leader » Fri Feb 25, 2005 12:57 pm

Griffey, can you make some examples that are relative to actual gameplay. What i mean is use your math but with groups of different units, say 3 tanks, 6 infantry, 2 artillery, and one fighter.. vs. say 6 tanks, 3 infantry,2 artillery, and one fighter. Account for retreats on rounds one two and three. note the results in combat effects and results in ipc lost by each side each battle. Their is simply no real world application to your math. I have never seen a battle of 30 infantry vs 18 tanks. Anybody knows immediatly not to start such a battle except axis and allies (TM) RTS A.I. set on "high" mode due to the IP carnage lost by tanks. This form of science has to reflect gameplay and only proves in a very narrow way given very narrow parameters what would happen. They do not conclude that the entire "system" is bankrupt. I dont mean to play your antagonist, but these results really prove very little. If you can show us how and with real game groups of units with the advanced values plugged in on d12 and the results still show what you seen to have in mind BEFORE posting your figures, then ill be a believer too.
We really need an Axis and Allies World War one game so i can play that on August 1st, 2014.

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Post by Krieghund » Fri Feb 25, 2005 1:02 pm

I boiled all this down to 3 tiers in my combat system:
  • Air-to-Air
    Air-to-Ground/Sea & Artillery*
* Includes AA & Battleships

This is much simpler and pretty much captures the same effect. I am not sure why you have tanks firing before artillery. It would seem to me it's the other way around.
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Practice, not theory

Post by Griffey » Fri Feb 25, 2005 4:46 pm

The inverse square rule has several practical applications.

First, players have always used it inductively. They don't do the math, but the smart ones figure out from experience pretty quickly that infantry is about 40% better as an IPC investment than tanks, and act accordingly. I've won several times as the Allies by building nothing but infantry, transports to move them, and a very few tanks. All other units were a waste of money. (OK, once in a blue moon I had to build some fighters and a carrier to protect transports.)

Second, the math gives you a handy formula for knowing what the IPC loss equivalent on each side will be in an upcoming combat round. If a cost 5 d6 (3-3) tank is rated (3-3) in IPC equivalents, then a cost 3 d6 (1-2) infantry is a (1.65 - 3.3) in IPC equivalents. This means that on the average, if you attack a group of three tanks with six infantry, you will on the average get the better of the enemy in IPC losses in the first round of combat. You would never know that just eyeballing the situation and counting combat factors. Of course, you should lynch any player doing this with a calculator while playing friends.

Third, knowing the math is essential if good software is ever to be develped for this game. The computer version was dull, because the software was so passive and predictable.

Fourth, knowing the math makes for better designed games. I don't like it when players are forced to buy the same thing all the time to win. Using "simultaneous fire," it's important to know how to jiggle the costs for units to make them more equal as an IPC investment. Its also important to know how to jiggle the costs of units if you're using a sequential fire combat sequence, such as the "Blitzkrieg Combat Sequence." You don't want one or a few units to be so much better as investments that people never buy anything else.

Fifth, knowing the math helps you think about how changing the map and the combat sequence will change play balance. A bigger map and a retreat provision is going to help the Russian a lot. If the old costs and strengths are used, the Axis will never win. In the original game, the big advantage the attack had was that since the defender could not retreat, the attacker could snowball an initial small advantage into a crushing defeat for the defender, after a few combat cycles. If that advantage is taken away, the game has got to be compensated with other advantages for the attacker. One way is by adjusting costs, the other by adjusting combat sequences.

I hope I've answered your question.

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Post by Imperious leader » Fri Feb 25, 2005 5:40 pm

Nothing that you posted answers this question:
3 tanks, 6 infantry, 2 artillery, and one fighter.. vs. say 6 tanks, 3 infantry,2 artillery, and one fighter. Account for retreats on rounds one two and three. note the results in combat effects and results in ipc lost by each side
In combat as the attacker we soak off the fodder which invaribly is infantry and combine the attacks with other more expensive units that will yield better results. I want my infantry to die, while i kill more of his infantry with my artillery and tanks, followed with a quick exit and into a safe territory. None of your math accomplishes or reflects this reality. This sidestepping with "inverse square root coeffecient minus cost" does not reflect the logic of the advanced axis and allies game mechanics
We really need an Axis and Allies World War one game so i can play that on August 1st, 2014.

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Post by Imperious leader » Fri Feb 25, 2005 5:46 pm


First :Their are no more a/a guns. They are built into Industrial Complexes. Id say for each attacking Bomber owner of the IC gets a roll one d12, with a 1 or 2 equals a hit on a Bomber.

Second: All units are to be classified for the purpose of combat into the following
Infantry and Mechanized= class 1 units
Armor and artillery= class 2 units
Fighters and Bombers =class 3 units

Third: Each surviving Artillery unit can now fire at one plane at the end of all combat rounds.

Forth: Bombers roll twice for their attacks ( 2 hits possible)

In all land combat when one side has no planes and the other does have planes, Those planes conduct air superiority attacks on enemy forces as follows: Each plane rolls for attacks and all hits are preemtive (no return fire) The plane hits are the choice of the attacker . The hits are removed and the planes have no further part in combat.

CASE TWO: If both sides have planes then the attacking planes are rolled, and the defending planes are rolled. Both take all hits from planes first, followed upon chosen ground units. All hits that are assigned to land units from planes are preemtive with no defending rolls against the planes.NO further combat with planes takes place. NOTE: Bombers get to roll twice against land units, but once against defending air units, and at a lower attack/defense value (example: say they are at eight/ eight for attack and and eight for defense, but against planes they are one die at 4 in each catagory

CASE THREE: In combat with ground units only (after air combat effects are conducted) consider the following:

All class TWO units fire first, with the attacker rolling first , then the defender, all hits are taken from class TWO unit mix (defenders choice) The owning player can choose which of his class TWO units are removed, however. If their are no class two units then class ONE units can be eliminated.

All class ONE units now roll, attackers followed by defenders, again all loses are from class ONE units first (owning players choice). If their are no class ONE units left, then class TWO units can be used.

Retreats are handled in manner i have posted under retreats, partial, or full. Planes from both sides may retreat to adjacent territories after their preliminary combat round. If they choose to remain in the territory and are the last surviving piece following battle, then they can still retreat to an adjacent territory. Planes cannot take an enemy territory, only land units can do this.

Each surviving Artillery piece can now fire at one plane that was used in combat. Their anti-aircraft value is fixed at say 2 or 4 ???

Defensive air support: planes from adjacent territories can assist in defending in the air combat that is performed before land combat. They are simply brought into this combat on that round.

Their no no more coastal air support, since now carriers have their own naval fighters and i dont want to mix these units . Plus their was nearly NEVER any case of planes taking off from MAINLAND territories and sinking groups of warships. They came from islands which are covered under naval fighters.

Now get out some pieces and playtest this. You will notice the following:

Planes no longer keep a stack of plastic safe from destruction, they have too much influence previously, However air superiority is firmly addressed.

Bombers get some value into land combat, which is why you buy them

Artillery have more value since they roll against planes at end of combat.. Will you lose a tank or an artillery piece when you see that you have a chance to hit a plane??

Enemy tanks can be destroyed now , no more "hiding" behind stacks of Infantry

Remember breakthru and exploitation:

Breakthrough and Exploitation: Following combat, any additional armored or artillery class units, mechanized, or air units not delegated during the movement phase or the combat phase and residing adjacent to the original territory that an attack is conducted can participate in breakthrough and exploitation. They now move up to their full movement capabilities and conduct a new attack. The first space entered must be the original captured hex and the second is subject to a new attack. Note: Airborne units (paratroopers) actually land in the territory they attack. Note: All normal rules of combat and retreat apply.
We really need an Axis and Allies World War one game so i can play that on August 1st, 2014.

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Post by Griffey » Fri Feb 25, 2005 6:46 pm

Dear Imperious Leader,

I didn't answer your question directly for two reasons. First, you didn't give me enough information to do the math. Which side is attacking? Which defending? What are the factors on both sides? What are the costs of each type of unit? What is the exact combat sequence? Are any units exempt from fire? Etc.

Second, you can't discover anything fundamental about the dynamics of a game by asking questions like that. Doing the tedious calculations necessary to find out which side is likely to win such a battle is unimportant. The important thing is that game designers know if their game design is going to result in imbalances in the game, imbalances that clever players will exploit to produce similar outcomes in most games. To do that, careful examination of the costs of units and their combat factors, and the combat sequence is required.

The reason I use the examples I do is that they more clearly illustrate what I'm talking about than if I used more a abstract illustration. If I had written, "On the average, a cost 5, d6 (3-3) tank attacking cost 3, d6 (1-2)enemy infantry will kill 1.5 IPC per turn, or 30% of its own cost, while the defending infantry will kill 56% of its own cost," I would be saying much the same thing, but in language more difficult to grasp intuitively.

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Krieghund's sequence

Post by Griffey » Fri Feb 25, 2005 6:59 pm

Dear Krieghund,

Interesting sequence. If I understand you right, you are saying each line gets a "first shot" at later firing units, in this order:

1. Aircraft fire.
2. AAA, battleships, and artillery fire.
3. Naval units, tanks and infantry fire.

So, e.g., if the defender puts a hit inflicted by an enemy fighter onto one of his own defending AAA or artillery units, it cannot fire?

I like it. Letting the battleship fire first is hugely important, because it's so expensive.

By the way, do your battleships and artillery fire by attrition, or by normal combat values, d6 4 for battleships, d6 2 for artillery? The latter, traditional method, I assume. The reason I ask is that you put them on the same line as AAA, which traditionally fires by attrition.

The only thing I don't like is the last line, which is subject to the inverse square problem mentioned in my original post on this subject.

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