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Axis and Allies 2nd edition had two primary ground units: infantry (1/2/1/3 attack/defense/move/cost) and armor (3/2/2/5). Axis and Allies Revised increased the defense of armor to 3 and added an artillery unit (2/2/1/4) that has the special ability to increase the attack value of any accompanying infantry from 1 to 2.

Don Rae's famous infantry push mechanic was written for 2nd edition rules and argues that a good player will predominately purchase infantry, only buying tanks when they have established solid defensive lines.

How does the addition of the artillery unit and the increase in the defensive power of armor change the optimal balance of ground forces?

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6 Answers

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I have to go in the opposite direction of the other answers and say that artillery isn't very useful. If you run sims to try and flesh out what is the optimal mix, you will probably find that using artillery is better. However I found that when actually playing the game, tanks have at least 3 significant advantages over artillery.

Retaining their offensive power

When attacking a territory that is well defended, you can count on losing a lot of infantry. Since the third point for offensive power of artillery is dependent on having an accompanying infantry piece, your forces will lose significant offensive power when you start losing those pieces. Since tanks aren't dependent on the infantry, you will retain your offensive power longer.

While this is covered in the simulations, it is important to realize that the simulations favor artillery if you limit the size of the forces by IPCs. If you limit your forces by number of units, tanks fare significantly better than artillery because they retain their power.

Gauging power by IPCs makes sense if you are talking about land battles in Europe, Asia and Africa. However if you are doing amphibious assaults(or your supply of troops comes from the sea) you are going to be limited by the number of transports and therefore the number of ground troops. When you have a navy offshore worth 100 IPCs and another 50 IPCs of aircraft supporting the invasion, I don't think it makes much sense to decrease your ground power just to save 2 or 3 IPCs(especially if you are losing planes to keep the last ground troop alive).

Increased defense

In my experience the main challenge isn't taking a territory but actually holding on to it. While artillery give a boost to offensive power, that extra IPC doesn't do anything for you when defending. Since tanks defend on 3, they also give an added boost for defense.

Moving 2 Spaces/Blitzing

This is the most important advantage. While it is not very important in some theaters, it is critical in the Germany/Russia land war. Artillery will take 1-2 turns longer to get where they need to be than tanks. While the math may show artillery is optimal in these battles, they won't have any value if they're not at the battle.

When I'm playing that theater, I will often purchase a couple turns of infantry, then tanks then fighters and bombers. I try to time it so that when the main battle is fought, all the units from previous turns will be able to participate. If you are running with an optimized infantry/artillery mix, the player on defense is going to have several more turns worth of units in the battle.

While you may purchase a 15 IPC industrial complex in one of the 3 IPC territories to counteract this, it will still take 5 turns of purchasing artillery before you break even and those artillery will still have the above disadvantages.

Summary

I get the impression that you are looking more for a math oriented answer to what the optimal ground forces are. My general point is that there is no optimal mixture because everything is too dependent on the situation.

A math based solution isn't capable of taking into account:

  • the possibility(and costs) of the opponent's counterattack
  • how long it takes to move your forces into position
  • the added value of the territory you are conquering(and the loss of it from your opponent)
  • the time component(since territories generate IPCs, they are more valuable if conquered sooner than later)
  • and probably a bunch of others I haven't thought of
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Doesn't have to be math-based at all. I liked your answer and the counterpoints it provides to a more myopic tactical calculus. –  Adam Wuerl Mar 12 '11 at 21:59
    
Also, interesting point about the calculus changing in an IPC-limited battle, as most lines on open land would be vs. in an amphibious assault, where you're likely to be unit-limited. Very insightful. –  Adam Wuerl Mar 14 '11 at 13:02
    
The first two points are simply wrong -- tanks retain offensive power less well and have less defense than inf+arty. Comparing based on number of units is nonsense, since there are no stacking limits in the game -- the only limit on the number of units is how many you can afford –  Chris Dodd Mar 14 '11 at 17:53
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@chris The question was asked about Axis and Allies Revised edition. Adam posted a link to the rules in his question. The comparison is between tanks and artillery and not tanks and infantry. Tanks have more defense than both infantry and artillery. That is fact, not opinion. Also, comparing based on number of units is relevant when supply is based on transports since transports are limited in the number of units each one can carry. I explained this in my answer. –  juan2raid Mar 14 '11 at 18:41
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I would say the addition of artillery makes tanks completely moot -- you're always better off buying infantry and a single artillery to go along with any attack. The tanks just do 50% more damage than infantry on both attack and defense, for a 67% higher cost, and no increase in their ability to absorb damage.

edit

To answer Adam's comment, an artillery plus two infantry costs the same as two tanks, and will inflict the exact same 0.1 losses per IPC both defending and attacking. An artillery plus 7 infantry costs the same as 5 tanks, and inflicts .1067 losses per IPC. That may not seem like much compared to the tanks, but combined with the fact you need large amounts of infantry to absorb losses anyways, its much more efficient and becomes more efficient as your army becomes larger.

The only real advantage of tanks is the two-space move, which is IMO rarely significant

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You missed the most important points about tanks - their ability to move 2 spaces and especially their ability to blitz. The 2-point move means you can threaten more areas than infantry or artillery, forcing your opponent to defend more areas. And blitz allows you to exploit a defensive hole much better. –  DJClayworth Mar 11 '11 at 17:00
    
An infantry and artillery have a 1/9 chance of getting two hits, a 4/9 chance of getting 1 hit, and a 4/9 chance of getting zero, at a cost of 7 IPCs. A tank has a 50/50 chance of getting a hit for 5 IPCs. So the expected value of hits per IPC while attacking for inf+art = 2/21 = 0.95, while for armor it is 0.10. As DJC mentions, armor also has a blitz ability. Now on defense, a tank is still 0.10 hits/IPC but inf+art has increased to 1/4 of two hits, 1/2 one hit, 1/4 no hits for 1/7 = 0.14. So the calculus above seems a little too simplistic. –  Adam Wuerl Mar 14 '11 at 12:58
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You should still be purchasing mostly infantry to absorb the hits of your opponents. The difference is now, your additional purchases depend on your strategic posture. If you're satisfied "slugging it out" on this line with no intention of offense, you should purchase mostly infantry, and maybe a few tanks that will never be threatened by enemy fire. If, however, you'd like to maintain an offensive capability, you would purchase mostly infantry, and then many artillery in order to enable your infantry to be a credible threat on offense. A few tanks would still be called for, but again, only after enough infantry was available to reliably ensure that the tanks are safe. Essentially, think of tanks in Revised as "Light Fighters"; they provide some useful hard-hitting power, but you don't really want to risk losing them. Artillery is only really useful when you're transitioning (or want to be able to transition) to an offensive role with your infantry; on defense, pure infantry spam is still better.

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This seems like a good set of heuristics that seems to jive with the quick math I did in a comment to Chris Dodd's answer. When on defense infantry is your best bet, with artillery being a simple way to increase their attacking power. Armor are then added to round out the force once the lines are set and defenses sufficiently strong. –  Adam Wuerl Mar 14 '11 at 13:00
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With this change, armor is severely weakened - the purchase cost is simply too high for something only slightly better than infantry. The only exception is if your factories are too far from your front or you are facing light defenses.

In those cases, such as a large number of undefended territories near one of your factories, tanks additional movement can come in handy. It offsets their purchase cost significantly if your tanks seize two territories the turn after construction.

Tanks are also marginally better if you are launching an amphibious attack, as you can get slightly more punch per transport (assuming 1 infantry + 1 tank per transport, which is what I believe they can carry in the current version) with a similarly more powerful defense for your beachhead.

This problem disappears (somewhat) if you adjust the tank purchase cost to 4 OR up their movement to 3. I'd go with the purchase cost reduction, personally.

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I've played in games where infantry were neglected and tanks and planes were the most purchased units. For example, if Germany buys all tanks for one round and all fighter for the next, they will be at a GREAT advantage in attacking and taking territories.

In the case of Russia, this is different. Russia is at a monetary disadvantage and a mobility disadvantage. When Germany comes knocking on your door, the best thing to do is purchase infantry like it's going out of style. I had the Russians having 32 infantry and they held off the German invasion of about 12 tanks and 10 or so fighters and a few bombers. Each infantry has a 33% chance of hitting in defense, and for 3 IPC's, you can't beat it.

Infantry provide the best defense for the IPC's spent, but this is not a defensive game. It is a game of tact, wit, offense, and luck of the die.

One cannot neglect infantry, but you also should not focus on them.

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If you only consider a single fight on land, the perfect combination is int + art, 0 tanks.

If you consider amphibious fights, tanks and infantry is best since you have to get more transports if you're going with inf+art.

But A&A is not about single fights, it's about winning the game and to do that you need success on both a tactical and strategical level. The main advantage of tanks and fighters is the ability to threaten a larger area, which can force your opponent into leaving troops where they don't do any good except defend.

I typically buy about 3 inf to 1 art and 1 tank and perhaps half a plane.

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