# Infantry as Superior Defensive Purchase — Still True in Revised?

Don Rae, in his Article #1 concerning correct purchasing in Classic, comes out strongly in favor of purchasing infantry in large numbers, primarily because of its defensive value relative to tanks (the only other land unit in Classic). (He also advocates purchasing infantry as part of the “Infantry Push Mechanic”, but that’s another article topic.)Several folks have asked whether Don Rae’s points are still valid in Revised. This article examines Don’s argument for purchasing infantry in Classic based on its defensive value and discusses how the rule changes in Revised affect his argument.

Don’s article on correct purchasing starts out with the following observations about infantry:

“Infantry

No matter what anyone says about any purchasing strategy, the Infantry unit is your first choice purchase piece consideration, as it is your most valuable long-term operations unit for mainland operations, before anything else. Simply put: you must always buy sufficient infantry first, then your attacking pieces like tanks and fighters, before advancing your fronts.”

This rule is not as hard and fast in Revised because the rule-changes affect the value and utility of armor vis-à-vis infantry AND add a new unit – artillery – which is useful on offense, but less expensive than armor. Let’s consider Don’s arguments here:

“1) The infantry unit is the most effective land defense you can buy for your bucks, period.

Here’s the breakdown on “land-based defense attack response” value, cost wise:

3 Infantry – Averages 100% Defensive Hits for a Cost of 9 IPC’s, 2x Hits cost 18 IPC’s

3 Tanks – Averages 100% Defensive Hits for a Cost of 15 IPC’s, 2x Hits cost 30 IPC’s

1 Fighter – Averages a 66% Defensive Hits for a Cost of 12 IPC’s, 2x Hits cost 36 IPC’s

1 Bomber – Averages 16% Defensive Hits for a Cost of 15 IPCs, let’s just forget about 2x hits on defense

In the long run. Infantry are your BEST and CHEAPEST defense against a land force of any kind. Infantry will hold off any invasion for as long as possible, on this basis alone, if bought in large quantities, and most importantly, it forces your opponent to deal with it, as this forces a counteraction in your opponent, by having to generate and buy more infantry themselves!! See the point below…”

First, let’s translate a bit. Don is saying that, because infantry (for example), hits on defense on 1 out of 3 rolls, it takes three infantry to guarantee (on average) at least 1 hit per round. Those 3 infantry cost 9 IPCs. Two hits, therefore, cost 18 IPCs, etc. Now, let’s look at how these pieces stack up in Revised:

3 Infantry – Average 100% Defensive Hits for a Cost of 9 IPCs, 2x Hits cost 18 IPCs

2 Tanks – Average 100% Defensive Hits for a Cost of 10 IPCs, 2x Hits cost 20 IPCs

3 Artillery – Average 100% Defensive Hits for a Cost of 12 IPCs, 2x Hits cost 24 IPCs

In Revised, two tanks do the same damage, on average, that three tanks used to do on defense in Classic, at a cost of just 1 buck more in IPCs than 3 infantry. The cost is just 66.67% of the cost of one hit in Classic (i.e., 10 IPCs in Revised vs. 15 in Classic). Artillery are not far behind – just 3 IPCs more. When you factor in the offensive value of the tank and artillery pieces, they become even more valuable:

6 Infantry – Averages 100% Offensive Hits for a Cost of 18 IPCs, 2x Hits cost 36 IPCs

2 Tanks – Average 100% Offensive Hits for a Cost of 10 IPCs, 2x Hits cost 20 IPCs

1 Infantry, 2 Artillery – Average 100% Offensive Hits for a Cost of 11 IPCs, 2x Hits cost 22 IPCs

Thus, offensively speaking, tanks are a bargain compared with infantry! They also have the great advantage of mobility that no other land piece possesses – i.e., the ability to blitz two spaces. And when you compare the cost of each Defensive Hit for infantry (9 IPCs) versus the cost of one Offensive hit for tanks (10 IPCs), and then factor in the fact that the offensive player usually has the ability to bring air power in support of land-based attacks (and naval power for amphibious attacks), the defensive advantage that infantry possessed in Classic has been largely neutralized in Revised.

“2) The infantry units are the cheapest form of stackable, disposable units to supplement offense.

When faced with a lot of infantry on defense, you should know that your forces will always be hit often and regularly on average die rolls, so this MUST be taken into account when planning attacks. Infantry on the defense will always overcome an equal invested IPC amount of attacking units on their own, on average! (see the “Armor” discussion later on this article for an example of this.)

Therefore, you will need expendable units on the offense to deal with this. Again, your lowly Infantry unit shows it’s value in performing this task. Your offensive pieces, such as tanks, fighters, and bombers, should never be at risk on any attack when conducting an offense, and just as importantly, should never be left alone on the defense after an attack!

If an attack is conducted, leaving nothing but expensive units, you can guarantee that they will be attacked. THIS IS BECAUSE IT IS ALWAYS ADVANTAGEOUS TO ATTACK AND DESTROY UNITS THAT COST MORE TO REPLACE THAN THE UNITS THAT YOU WOULD LOSE IN THAT BATTLE, LAND OR OTHERWISE…THIS SHOULD ALWAYS BE DONE, REGARDLESS OF ANY TEMPORARY TACTICAL DISADVANTAGE THAT MAY RESULT FROM THIS.

Considering all of this, a further point develops: If you use your infantry on any offense to supplement an attack as losses, you will probably need more infantry to strengthen your front after these losses occur. This means that you should never have a tactical turn where you don’t consider buying infantry, because you always need more infantry to replace losses on your front lines. If you can remember this in advance, always when you conduct your purchasing…your games will always be long, developed properly, and your front-line forces will always be as tough as nails.”

All of this is still largely true – infantry are cheap and good fodder to start your stacks with, even in Revised. However, there is one caveat – it IS advantageous to bring tanks into a battle, even at the risk of leaving them subject to a counterattack – if you can afford the losses more than your opponent. For instance, a strong Germany attacking the lines of a weakened Russia – it is necessary and appropriate to wear down Russia with repeated attacks, even at the cost of losing tanks, IF Germany can afford the losses more than Russia, because this accelerates Russia’s fall. Similarly, America throwing its tanks with reckless abandon against German lines in Africa (or Europe) – again, this may be necessary to bleed off troops and tanks that Germany can sorely afford to replace. But the larger point remains true – you will always purchase infantry to supplement your offensive pieces, and will do so BEFORE you purchase significant offensive pieces, since the infantry take longer to reach the front than tanks or planes.

Another point worth mentioning is the change to the transport rules. In Classic, a transport could carry either two infantry or ONE tank. In Revised, a transport may carry one infantry and one of any other piece – another infantry, a tank, an artillery or an AA gun. This rule change greatly enhances the value of the tank (and artillery) as an amphibious assault piece, because unlike in Classic, carrying the tank does not reduce your transport’s capacity by 50%. Instead, you can still carry a total of two pieces no matter which combination you pick – as long as one unit is an infantry. This means you will usually still purchase infantry to fill half of your transports, but a tank is a much more viable purchase option than before, especially for America’s “shuck” operation. America’s “shuck” is all about numbers, so the fact a tank purchase does not reduce transport capacity makes all the difference in the world in terms of increasing the viability of tanks as an alternative purchase to infantry.

**Category**: Axis & Allies Revised, Strategy

But even though tanks have 3 defense now and aren’t that much more expensive than infantry to score two hits, an additional point is how many hits they can take.

The three infantry scoring one hit (on average) can take 3 hits, while the 2 tanks can just take 2.

So you should still consider buying much infantry for you frontlines with support of tanks (or fighters).

It is not possible for any combination of units to grant 100% chance for a single hit on attack or defense. Probabilities are not simply additive. 3 infantry does not grant you a 100% chance per round for a single hit on defense!

For units A and B, the probability of A or B (or both) hitting is

P(A or B) = P(A) + P(B) – P(A and B) = P(A) + P(B) – P(A)*P(B)

So 2 infantry gives you 2/6 + 2/6 – 4/36 = 5/9 (~56%) chance for a hit, while 3 infantry gives you 5/9 + 2/6 – 10/54 (~70%) chance for a hit.

Percentage chance of a single hit on defense per IPC would then be:

3 infantry => 7.82%/IPC

3 armor => 5.83%/IPC

3 artillery => 5.86%/IPC

Similarly for attack,

3 infantry => 4.68%/IPC

3 armor => 5.83%/IPC

3 artillery => 5.86%/IPC

John’s right, the “average” hit idea is extremely misleading. Let’s say you took 15 IPCs, and split them either into 5 infantry or 3 tanks. You want to know how likely some success can be expected from your new troops. To figure out the probability of some success, you take the probability of total failure and subtract it from 1. So …

The probability of at least a single hit from your 5 infantry is:

1-((2/3)^5) = 86.8%

The probability of at least a single hit from your 3 tanks is:

1-((1/2)^3) = 87.5%

Ok, so the probability that they will remove one or more is slightly in favor of tanks. The main advantage for the infantry purchase comes from their numbers. Let’s say your enemy destroys exactly 1 of your army. You now have 4 infantry or 2 tanks. Not only are you much closer to losing the territory if you chose tanks, but the effectiveness of your army has changed:

The probability of at least a single hit from your 4 infantry is:

1-((2/3)^4) = 80.3%

The probability of at least a single hit from your 2 tanks is:

1-((1/2)^2) = 75%

I could have picked any number of troops to lose here, the argument would be the same. If you lose 2 units, the tanks will only score 50% of the time, as opposed to your infantry removing at least one enemy 70.4% of the time. If you lose 3 units, the tanks are gone and the battle lost, but your infantry are still hanging on for another round.

You might expect tanks to compensate for their lower numbers with higher performance. This doesn’t happen. Your 3 tanks will take out 3 enemies around 12.5% of the time. 5 infantry will meet or exceed this level of damage 20% of the time.

In every way, infantry are superior to tanks (and indeed, anything else) for defending land. If you know the fight is coming to you, you should always buy infantry. Of course, you might have other considerations … should I try to sink their ships or fight them on the beaches? Will tanks be enough to win on defense, and once I’ve wasted their attacking force, I’ll be in a grand position to counterattack? I’ll leave that up to you to figure out.

Doing the math for this can be cumbersome. I recommend using the binomial calculator at http://stattrek.com/online-calculator/binomial.aspx