Calculating the outcome of a battle is easy, but nonetheless many people don’t understand it. This thread is a nice example of how some people, often experienced and seasoned players, don’t fully grasp the core combat mechanic of Axis and Allies. To Keredrex, the 2nd poster in this thread, winning a combat is done by high combat values of the participating units. Ofcourse, combat value is very important, but it’s not the most important factor. Ashoka, the 3rd poster, has a better understanding: combat is won by the side with most units. And he is most right!

Before I go on about how to assess combat in A&A, I’ll introduce a bit of terminology.

The **hits** of an army are the amount of succesful enemy dicerolls an army can take. Typically each unit can take one succesful enemy diceroll, and the unit is deemed a casualty if it does. So most of the time, an army has as much hits as it has units. For instance, an army of 3 inf, 1 rtl, 1 arm has got 5 hits. There are some exceptions though, for instance in AA42, a battleship can take 2 succesful enemy dicerolls, and is therefore deemed to have 2 hits. An aircraft cannot be taken as a casualty by a succesful die roll of a sub, so when attacked by subs, an aircraft has 0 hits. So a fleet of 4 BB, 1 AC, 2 ftr has 9 hits when attacked by subs. Lastly, an AA-gun, though taking part in the battle, cannot be assigned a casualty, and therefore has 0 hits. So a defending army of 3 inf, 1 rtl, 1 AA has got only 4 hits.

A second important term represents the combat value of an army, and it goes by the name of **pips**. The pips of an army are the combined total combat value of an army, it references the maximum number of dots on a die which still amount to the hit of a unit. For instance, an army of 1 arm has got 3 pips. An army of 4 BB 3 DD has got 22 pips. Often, the pips of an army depend on whether the army is defending or attacking. 4 inf 4 bmr attacking has 20 pips, 4 inf 4 bmr defending has only 12. There are more exceptions: a sub has got a surprise strike when there is no enemy DD present. This makes its pips more powerful than the pips of other units. On average, 2 pips with surprise strike are equal to 3 normal pips, and 1 pip with surprise strike is as powerful as 1,5 without. A battleship has got the coastal bombardment option, but this only happens in the first round of combat. As a rule of thumb, count coastal bombardments as 2-3 pips. An AA gun also only fires one round as opening fire, but since it specifically targets the strong bombers and fighters, just count the total number of planes the AA gun is firing at as the pips of that particular AA gun. The last two examples make things more complex, so I’ll let you stick with these rules of thumb. A final note: the pips of attacking infantry also depend on the number of attacking artillery. Don’t forget this!

The last term to be introduced is **skew**. Skew is a measure for the amount of cannon fodder an army has. It’s hard to measure skew in an absolute way, as we did with hits and pips, so I’ll only briefly touch it here. Skew is the sum of the difference between the pips of a hit and the average pips per hit of an army. For instance, an army of 4 rtl has got 0 skew, but a defending army of 2 inf 2 arm has got 4 skew. Note that both armies in this example have got the same hits (4) and pips (8 ), but the skew of the 2 inf 2 arm army is higher. It’s clear that the 2 inf 2 arm army, when attacking the 4 rtl army, will have the advantage, and will emerge victorious more often, because after a few rounds of combat it will still have its tanks whereas the opponent will only have artillery. The infantry functions as cannon fodder, thus giving the inf+arm army a good skew. This absolute measure is not simple, and it’s not very important either. The important thing is that having cannon fodder is a good idea, and we call the army with more cannon fodder the army with better skew. Or look at the difference between your strongest and weakest units in the army in terms of pips. Having much weak units and much strong (== high skew) is better than having much average units (== low skew).

Note that there’s one unit which introduces excellent skew in an army: the battleship. An army of 1 battleship has got 2 hits, 4 pips, thus an average of 2 pips per hit, of which the first hit has got 0 pips (you don’t loose pips of a BB when taking the first hit), and the second hit has 4 pips. So the sum of the difference with the average pips (== the skew) is |(2-4)|+|(2-0)|=**4**. Per hit, this is an average of 2 skew, with the average of pips per skew also being 2. Barring negative pips, this is the maximum possible skew for a 2 hit 4 pip army. So a BB not only has the most hits and pips of any unit, but also the most skew. This is why a BB is a very strong unit, worthy of its high price of 20 ipc’s.

All three of these measures -hits, pips and skew- are an indication of the combat strength of an army. Not all of them are equally important though, so here follows the basic combat concept of all A&A combat:

**HITS > PIPS > SKEW**

It’s clear that both the hits, the pips and the skew of the participating armies are important when assessing which army will probably win the battle, but this formula states that hits are more important than pips which in turn are more important than skew. This formula also means that big armies with cheap and weak units will beat small armies with expensive and strong units. Or that battles between armies of equal size with more or less the same combat strength will be won by the side with most cannon fodder. This formula explains why the infantry push in AA2nd was so powerful, or why an army of only airplanes needs to be protected against an army of ground units (airplanes, besides being expensive, have no cannon fodder, which is bad skew).

An easy way to use this formula in a real battle is by first assessing the hits of both armies. If you got twice the hits, you’ll almost always win. 4 inf attacking 2 arm will most often be won by the 4 inf, even though the pips of 4 inf are worse than those of 2 arm. This is what is meant by hits are more important than pips. So when assessing a battle, and you notice you have much more hits, don’t bother counting the pips, you’ll more than likely win. Having much less will result in a loss. Having about equal hits as the opponent, warrants more research.

This extra research constitutes the 2nd step of assessing combat outcome, and it is done by calculating the pips of the combating armies. If hits are about equal, but you’ve got a (much) greater amount of pips, you’ll win. For instance, 4 ftr attacking 4 DD will favour the ftrs, even though hits are equal. 4 ftr attacking 5 DD will favour the DD’s however -though the ftrs have more pips- because the DD’s have more hits. So if hits is about equal, but you have better pips, you will win. If you got worse, you’ll loose, and if pips also are about equal, proceed to the third step.

The last step involves assessing the skew of the armies. A big difference between pips of your weakest and strongest units usually is a good sign. 2 BB will mostly win against 4 DD, even though both armies have equal hits and pips. It’s worth noting however that you’d rather have more hits or pips than a better skew: 2 BB will loose against 5 DD (more hits and pips despite having worse skew) or even against 2 DD 2 Cru (equal hits, but more pips, less skew). Note however that skew is already a very detailed assessment. 2 DD 2 Cru vs 2 BB will be mostly won by the DD’s+Crus, but there’s still a reasonable chance (about 11%) that the battle will be a tie (both armies obliterated), and a substantial chance (about 41%) the BB’s will win. This leaves only 48% chance the 2 DD 2 Cru army wins, even though this still is the most likely outcome! Whoever told you Axis & Allies is simple, is ofcourse mistaking ;)

This immediately brings us to both a drawback and an advantage of this method: the dice can ruin an otherwise fine assessment of a battle, but this method allows to estimate how often this will happen :D Having double the hits of an opponent means the chances of loosing are very small. Having about equal hits, and a lot more pips also points to a battle you shouldn’t loose, but loosing is a distinct possibility nonetheless. Having a bit more hits, but a bit less pips and skew points to a very balanced battle, which will mainly be decided by the particular dice rolls. If hits and pips are about equal, even having a vastly superior skew doesn’t mean you’ll win the battle for sure. On average, yes, you’ll win, but the opponent still can win if he has even only slightly better dice. This formula assumes the dice favour each side equally, which is ofcourse not the case in reality. As a rule of thumb, try having either a lot more hits, or slightly more hits but clearly better pips, and you should do fine. Having only better pips is already risky, and counting on your better skew to win the day can be ruined by one bad die roll. Ofcourse, knowing this is also a weapon against the opponent. Let him waste critical resources on a battle with only a slightly better win chance, or try a 50/50 battle as an attacker, to completely crush your opponent with lucky dice, and to retreat with minimal losses when the dice bounce bad. Hmm, this brings me to two little remarks:

First remark:

The hits>pips>skew method doesn’t take expensiveness of units into account. An army of 2 ftr attacking 2 inf is a bad idea, because the infs are much cheaper than the ftrs. Pips and skew however favour the 2 ftr! The same goes for strategic properties of units: if a transport threatens a key territory, it might be worth sacrificing a few bombers to get it killed. This method will help you estimate whether you will win or loose a battle, but it’s not the only factor to decide whether engaging in battle will be advantegeous or not.

Second remark:

Everything else being equal, the attacker has the advantage, because he can retreat if he chooses to. The presented method doesn’t take retreating into account. For instance, 3 arm vs 3 arm, hits, pips and skew are equal, there’s an equal amount of ipc’s at stake (10 for each army), and we assume there are no further strategic repercussions of winning or loosing for either side. If the battle goes bad for the attacker, for instance if the defender gets two hits in the first round and the attacker only one, the attacker will probably retreat, because his chances of succes have become much smaller, and he rather keeps his last arm than risking to loose it for little gain. The defender hasn’t got this choice! If the situation is opposite, the attacker scores two hits in the first round, and the defender only one, the last arm of the defender is doomed, and there’s a substantial chance it won’t take another enemy arm with it in its grave. So if this battle is fought a zillion times, with the attacker retreating when the battle starts going awry, on average, the attacker will win some ipc’s. I estimate the gain to be about 1-2 ipc’s. However, due to retreating when the battle goes bad, the defender will win most of the time! This seems contradictory, but try to see it like this: when the attacker retreats, the defender will have won by a small margin (one or two arm are left over for the attacker), but when the attacker wins, the defender is obliterated (he cannot keep any arm alive when defeated). Thus is the effect of being able to retreat, which is also something to take into account when assessing battles.

I think I told you guys everything I know, and I hope it’s not too confusing. I’ll summarize for one last time:

Calculating hits, pips and skew allows to judge the combat strength of an army, if you take into account that hits > pips > skew. This method also allows to give a rough estimation of how risky a combat will be. Even though this formula is quite handy, it doesn’t take strategical implications into account, nor the fact that an attacker has the option to retreat. Use the method wisely, and you will gain the edge over an unsuspecting opponent. Now go play and enjoy the game! And try to win ;)