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 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

@Gargantua:

How precisely is this supposed to be “simple” or “open” to new gamers?

Yep it’s tough, but there isn’t a simpler version

But a good board game designer makes its games “easy to learn, hard to master”. It’s a cliché, but it’s true. Unfortunately, Larry Harris does not always adhere to this principle.

@Granada:

Sorry, I think my logic is correct here, since while the first bmb dies on the 3rd-4th roll of dice, it will take 6 more rolls to get you to the 3rd-4th roll of the second half dozen of rolls. Of course, we work with averages because average is what is likely to happen most often: there is no mean when rolling a dice; and it is exactly between the 3rd and 4th roll when the cummulative likelihood you roll 1 exceeds 50 %.

Mathematics doesn’t agree:
“average” != “what is most likely to happen”. What is most likely to happen is an event with the biggest chance, given a set of events and a probability function over the events. For instance, let’s take the set of chances of a bomber dieing in raid N. For N=1, this is 1/6. For N=2, this is 5/6 (not dieing raid 1) * 1/6 (dieing raid 2). For N=3, it is 5/65/61/6. So the chance of dieing in raid N = 5/6^(N-1)*1/6 = the probability function. Dieing in raid 4 has a chance of 9.6%. As told, dieing in raid 1 has a chance of 16.7%. So according to your own definition (“most likely to happen”), it should be the first turn, which contradicts your conclusion of 3rd/4th turn.
Ofcourse, you can use other sets of events. I’ll indulge you, and define the set you mean, which is cumulative: chance of getting shot down before raid 5, and chance of getting shot down on or after raid 5. Not getting shot down before raid 5=(5/6)^4=48%. Chances of getting shot down before raid 5 = chances of opposite = 1-48% = 52%. The result we can extrapolate is it is more probable to get shot before the 5th raid than after the 4th raid. But also: it is almost equally likely to get killed before the 5th raid as after the 4th raid (52%~=48%). Anyway, this is probably what you mean with “between 3rd and 4th”, only it should be “between 4th and 5th”.
The problem with this definition of the set of events however is that it doesn’t tell you at what raid the bomber will probably die (you need my first definition of the set to do this). It only tells you before or after what raid the bomber will probably die. Which is utterly pointless in the purpose of determining average damage. As is the first definition too…

Anyway, enough chit-chat, strategy talk.

USA 1: buy 3 bmr. Gives 4 bmr total. After that, buy 2/3 of a bmr every round. This way you’ll always have 4 bmrs pounding Germany from round 3 upwards.
Germany has an income of about 40. Let’s assume it needs 10 units each turn. So its best bet is to only repair Germany fully, giving you 20 IPC’s a turn to shoot at. With 4 bmrs, this will seldomly (=in less than 1.5% of cases) be overkill (chances of getting >20 are (5/6)^4 -getting past AA with 4 bmrs- * 2.7% -throwing 21 or more, see http://anydice.com/-  < ~1.5%).

Using this strat, your land troops arrive one turn later, with 1 inf 1 arm (=8 IPC’s = 2/3 of a bmr) less each turn. This is the drawback.
What do you get in return? From turn 4 onwards (3rd turn you’re shooting at Italy, which doesn’t get repaired) Germany is denied 12 IPC’s worth of units, or 4 infantry. You always have 4 bmrs to support an invasion. You need less transports (remember, 1 less inf+arm means less units to shuttle). You start hindering Germany from turn 3, which is faster than you can do with any newly built land army + fleet (the invasion of Africa is done with the starting army + fleet). Lastly, Germany cannot use Italy as a building point (for instance to build fleet or troops for Africa).

The initial investment is high (3 bmr turn 1, 1 bmr turn 2 etc.), but what strategy with USA hasn’t got a high initial investment? After this investment you trade 8 IPC’s for 12 IPC’s each turn. It is a decent trade-off, possible in 1942 because bmrs are cheaper. Can you show me a strategy with US that trades IPC’s faster?

All I am saying it is a “prayer” based method, not a strategy.

It is not a prayer, but a decent strat, the quickest one I know to trade American IPC’s with Germany. I hope my point is more clear now.

@Granada:

Moreover there is another important factor coming into play omitted in the CS analyzes. The truth is that your first bmb is killed on average on the 3rd to 4th roll of dice for the AA gun and on every sixth roll only from then on.

Sorry, this is wrong. Given a chance of 17% (=1/6) to hit a bomber, the chances of not being hit after 3 raids are 58% (=(5/6)³), and 48% (=(5/6)^4) after 4 raids. Even stronger, there’s a decent chance (40% = (5/6)^5) that your bomber even survives 5 raids. Or a 16% chance it survives 10 (!) raids, etc. All I’m saying is you can’t say a bomber will die “on average” after x turns, because that’s not the way chance works. At most you can say that there’s a ~50% chance a bomber lives past 4 bombing raids. If that’s your definition of “on average”, be my guest, but I don’t see how this could contribute to the effectiveness calculations of a bombing raid.
If we follow your reasoning, every bomber built will fall after 3/4 bombing raids, because there is no inherent dice difference between the starting bomber and the newly built bombers. The former is, ofcourse, a false statement.

So I agree with the Caspian Sub, mathematics-wise it executed the correct calculations, in this respect their reasoning is 100% solid. The only thing I’d like to add that USA executing a bombing campaign against Germany -buy 3 bmrs the first few turns to bomb the greycoats back to the stone age- is a viable strategy: it is a swift way to use American IPC’s to hamper Germany’s war effort. It’s faster than stacking up in UK and invading Europe mid-game. It’s about trying to fully utilize USA’s IPC’s, which often is not trivial to do.

Other than the low income, Russia fits your bill perfectly. It’s easy, so you won’t make too many mistakes, and it doesn’t pose a hard challenge, just keep the Germans and Japs out of Moscow.

Germany has a higher income and thusly allows for more mistakes, but it’s harder to play good (3 fronts: East, Atlantic, Africa) and poses a greater challenge, and makes you play with a navy.

All the other nations need a big navy, making the game more complex, so those are a no-go. All in all, you just want a nation that’s easy to play, and Russia is the easiest one. But what’s the point of playing A&A if you’re not into complex games?

@special:

Only Germany qualifies to your wishes

No, it doesn’t: it’s not easy to play and it does have a navy. But then again, there are no nations that qualify to all your wishes. My advice: look up some Russian strategies, and try to play that one, it is by far the easiest. Good luck!

@Rakeman:

I’m surprised more people aren’t suggesting attacking the American fleet G1 with that sub… 1/3rd chance you sink 2 transports and 1 cruiser for nothing (I did some simple math… 1/3rd chance you sink them, 1/3rd chance they sink you - 2/3 * 1/2, and a 1/3rd chance a second round of combat, so basically it’s a 50/50.  But if you win, you do 26 IPC worth of damage, vs. taking 6 IPC worth of damage if you lose).  I personally consider this strategy kind of cheap, as it’s a decent risk but extremely high reward.  Of course, it will put the UK in a much better position as you are letting their navy start out at nearly full strength.  Perhaps that is the balance - having to deal with a full strength UK navy?

Thoughts on the G1 sub move?

This is bad game design, turning A&A into a gambling den. Our playing group plays with the “gentleman rule”, moving the German sub from SZ 8 to SZ 7. It can reach all important SZ’s from there, except the one with the American navy. Problem solved, you’re welcome Larry

About the “full strength UK navy”, you’re still killing the med fleet with air, so the navy is still cramped, and the bmr is useful in egypt too. And it’s not like Germany lacks any targets for fighters on R1.

I recall that revised OOB rules weren’t very clear on this, and that the LHTR specifically stated that a destroyer only allows hit units to fire back, but they do not cancel opening fire of enemy subs. So in your case, subs on both sides do opening fire at the same time, and destroyers allow each hit unit (non-sub, cuz they already fired) to fire back. So yes, the attacking subs get to fire back.

It all depends on the definition of how your destroyer “cancels” enemy subs. I too think this is a broken rule, and I thought that Spring 1942 repaired this rule, so that a destroyer simply prevents opening fire from enemy subs, thus when hit in opening fire, a sub without opening fire because of an enemy destroyer doesn’t return fire. This is the way how you thought, and how it ought to be imho, the rules work.

@Hobbes:

@Nix:

ok quick check of mape etc, seems to me this is revised with new units and new naval rules correct?

Pretty much. There are a few differences in the map, mainly in North America. There are also differences in

• Strategic bombing (it now causes damage to the IC instead of simply removing IPCs)
• AA Guns only fire during combat (no more firing when a plane overflys it)
• Fighter escorts during bombing is optional.
• No technology
• During amphibious assault only 1 ship (Battleships and Cruisers) per unit landed can conduct bombardment.

And finally most players seem to consider that it is balanced and a bid is not required.

• Units killed by an amphibious assault get to return fire

The reasoning is that combat ships protect transports, not the other way around.

Naval combat is completely changed from Revised. Mostly for the good: buying a couple of subs @ 6 paired with a decent airforce is now an option for Germany. Transports do no longer protect the fleet they should be protected by. Fighters are no longer clearly superior to any naval buy. Submarines have their unique role: attacking and sneaking throughout the oceans.

Transports no longer able to take hits is one of those changes, to be seen in an attempt to make naval warfare more diverse and interesting. For instance in Revised, when I played Japan and USA tried to kill me, I started with a headstart in fleet, bought 4ish transports and a carrier, and was safe untill round 5, even with USA going all naval on me. This is no longer the case, which opens up new possibilities.

If you really want to pull it off, you have to totally commit to it. Kill the Jap transport with the Indian des. Invade Ngu with 2 inf from Aus, invade Bor with 2 inf from ind, put the indian fighter on the hawaii carrier, move all inf in Per and Trj towards Ind,  put a British bomber in Nov or Sin. Depending on the battles of Borneo and Ngu, put the australian sub in SZ 47 or 45, put the Indian aircraft carrier in SZ 36 or 49 (to block any J1 reconquering of Borneo). Make sure you put 6 russian inf in Bry, and maybe buy a russian bomber to invade Manchuria with the 6 inf + bmr in R2.

The whole goal of this setup is to counter anything the Japanese player tries. If japan tries to kill off a lot of the British fleet, plus Hawaii and Chi, it will be very vulnerable to American (pacific), Russian (Manchuria) and British (sub+bmr) counters. If Japan concentrates it’s forces leaving few weak spots, a considerable part of the UK navy survives, and will annoy the Japanese for a long time, giving time to the IC’s to produce units.

The British bomber in Nov or Sin will hinder Japanese fleet builds, the spread out British fleet will cause serious headaches to the Japanese, resulting in probably at least a submarine surviving, combined with the british bomber in Sin, this is already something to take into account, the reinforced Hawaiian fleet is less tempting to attack because a counter on A1 is more likely.

Send UK fighters to Cau when possible, to defend USSR and threaten Fic. Build an IC in Ind, maybe even Sinkiang (if Japan pulls a complete fleet build with little transports J1). Build some extra arm with USSR in Cau to quickly reinforce Ind or Sin when needed.

Even against an experienced player, this is worth a try. The one big drawback: it’s dice heavy. Bad dice will ruin this, good dice make this a genious opening (winning both Ngu and Bor really hurts Jap).

If Japan plays right, the IC will fall. That was the big con in revised, don’t know if it’s still this way in 1942.