Just want to throw some mad props your way, Mazer/marvinmartian (and the rest of the editors’ too). CSub was in many ways my ideal A&A group. It had easily the highest level of A&A strategy analysis I’ve seen. I don’t want to knock this site–obviously I like it enough to be pretty active here!–but most of the forum threads are rules questions or superficial discussions, and truly in-depth analysis is rare. I suspect the same is true of most other strategy forum sites. By devoting itself to serious strategy discussion, CSub claimed a unique and extremely valuable niche in the A&A world. I miss it!
Posts made by uffishbongo
RE: Caspian sub people, where did you go?
Question regarding Soviet NO
The one involving Archangel says there must be “no other Allied forces…”
This is probably a stupid question, but does that include AA guns? I’m so used to retreating the British gun to Caucasus and now I may have knocked out 5 of my own IPC’s by doing so. :x
RE: Mathematics and Axis
This thread appears to be long dead, but I never get tired of math questions!
To answer the original question: The statistics of when a bomber gets shot down are determined by something called the geometric distribution, which you can find plenty of info about at http://en.wikipedia.org/wiki/Geometric_distribution. The geometric distribution describes the first occurrence of an event when you make repeated, independent trials. For example, the number of times you have to flip a coin before getting heads; the number of times you have to be dealt a poker hand before getting a royal flush; and the number of times you have to roll a die before getting a 1 are all described by geometric distributions. Once you know the probability of success in a single event, the geometric distribution tells you how long you have to wait before seeing the first success.
Some of the information for the geometric distribution:
–-The probability of getting your first success (in our example “success” is the bomber getting shot down!) on the nth turn is (1/6)*(5/6)^(n-1). This is because, in order to be shot down on the nth turn, the bomber must first survive the preceding n-1 turns, which has a probability of (5/6)^(n-1), and must then be shot down on turn n, which has a probability of 1/6.
–-The probability of getting your first success by the nth turn is 1 - (5/6)^n. This is just 1 minus the probability of the bomber surviving the first n turns. (It’s also the sum of the probabilities of getting shot down on turn 1, 2, …, up to n, but that’s the long way to do it!)
Given this, a number of other facts can be calculated (I’ll spare you the details…) The question “When will the bomber, statistically speaking, be shot down?” has three different answers: the mean, median, and mode. Here’s what each of those is:
—The mode is the single turn on which the bomber is most likely to be shot down. This may be surprising, but it’s the very first turn! The probability of getting shot down is the same (1/6) on all turns, provided the bomber makes it to that turn , but first it must survive all the turns before it. Hence, the first turn is the most likely turn-of-death since the bomber doesn’t have to survive any prior turns in order to reach it.
–-The median is the first turn for which the bomber has a 50% chance of getting shot down before it. This is the fourth turn, because the probability of getting shot down on one of the first four turns is 52% whereas the probability of surviving the first four turns is 48%. So it’s about 50-50 whether the bomber survives at least 4 turns.
–-The mean , also known as the expected value, is the average number of turns that the bomber will survive. This is 6 turns. It turns out that you can actually calculate this by taking the reciprocal of the 1/6 probability of getting shot down on a given turn, although the reason why that works is slightly less obvious than it might seem.
So, which of the mean, median, and mode is the most useful? When should we expect to lose the bomber? Well, the mode is the least useful for answering this sort of question. One can make a case for either the mean or the median, but for the types of calculation that people usually have in mind, the mean is the way to go. For example, if you’re trying to figure out the average amount of economic damage inflicted minus damage received from each bombing raid, then the statistic you want is the average, aka the mean.
Of course, the question of whether bombing raids are worth doing involves a lot more than calculating the average IPC’s lost and destroyed. My test: If you want to decide whether bombing a given country with your country is useful, ask yourself, “Would I destroy $10 of mine if I also got to destroy $10 of theirs?” If the answer is “Heck yes!” then SBR’s are useful. For example, Japan bombing Russia generally makes sense, as does US or UK bombing Germany. A weaker power bombing a stronger power is usually not so smart.
RE: Where to find competitive A&A games at?
Just wanted to mention another place to play online, which probably won’t be going AA50 anytime soon (so if you want a place to play Revised for a while, it’d fit the bill): the IAAPA, which can be found at axisandallies.net
This is one of the oldest A&A clubs around, and these folks are so old school that most of the gaming there is still 2nd edition! That’s right, Revised is cutting edge at the IAAPA. However, don’t be too quick to dismiss them, they have some very good players including some very good Revised players. I’ve played in a number of their Revised tournaments (they have three per year) and have never made it to the finals.
RE: Japan Naval Defense (WARNING: LONG)
Thanks for the comments everyone!
DM: I forgot all about the articles section–I rarely even think to look there. I agree, that’d probably be a better home for this.
Zhukov: I’m getting to like air more and more as compared to subs, but the one thing that makes me wary about going entirely air-based is that if I have to switch to defense then I want some boats in the water…ideally you can stay on the offensive (or the buffer-method-defensive) but subs give you some flexibility in case you need defense in the water too. But I always feel a little reluctant buying them, I’m always happier getting fighters. I didn’t go into this in much depth in the article, but I also love how fighters are dual-use land/air units…at the right time you can suddenly move them all onto the mainland and have a huge threat to Moscow, or possibly even go rescue Berlin.
Jen: It’s probably possible to go KJF without any help from the dice, but I’m not good enough to do it. Like you, I only go KJF if I’ve gotten an invitation to do so in one way or another. One extreme example was my game against Switch where Japan got murdered in J1 not only in Pearl, but also in Borneo where the British fleet was…he came out of that turn with 1 out of his 4 capital ships left, and I think only 2 or 3 planes too. KJF was a no brainer at that point!
Japan Naval Defense (WARNING: LONG)
This is a collection of thoughts about how Japan can defend against the US navy. It’s long enough that it’s more like an article than a regular post; I hope that’s not too pretentious.
The topic of this article is how to respond to a particular Allied strategy that I think is fundamentally flawed, but that I nevertheless come up against regularly in league play. I suppose that by trying to convince people to stop using a flawed strategy against me, I’m not really doing myself any favors. What can I say, I’m just that magnanimous. Ideas from this article could of course be applied to other situations, but a lot of the specifics will be different.
The strategy I have in mind is one in which the UK and Russia go against Germany, and the USA goes after Japan. Theoretically it might be possible for the US to do this with a Sinkiang complex plus navy, but without Russian help the complex is doomed, so play generally proceeds by getting into a naval arms race with Japan. The primary objective is to out-build Japan’s navy enough to go island-hopping and secure a decisive income advantage. Once that’s been done you can kill Japan’s navy, push them off the mainland, etc. A secondary objective would be for Japan to spend all its money on boats in order to stay ahead, relieving any Japanese pressure against Russia and enabling them to put all their troops on the German front.
It’s about time for some disclaimers:
(1)This strategy can be OK in response to specific game events , by which I mean, if Japan eats crow in Pearl and allows you to wipe out two of their capital ships on USA1. But if Japan comes out of J1 with its whole navy and air force intact and a strong Pearl and you take this approach anyway—which I’ve seen happen plenty of times!—you are trying to climb a very steep mountain.
(2) I’m not trying to say that KJF is bad in general. What I am trying to say is that if you want to go KJF, go all the way. Use all three Allies and hold nothing back. If you go half against Germany and half against Japan, it’s not enough, unless the dice are very kind to you.
TWO KINDS OF DEFENSE, AND NAVAL BUILD STRATEGIES
There are two kinds of defense in A&A. The first, which I’ll call “survival”, is making sure your stack is powerful enough on defense to survive if attacked. The second, which I’ll call “buffering”, is making sure your stack has enough offense that the enemies don’t dare move within range. It’s usually preferable to play the second kind of defense when possible, and fall back to the first only when you must. This keeps your income higher, and reduces the danger to your critical territories.
Which kind of defense you’re playing affects your purchasing strategy. If you want to play the more aggressive form of defense, the key statistic is the attack power of your units, not their defense power. Conversely, your aggressor’s ability to advance on you is based on the defense power of his units, even though he’s the one going on the offensive. So everything is kind of backwards.
One specific way that this affects purchasing strategy in the water is how many fighters you buy per carrier. If you’re going for survival-defense then you want two fighters per carrier. However, if you’re going for buffering-defense then you want four fighters per carrier. This is because an attacking carrier can usually support four fighters, provided there is land reasonably close by: Two fighters start on the carrier, attack the sea zone, and then land on a nearby island or continent, while two fighters do the reverse (start on land, attack the sea, and land on the carrier).
BATTLE STATISTICS AND PURCHASING STRATEGIES
Suppose you and your opponent are both given $10,000 to buy the most powerful navy you can. What should you invest in? Subs? Carriers and fighters? Battleships? Some kind of mix? What gives you the most bang for your buck? Well, this is where it gets mathematical…if your eyes glaze over, just skip to the parts in all caps.
There are three statistics that measure how powerful a given army is: punch, count, and skew. The punch is the sum of all the attack values of the attacking units, or defense values of the defending units. (Your expected number of hits will then just be your punch divided by 6. For example, 3 inf 3 tanks attacking have a punch of 12 and will get 2 hits in an average round.) The count is simply how many units are in the army. Skew is harder to quantify, but it has to do with how “spread out” your combat values are; if you have some high-power and some low-power units it’s generally better than a bunch of mid-range units. (For example, 100 inf 100 tanks attacking 200 inf will almost always win, even though their punch and count are identical. This is because the attackers can take some hits without losing power as fast as the defenders).
So how does all that math affect purchasing strategy? Well, one simple way to proceed is to calculate which purchases give you the most punch per IPC. Unfortunately this won’t account for count and skew, but some hand-waving descriptive arguments can help figure out how those factor in.
At first glance, here are the stats:
The moral of the story seems to be that both sides should just buy fighters. Unfortunately, one quickly realizes that without carriers this doesn’t actually help your navy much! A more relevant statistic would be to compute punch/IPC for a carrier group, meaning a carrier plus all the fighters it can support. Recall that a defensive carrier group consists of a carrier with two fighters, whereas an offensive carrier group consists of a carrier with four fighters. We then have the following revised table:
So, what to make of this? If you’re looking to go on the offensive—or, if you’re looking to go on the defensive using the buffer method—then carriers and fighters are slightly less efficient ways of getting punch than subs, destroyers or bombers. When you factor count into the equation—an offensive carrier groups costs $56 for 5 units, whereas you could get 7 subs for the same price—it becomes clear that subs are your best bet for adding to your offensive punch. However, on defense the picture is not so clear. Carrier groups give you significantly more defensive punch per IPC than subs do, but subs give you significantly more count (50% more, in fact). Tough call. Personally I would still go with subs as my mainstay, since their count advantage seems to be wider than the carrier group’s punch advantage.
The other moral of the story is that, just as in the land war, defensive punch is cheaper than offensive punch. This implies that if you and the Americans spend the same amount of money, given long enough they will eventually reach the point where they can safely advance within range of your navy. Of course, with your initial head start that may take a while, by which point your income could be higher than theirs due to gains in Asia. But it is good to know that the long-term situation favors their ability to push forward if all other things are equal.
But wait, there’s more! Why did I leave the solo fighters on the list? Didn’t we decide they were just a fiction? No, there are circumstances where their statistics are relevant. Considering the following two applications:
(1) MAX OUT YOUR EXISTING CARRIERS FIRST! If you already have a carrier and you don’t have all the fighters for it, then buying more fighters to fill it up is effectively adding to your army at the solo fighter rate rather than the carrier-group rate. The application to Japan is, BUY YOUR 8TH FIGHTER BEFORE GOING HEAVY ON THE SUBS. With your two initial carriers you can bring 8 fighters to the battle. Until you have those 8, more fighters are the fastest way to add to your offensive punch.
(2)If you station air on an adjacent island, the fighters don’t need a carrier. For instance, if you’re anticipating a big battle in SZ 45, then you can park your air on the Caroline Islands and it’ll be two spaces from SZ 45—so, no carrier needed! You can buy as many fighters as you like. So you really can add to your force at the solo-fighter rate. This option is competitive with subs as the best overall offensive purchase; you get 20% more punch than with subs, but 20% less count.
So far I’ve just been considering the effectiveness of different units and purchases in the abstract. Time to look at the geography of how a US invasion might proceed, and how to fend it off.
US INVASION STRATEGY
It’s well known that the favorite US invasion point is the Solomon Islands and its corresponding sea zone, SZ 45. This because (a) it’s only two moves from SZ 55, so US builds can get there in one turn, and (b) it’s within two moves, hence one turn, from all the key islands: East Indies, Borne, Philippines, and even Australia. Thus, a massed American fleet off LA can move to the Solomons in one turn, and then go crazy all over the islands.
As soon as it’s safe the Americans would like to build a factory in either Borneo or the East Indies. This allows them to build ships right in the thick of the conflict. Borneo is a more aggressive option, since its sea zone is only two moves from Japan; the Americans have to be doing pretty well to be able to put that factory up. East Indies is three moves away and hence may be feasible at an earlier point, but of course the flip side is that it puts less pressure on the Japanese navy because of the extra space.
In summary, the basic USA invasion proceeds as follows: move to SZ 45, start taking islands, put up a factory on one of the big islands, and start producing ships in Japan’s backyard.
SIMPLISTIC JAPANESE COUNTERMEASURES AND HOW THEY FAIL
Since the Solomons are the linchpin of US invasions, perhaps the way to counter is just to make sure enough firepower is within reach of SZ 45 to kill anything that moves there. So with Japan you can just mass your fleet in SZ 60, and make sure SZ 45 is a deadzone, right?
The reason this fails is because the US can buffer with a sacrificial lamb. They move most of the fleet to SZ 45, but leave one cheap straggler in SZ 51. All the glorious Japanese battleships are now prevented from attacking, as are the transports you might use for fodder. If the Americans are smart enough to buffer with a destroyer then your subs can’t get there either. Attacking with pure air against a fleet with lots of transports to absorb your hits gets real ugly real fast.
Buffering like this allows the US to invade with an inferior fleet. You can send your fleet down to chase them, but they can grab a few islands, continue to protect their main fleet with a buffer, and put up a factory before you manage to pin them down. Few things are more frustrating than chasing an inferior fleet around the South Pacific while they take your valuable islands from you and continue to send reinforcements in from the east!
BETTER JAPANESE COUNTERMEASURES
In order to avoid this kind of scenario, it’s best to stay far enough ahead with your naval builds that the buffering strategy becomes impossible. The key is to have your main fleet sitting next to SZ 45, not two spaces away, so that the US can’t protect itself with a buffer.
If your fleet is a lot bigger than the Americans’, you could take the offensive and push your fleet up to Hawaii or Wake. However, staying on the offensive in the Pacific will take a lot of your resources, and you’d rather be putting some ground troops in Asia to grow your economy and pressure Russia. Hence, a more economically efficient option is to create a stalemate: you hang back and make them make the first move, but keep enough power to make that move costly. Hence, you want your main fleet buildup to be in a spot that (a) is out of reach of SZ 55 (so you don’t have to worry about your survivability against an American attack—you can guarantee that you’re the one threatening to attack), and (b) is adjacent to SZ 45. This means the Caroline Islands is the place to go.
If you have ships farther west that are within reach of SZ 45—say, SZ 37, or either 38 or 46, or 48, etc—these are still OK because the US can’t reach far enough to buffer against them. It’s really just the SZ 60 fleet that can be made ineffective by a Wake Island buffer. So you can still send your boats to grab Australia, deal with an annoying British fleet in Borneo, or whatever, while still keeping an eye on the Solomons.
However, your default buildup spot is the Carolines. You should park your battleships there, and at least one carrier. Once you’ve built up to your 8th fighter (see above) you will want to start getting some subs in the mix. Build them in SZ 60 and then move them to SZ 50 on the subsequent turn. Note that this requires you to stay a turn ahead of demand, because there’s a turn delay between when you build the subs and when they are (unblockably) threatening SZ 45.
As mentioned above, you can buy beyond your 8th fighter if you plan to station some air on the Caroline Islands. This gives you more punch but less count than subs, so it’s a judgment call. However, this has the additional advantage that your purchases go into effect immediately: If you move an already existing fighter from the mainland to the Carolines (or from the mainland to your carrier and one from the carrier to the Carolines), then your new fighter purchased in Japan is threatening SZ 45 and will have the potential carrier spot opened up to it that was vacated by the fighter you moved to the Carolines. So if you need to up your threat to SZ 45 and can’t wait a turn for your sub purchases to move into position, a fighter purchase can do it more quickly.
You will need to think about defending SZ 60 against air. You’ll probably have a couple transports operating there, and your new sub builds. This makes a juicy target for air in SZ 55; they can go on a raid and move a carrier up to SZ 57 to pick them up. Since this would likely be suicidal for the carrier, it may not be worth their while, but you need to keep an eye out for that move and think about whether to leave some air defense in SZ 60. If the air threat is small, a destroyer should do the trick; if you need more, you can leave one of your carriers there.
Let’s talk about where to station the fighters. Four of them will be on your carriers, able to hit SZ 45 and then land on an island or mainland. The other four, then, can start anywhere within four spaces of SZ 45. This means you can put them as far up as India and Yakut and still be able to make it in four spaces. If you haven’t held India or Yakut yet, or just want to provide more complete coverage of the Pacific, try FIC and Buryatia. Either way, you can keep using four fighters against Russia while still maintaining the threat to SZ 45. A bomber stationed in Buryatia is great too; it can hit the key Pacific spots, can reach all the Russian territories east of Caucasus, and can SBR Moscow, all from the same place.
Sometimes things go wrong. You make a blunder, or the dice get screwy, or whatever. Ideally you’d like to prevent a move to SZ 45, but suppose it happens. Then what?
Well, my favorite fallback spot is FIC. There are two reasons for this. One, I always build a factory there J1 if the Russians and Brits didn’t go bananas with a crazy KJF starter. (My favorite J1 purchase for a KGF game is 2 tran 1 IC after bidding $1.) Second, it’s right next to your three big islands (East Indies, Borneo, and Philippines). You can let the US get Okinawa and New Guinea, those are small potatoes, but you want to protect your big islands.
If you’re forced to fall back, then, the basic maneuver looks like this:
(a) Move fleet to SZ 36, and build up to 3 more ships there (subs most likely, maybe a destroyer)
(b) Build more air in Japan if you have the money for it.
The result is that you can deadzone the three valuable islands. What’s more, because FIC is adjacent, there’s no way for them to use a buffer to sneak in either. So even after they push to SZ 45, you may be able to keep them away from your big targets for a few more turns.
If you do this, MAKE SURE THEY DON’T GRAB TOKYO! Moving your fleet down from SZ 60 to join the others in SZ 36 leaves you open to invasion. Station some air there, and buy a couple inf if you need to.
SUMMARY: HOW TO REPEL AN ILL-ADVISED AMERICAN FLEET BUILDUP
–First, make sure it really would be ill-advised. That means not losing your initial fleet. If you go heavy into Pearl on J1, which I still usually do (even though it’s becoming less fashionable these days), make sure you come out with your BB and CV and 2 ftr and one other ship if at all possible. This means attacking with your DD and sub (if it survived) is a good idea, it may mean losing your bomber before a cheaper ship, and if things go wrong you may want to non-combat your transport from SZ 60 to help out. Better to start a little slower on Asia than to lose your fleet.
–Buy up to your 8th fighter soon. Station 4 on your carriers, 4 on the mainland but still within reach of SZ 45. This way you can use them against Russia throughout the naval standoff. Bomber goes on Bry or possibly FIC.
—For the first few turns, you shouldn’t need to buy more boats except some transports. Focus on grabbing land in Asia, while always calculating to make sure you’re deadzoning SZ 45 adequately.
—If the Americans continue to get serious about their naval builds, start getting some subs while continuing to make ground units. Station your main fleet in SZ 50, move your sub builds there the turn after you make them, and keep your 8 ftr within range.
—Consider adding more fighters, to be stationed on the Carolines (or New Guinea), in addition to your sub builds. Also make sure you have one destroyer in SZ 50 to cancel out their sub’s special abilities.
—If you have to fall back from a superior fleet, pull back to SZ 36, build more boats there, build more air on Japan, and make sure to adequately protect Tokyo. This should buy you some more time before your key islands fall.
RE: My Axis Game from Last Night, or- "A Crushing Fascist Victory"
I disagree with your analysis–from what it sounds like, UK1 was played quite well. Ignoring Japan for a few rounds is not a problem. As far as I can tell, the main factors contributing to Allied loss were
—not contesting Africa (big one!)
—losing the British fleet (carelessness + your luck)
—Panicking on the USA west coast–your landing in Canada could have been handled easily
Sounds like there was solid Russian play all the way through, and mostly sound Allied play, but with the aforementioned oversights. If he had shut you out of Africa and not had to rebuild the USA fleet, I’ll bet Germany would have been about ready to collapse by the time Moscow fell. Generally the Allies can win if Berlin falls even a round or two after Moscow. I don’t think the idea of letting Japan go for a while and going full bore against Germany is wrong as a big picture approach, it just sounds like a couple of the details were botched.
RE: Way to not get raped with uk?
Actually, if I was Germany and saw a Russian fighter in Egypt I would start watering at the mouth…anytime I get a chance to kill a Russian fighter I become very happy. Russia’s fighters are essential to its ability to trade territories and keep its income up, and it generally can’t afford to replace them.
With a bid in Africa the Germans can bring up to 6 ground units and 2-3 planes into Egypt on turn 1. There’s no way you can withstand that. Even without the bid they can get 4 ground units and 2 planes for almost a 90% chance of winning. I would go for that pretty much every time with the Germans.