I think something that you should have mentioned is how SBRs are a potentially good way to put pressure on a nation you wouldn't otherwise be able to attack. An example of this being Japan doing SBRs on russia after taking India to help the German effort before its land units are in range
I actually ran a simulation of 10,000 strategic bombers independently using Python. Each bomber bombed until it was shot down, and I got some interesting results. The bombers did average around 17.5 damage per bomber(actually 17.6). But the median damage done was 11. This is because 1/6 bombers do no damage whatsoever, while there are few bombers that do crap ton of damage because they never get shot down. However, even the ones that do a lot of damage take several round to rack up that damage. It may be viable if you are going for a super long game and plan on dozens of strategic bombing runs, but I say in the short term, bombers are always better doing something else.
Going into a game thinking "I am going for a SBR strategy this game" is a losing move, but they will be relevant about twice a game in my experience. The rule does serve a crucial purpose, however, which is that if the allies have already secured a definitive victory in the G40 game but the axis will not surrender until the bitter end, the US can simply build 8 bombers on its turn instead of building more ground units that won't be relevant for 4 turns and prevent Berlin from stacking infantry so S.U. can finish the game. It has been a big time saver for me in the past no matter how ineffective😂
Theory: A 1 in 6 chance of being shot down means it survives 5 missions. Reality: A 1 in 6 chance of being shot down means that over 6 missions the bomber will die, randomly, on one of them. Therefore - on average - after 3.5 missions. Conclusion: Dice are evil.
Reality is that for each toss, there’s a 1/6 chance to roll a 1, independently of each other. This means we have a "geometric distribution". And we know that when we have a geometric distribution, the expected value X to get the first success (shooting down a bomber in our case) is E(X)=1/p. And as p=1/6, E(X)=6.
@@countdooku6176 but most of that is driven by the extremes, right? A few will survive many, many missions while *most* of them die in less than 6. that sort of supports what this video was saying... bombing raids are just a very flukey mission, much more luck dependent than most combat in the game.
@@luddite31 welcome to my games, LOL. I had 3 subs an a cruiser go up against a destroyer with a transport. Destroyer survived and wiped out my small fleet.
@@luddite31There is definitely an impact from the long tail and it does likely cause most of the variance seen in this video. More broadly, how impactful it is would depend heavily on the game length. I simulated the missions mm 100 bombers and they had an average of 4.9 successful missions before being shot down, pretty much bang on the expected 5. The median was 4 successful missions with one bomber surviving 24 missions, showing the tail. But a game is unlikely to last 24 rounds, so you wouldn't get nearly that many successful missions from that bomber. So let's cap the maximum number of successful missions for the bombers that survive the war and our averages are: Max 6: 3.56 Max 8: 4.02 Max 10: 4.29 This means that, for bombers you start the game with and launch a strategic bombing raid every round until the game ends after round eight, you can expect an average of 4 successful missions. In that same eight round game, bombers you are first able to use on turn 3 will have an average of 3.5 successful missions. On top of that, your sample size in a real game will be much smaller with fewer bombers flying fewer missions so real experience will be much more volatile.
@@88porpoise nice analysis, thank you! I think in practical terms, that means it's really not worth it to go strategic bombing unless either (a) you know the game will go on a really long time or (b) you just feel like gambling and have nothing better to do with the bombers.
Great breakdown. The buddy I play with almost always refuses to do bombing raids. He is convinced the AA gods are out to get him. As a result, he has severe PTSD from raids. Looking forward to more AA vids.
I laughed out loud at “sitting around scratching it’s ass”. Excellent video! I think every AA player struggles with the risk/reward of sbr’s. I once planned strategically two use sbr’s but on the first roll for the AA gun my opponent rolled 3 dice and got 2 hits. Devastating.
In one (classic) game I got heavy bombers as the US. I wanted to do strategic but my allies insisted on suicide attacks to hit units. Thing is I only had bombers so after the first attack I would lose all my bombers.
I have always analyzed this and decided that you only do it when you are Britain and have too much money... then just bully Berlin. But hey, maybe I am proven wrong today. One time my dad and I were playing A&A 1942 and each time he and I tried to do a bombing raid, EIGHT TIMES IN A ROW the AA guns hit the bombers. So we just stopped ever since that incident.
Actually USA is more likely to use it as UK is typically invading Germany and using their Bomber to support. USA, being far away, can get in the game by using Bomber this way in early turns. Still very risky though. Usually Bombers are more valuable for fights and needed for that every turn anyways. I play by old rules as FYI as I only have older versions.
Fantastic A&A video, I was compelled to watch every minute (which is rare for me). In my variant that I am currently working on, Bombing raid rules are very different... would love to share the ideas and get a similar breakdown. Keep up the great work, your style is very refreshing for our community (and congrats on winning the Sea Bass tripod).
Very interesting. I am in agreement with your last scenario in that it makes more sense to use them in attacking other units to boost the odds in you favor. Definitely opens up your eyes a bit on how to combine units to maximize damage. Great video
I used to love bombing raids, especially against Germany in the opening rounds until America got itself into Europe. Now I'll almost always prioritise my bombers for battles. Thanks dude, glad you enjoyed the video
Worth it if Allies...even if results even (trading IPC) because Allies typically have IPC advantage. That said, agree that use bombers for ops whenever possible, esp vs high value targets (ships!), bomb if nothing better to do.
I typically argue against bombing raids for the same reason I argue against G1 sending 1 sub to attack U.S fleet. On average you gain 1 or 2 IPC advantage over full sending SZ7, but what happens if you lose SZ7? If you get slaughtered SZ7 as Germany you face an extremely hard game. So the expected value is deceptive. When you win you have a slight win, when you lose you have a massive loss.
I love your videos, thanks for including Anniversary as well as 1940 version in your analysis. I would love to see a video featuring subs with possible alternative rules similar to your video on cruisers.
My take away is that I should probably be committed to multiple bombing raids with multiple bombers over the long term. One single raid seems like a lot of risk with little return.
You covered a lot of scenarios so I'm surprised you didn't consider SIX Bombers making a run. One gets shot down, the rest do 3.5 damage. Or going in pairs 7, 7 and 3 damage for the solo. 15ipc for the bomber versus 17 damage puts you up by 2. Or as I take form the video they are 12ipc now so you are up by 5 ipc, or one tank dead. And as you have already pointed out, while this might give an edge you have to consider the war in total. Allies up in money might be able to run this strategy by economics. A 12 for 17 ipc swap being very much to their advantage. But you'll get far more use in sending your six bombers into actual combat where you get more than one turn and the AA gets only 1 shot at each. with the bombers killing at least an infantry, or 3ipc. But you'll need some ground forces to protect them from loss. Things get complicated.
So, an interesting development is that AA guns now have a maximum of 3 targets. If you get 4+ bombers all on the same area then you can force the enemy to spend IPCs on every industrial zone they have so as not to be giving you free shots at them. You're unlikely to hit the damage cap with fewer than 6...
My thoughts mostly align with your conclusion: that if your bomber isn't going to be involved in any combats this turn, you might as well send it on a raid. However, in my opinion, if your bomber isn't going to be in any combats this turn, then it'd be smarter to move it to a better location for next turn. Which is almost guaranteed to be possible, since bombers have such long ranges. I've been playing Axis and Allies with my friends for years, it was honestly the game that got me into board games, and in all that time, I don't think I've ever done a SBR. Which is a shame, but I can't think of any way to make it more appealing without making it overpowered.
I think you missed one very big point. If a bomber is shot down in the first run, it can't make any further runs. You need to weight the average damage per turn by the chance that it survived that long. A single bomber has a 58% chance to survive 3 runs. In round 7 the theoretical (by this time only 27% being actually still around) bomber would have dealt an weighted average of 12.6 damage. How many games take 7 turns before it is not apparent who has won. here comes the catch - should you have 6 bombers at hand at the same time, the logic of 1 is shot down and the rest do 17.5, creating a nice profit, hold true. I think the biggest element in bombing is that a Russia/Germany can't stack up high with Infantry and thereby killing them earlier.. However I like the conclusion that considering the opportunity costs, raids are hardly worth it.
You missed one aspect, timing. You do indeed on average lose one bomber every 6 raids. So using six bombers, you lose one and do on average 17.5 damage, using 3 it will be the same but o er two turns. Not using low luck dice, but rounding 17.5 to 18 is close enough, one bomber does 3 damage per round and pays itself back over time. It's more than the 2 IPC value of a 2/3 hit on an infantry. But time is money too! The more damage you do quickly, the more worth it will have. Killing troops and gaining territory is worth more at the start of the game! In addition fighters and bombers share the unique benefit of doing damage from behind an infantry meat shield and not having to move into the territory. This saves money on tanks that might otherwise be lost on the next turn. Finally planes can fight ships, which are expensive for their power. The bomber has a huge threat range, especially limiting placement of lone transports or weak fleets. Having lots of planes means you need less ships. When fleet dominance is lost or won, you can still put the planes to good use while remaining fleet becomes mostly useless. So when investing into bombers, it's best to use their strength and not use them to just trade IPC with a delay.
Agreed! I'll add another point: Because the AA fires first and in 1/6 cases prevents the bomber from doing damage, the true average damage isn't 3.5, it is ~2.9. Add this to your point that time is money, and it doesn't look good. "Hey you, 30-year-old! I have a deal for you: Give me $1200 now, and I'll give you 300$ when you're 40, another $300 when you're 50, and so on every ten years! Just live long enough and you'll end up with more than the $1200!"
Bombing raids in numbers mean 0,9 IPC on average more damage than suffered. The math is as follows: 0,8333 * 3,5 - 0,1666 * 12. That does not answer the question, as the author already pointed out, whether they are "worth it". There is an opportunity cost (the bomber can be used for other fighting) and then there is the value of the damage to the factory. Inversely the cost for a bomber for the US e.g. is less than the worth of the damage to e.g. Germany (in a Germany first strategy). Same can be said for the damage to the USSR by the Japanese. As the USSR is starved for resources while the Japanese usually aren't.
i used to complain about crazy battles, where the 1% thing happens. But in a game of AnA how many of those chances happen? dozens of 1.6% opportunities at least in most games. say they are only from expensive things though maybe 20. and (0.984)^20 = 72% so that is over 1 in 4 chance of something crazy like that happening! I agree with your conclusion though. Good Job!
The biggest issue with bombing raids is even if you get decent odds it can take four turns to break even. But you potentially lose more on the ground in that time. That said bombers could be a good choice for the US and Britain on the first turn. That would maximize the damage they do over the course of the game, and they could be used in battle as needed.
I think in one or two places your probability might be a bit off or at least your presentation of it. In the case of 2 bombers, there's a 69.4% chance of both bombers getting through unscathed, but the chance of 1 hit is 27.8% and there's a 2.8% chance of suffering two hits. This means the average expected losses are a bit worse. Like it's not a major issue at all but every once in a while the results for exactly the scenario discussed rather than as bad or worse are given, and it does tweak a certain pedant sensibility. Overall though really good video, don't get me wrong. I think my biggest concern with strat bombers is paying up front for a hopeful net win over time. You take 12 ICs out of your economy on turn 0. Your opponent spends them on things that they can use to do things. Over the next 5 turns or so on average you average taking three or four IC out of their economy. The average is going to be 17 or 18 IC removed over 5 turns. Now, the question I have is would your opponent pay 18 IC over the course of 5 turns up front to deny you the use of 12 IC now? I feel like that is a deal that in some situations your opponent would gladly take, because they expect to gain more by having more materiel on the front than the 6 IC they expect to lose over time.
Thanks for the comment and thoughts! In hindsight I can see where some of my math is a bit off (stats are not actually my strong suit unless I have an odds calculator to do everything for me 😄). I think the main problem is that I assumed each bomber could survive 5 raids when in reality they could get shot down on their first run. So yeah SBRs are in fact worse than presented here. Maybe I'll redo the video one day Thanks again my friend
I think the math in this video is wrong. Assuming the bomber will survive 5 mission is iffy at best. Best way to look at it is: you do a SBR, you have 1 in 6 chances to lose 12 IPC (your bomber) and 5 in 6 chances to deal 3.5 IPC damage. So it's -2 +2.9 Over a long time you should expect to inflict 0.9 damage to your opponent more than the damage you take FOR EACH SBR.
Given on your turn you decide which engagements you make, and that you should only choose to fight battles where you expect to destroy more than you lose, I think that bombing raids are a poor return on your investment. As a rule of thumb if you lose x IPCs on your turn, your opponent should lose at least 1.5x IPCs, else you've had a bad go. Bombing raids are too marginal to be an effective use of your economy.
I like a well fought campaign, seems like a joy kill bombing away build $$$$, German production went up as more factories were bombed, as a machinist I have run WW 2 and older machines, these old machines are extremely thick and heavy, today's same machines are often thin wall castings and are easily broken, Germany often simply stood the machines back up, rewiring and back to work. With some of the fighter escort variants it can make a fun extra to the games, my first axis and allies had heavy bomber tech, unquestionably a superior war winning machine, each bomber rolling 3 Dice and unlimited damage on a Capitol, long range allowed bombing the United States from France, and they offer great ground support with just enough infantry
If you think AaA 1940 bombers are overpowered then you’ll get a kick out of this, I lowered the price of ALL aircraft by 2 IPCs each, including for my HBG 1939 and 1936 games because I like it BROKEN
It's called "Strategic" Bombing; it is meant to be used strategically. One game I played as Britain in version 1942, Germany put all it's effort first turn into devastating my Atlantic navy while landing all its luftwaffe on the coast ready to strike if I tried to rebuild a navy. When it came to my turn, I decided to say "the hell with building a new fleet." Instead I focused on building three tanks in India to help in the pacific... but I still had enough IPCs to build a bomber in England. And thus began the game where I, as Great Britain, did nothing to help the European campaign other than build bombers and devastate German production. Although many brave bombers faced their demise, I found the raiding gave the needed pressure/hinderance on Germany for Russia to defend against a less supplied German front while also giving time for America to beachhead in France. In a circumstance where I saw no viable option to rebuild my navy and Russia needed allied support ASAP complimented by the fact you can always rely on USA to transport a relentless amount of troops eventually, SRBs became the best way I could support in the European Theatre.
I’d say strategic bombing really depends on the nation. I play G40 where it takes a few turns to get the US into the fight. 2 turns to get from the US to the UK or Europe, and just 1 for North Africa. For the US, strategic bombing really is all they can do early on in Europe, and you gotta do whatever you can to slow Germany down, because if Russia falls, you can’t really get a foothold in Europe. You have to take down Japan and hopefully that will be enough. The UK can help bombing too. The Axis really should focus on taking territory. Russia shouldn’t be buying strategic bombers until, Germany is on the ropes. Then those bombers can help deal with Japan.
A stack of bombers can simultaneously deter transports/ and threaten bombing raids when there are no minor battles to tip the scales in. Feels like a tatic for when you are temporarily ahead and want to keep that advantage as the front lines are likely far from your production..
First off, I love the video and the math. I just recently became aware of your channel thanks to a recent video put out by YG. I've watched a few of your videos so far and can see you have some great stuff. Anyway, I've been giving some thought to your actual results vs statistics and I think I see the issue. Not all bombers will last until their 6th bombing run. You'll lose some in the first round, some in the second, some in the third and so on until every bomber is shot down by turn 6. I realize that the number of bombers participating will change each round as some are shot down so I'll put it another way. If you attack with 100 bombers each round, by round 6 your enemy should have scored 100 hits. The average lifespan of a bomber is actually 3 rounds. 3 rounds at an average of 3.5 damage per round gives you 10.5 damage per bomber, or 10-11 damage per bomber if we rounds it off which is just shy of an even trade and comes close to matching your real life results.
Hey man thanks for the comment! I rewatched this video a few months ago and realised there were a few flaws in my logic. What you’ve pointed out is the major one. It was wrong for me to assume that every bomber would survive 5 runs and base my math upon that assumption. Perhaps my logic stacks up on the grander scale (if we were dealing with hundreds of raids) but obviously you wont get so many in a real game, so losing one early is much more significant. I guess we can refer to the math I used as a best case scenario? And that obviously means that raids are a lot less worth the risk than I made them out to be. Perhaps that explains why I’ve lost the majority of games in which I relied upon them! I would say now that SBRs are best suited for the end game when you already have the upper hand and are not well suited for the early game as a means to gain the upper hand. Shame really, I used to love bombing the crap out of my enemies. Thanks for the clarification and I’m glad you dig my content!
@@CorporalClegg After reflecting on it even further, I agree. There is a high degree of variability (especially with smaller numbers in a particular game) but generally bombing runs aren't worth it unless you already are a fair bit ahead in the game.
Yeah man, its an old vid. Was my first shot at analysis. I'm aware the math is a bit flawed and therefore raids are probably much less effective than portrayed. I'll redo this video one day 😉
Other things come into play as well. Say Japan can successfully bomb India for, say 4-5 ipc's, and thus force the Brits to make some hard choices re: reinforcing India or creating a sustainable Atlantic navy. That's a possible head-scratcher for old Winston, no?
You know my answer, but usually the only time I SBR is when the factory is totally undefended or to put the nail in the coffin beforehand ⚰️ of attacking a CAPITOL- BTW I remember well of that game of yours in those 3 BOMBER kills!!!
The statistic damage ratio might seem to justify strategic bombing, but the opportunity cost tilts the scale completely one way. It isn't (usually) worth it.
13:01 Statistically speaking bringing 2 bombers is not “safer” than any other value given the more amount of damage you can inflict with grater numbers of bombers
6 fighters in Berlin will average 2 interceptor kills, at least $20 in damage to the attacker after the anti-aircraft fire, this is not a cheap raid, the defender may come out ahead between the AA fire and interceptor hits. 9 fighters in Berlin ??. Unlimited AA guns as a optional rule will deter a bored bomber command. Some rules allowing up to 3 AA shots per gun. 7 escorting fighters would kill one defending fighter after AA lossess
If you are bombing a major complex, the hell yes strategic bombing raids are worth it. If you are sending a bunch of bombers on a minor complex, tread with caution
I'll chip in with a 'yes' they are as Allies. And no they aren't as Axis. (early game only-first 6 rounds, give or take) Reason being the only thing you didn't cover in depth, which is opportunity cost. 12 IPC is 4 inf, 3 art, or 2 tanks. The Axis has a land war as it's absolute, #1, no question about it, priority. Forgoing those 12 IPC worth of land units, or even take it this way, 2 bomber = 1 fighter 2 inf 2 art. It's a tough ask to get as much utility from the 2 bombers as these 5 units you don't take for instance. The Allies have a different issue, logistics are huge for the first few rounds and getting some 6-movers is a big deal. Using a few to slow down Ger early on is an option that you can follow without having to rely on the G player making mistakes. And they help escorting attacks once you arrive in force, covering large areas of the map. If a game balances out and reaches later rounds, where you now have a situation with say 2-4 large stacks that are cautiously dead-zoning the other in search of VCs, the numbers as presented here become VERY relevant and the answer is yes for certain. It's a small advantage, but a few rounds of strat bombing can provide that needed edge for one stack to finally attack another, and statistically will do so more often than not. PS- Forgot to mention, and this won't be news to many I'm sure, the occasions for the USSR to EVER buy a bomber in circumstances that will make sense statistically are extremely few and extraordinarily far between 8>D
Anyone got a review of a new strat for me: if I'm Axis, I'm planning on using Germany to pull some forces to Africa and conquer, whilst the rest of my IPC is mostly going to bombers 1st round. I SBR Moscow round 1, and move closer but not attack Russia with lots of my troops. Next round with 4 total bombers (i think I can buy 3 round 1) I bomb Moscow again. Statistically I won't have lost one, even if I do lose one I will have forced Russia at this point to do 1 of 2 things: 1 is they pay to get Moscow producing men again which weakens thier already weak economy. 2 is they split their military between the two factories around Moscow. This weakens Moscow's defence. Next round I hit Moscow with all my forces including 4/maybe 3 bombers if I lost one. Germany should be able to take it with the Russian forces split up. Or depending on what Russia has done I attack another Russian factory territory (e.g. if Russia attacked Germany 1st round and I cant attack Moscow). All this while I Move West with Japan which should secure a Russian defeat.
I'd say Bombing is 100% NOT worth it haha. I've always lost 1 bomber every 2 or 3 round and Rarely make more damage than an average of 2-3 per bomber XD. So overall it always been a BIG loss for me every game.
I tried bombing Germany with the British bomber. Got shot down first attempt. Then tried the US bomber on Germany and it too was shot down first attempt. Finally bought a US bomber to bomb Japan and yes, it too was shot down first attempt. I knew at that point the computer was fucking with me.
