If you were to know three things about me, they would be:
1) I love Axis and Allies
2) I love statistics
3) I once wrestled a bear
If I can find new and interesting ways to combine the first two, then I’ve done my job for the day. As I was glossing over the list of changes in A&A:50, something in particular caught my eye – Bombers. Specially bombers cost less, down 3 IPCs to 12 IPCs per bomber. I began to strategize:
What is the cost/benefit analysis of a Allied Strategic Bombing Campaign (SBR)?
First some stipulations:
1. The Allies commit totally to Europe.
2. Due to their proximity to Berlin, only the UK preforms the SBR Campaign.
3. UK buys only bombers, using its existing forces mainly as defense.
4. The revised SBR rules of A&A:50 are in effect. ie. The damage caps on Berlin/Rome are 20/12 IPCs respectively.
Now for some statistics:
1. A Bomber deals 3.5 IPCs of damage on average per SBR
2. Statistically, the bomber is shot down on its 4th Turn (51.78%)
P(n=4) = 1 - (5/6)^4 = 0.5178
3. The bomber deals 10.5 IPCs of damage during its life span, a net loss of -1.5 IPCs
3*3.5 = 10.5 IPCs 10.5 - 12 = 1.5 IPCs
**What if the bomber manages to survive past the 4th Turn? **
1. For each successful bombing mission beyond the 4th, the bomber replaces itself.
2. The Expected IPC damage of a bomber is then 17.5 IPCs.
E(X) = Sigma(Profit/Loss Margin * P(X)) = +5.5; 12 + 5.5 = 17.5
Breakdown:
Rd Profit/Loss Margin Probability Net Probability
1 -12 0.1667 0.1667
2 -8.5 0.1389 0.3056
3 -5.0 0.1157 0.4213
4 -1.5 0.0965 0.5178
5 +2.0 0.0804 0.5982
6 +5.5 0.0670 0.6652
6 +24 0.3349 1.0
Results:
1. From a cost/benefit standout, Strategic Bombing provides an effective tool in the Allied Arsenal.
2. A single bomber’s worth is entirely dependent on whether it gets shot down on the 4th or 5th turn. However, a group of bombers delivers a significantly higher expected profit.
Comments:
1. Allies have a larger IPC base than Axis and can afford a war of attrition. Bombers fit into this role ideally.
2. It takes very little “skill” to conduct a SBR campaign.
3. Bombers are multipurpose and have the range to strike targets of opportunity. A corollary cost/benefit analysis should be used to determine which mission bombers should be sent on.
Actually, you should expect to take 12 * 1/6 in damage to your bomber per run. That’s an average cost of 2 IPC per round per bomber received for every 3.5 IPC per round per bomber dealt. (This is how we calculated SBR costs in AAR.) So technically speaking, every 6 rounds you’d lose the equivalent of a bomber.
6 Rounds * 3.5 IPC Damage Per Round = 21 IPC Damage per Bomber doing nothing but SBR runs.
Cost of the bomber: 12 IPC.
Net Gain: 9 IPC
So when would you break even? By the fourth round of SBRing, per bomber, you should have exceeded the cost of the bomber in damage to your enemy. (3.5 *4 = 14 IPC, Cost of a bomber is 12 IPC.)
On the 6th raid it gets shot down, so it’s 17,5 in damage on average, because AA guns fires before the bomber rolls during SBR attacks.
On the 6th raid it gets shot down, so it’s 17,5 in damage on average, because AA guns fires before the bomber rolls during SBR attacks.
Po
Actually this is right. I calculated my probability wrong. The expected value is 17.5
yes now calculate the radar tech hitting your bomber at a 2 or less… bombers go bye bye and dont pay for themselves if used that way.
yes now calculate the radar tech hitting your bomber at a 2 or less… bombers go bye bye and dont pay for themselves if used that way.
No reason to. If I saw my opponent pursue this strategy, I would question his ability. Apart from radar, the Air and Naval technology chart doesn’t really help Germany, aside from Jet Fighters. You could make an argument for Heavy Bombers, though I question where Germany’s bomber fleet would come from. Long range fighters, improved shipyards, and supersubs seem of marginal value to me.
Your chances of hitting Radar are rather slim. Let’s be generous and say for ever 4 dice rolls Germany unlocks a tech. Let’s also state on the third tech Germany unlocks Radar. Germany spends 60 IPCs to unlock Radar, equal to 5 UK bombers. Those 5 bombers have SUCCEEDED. They’ve forced Germany to divert precious resources away from Tanks, Infantry, or Fighters. 60 IPCs buys 20 Infantry.
Remember, the Allies can afford to trade time and space. The Axis can’t. Meanwhile the UK’s bomber fleet is still intact. They can divert to Rome, via the Stalingrad airstrip, or bomb targets of opportunity.
Again, you could make the argument that tech rolling unlocks other technologies as well. Which is true. Except, techs generally hit diminishing returns after the first. Having heavy bombers and jet fighters means Germany has to invest in both to maximize their potential.
A better approach would be for Germany to tech into Increased Factory production. At least then Germany can unlock other useful tech like war bonds, mechanized infantry (I question how well Germany is doing in Russia), and rockets. It still seems like a rather Hitler-esque stance. The SBR Campaign upsets you, so you decide to invest in V2 Rockets to exact revenge. We saw how that turned out.
As they say in Magic, “There are never wrong threats, only wrong answers.”
The same argument can be applied to UK investing in Heavy Bombers. Sure, you unlock better bombers, but you lose out on the opportunity costs. Would you invest in better bombers (60 IPCs worth), rather than buy more? Quantity has a quality of its own too.
you’re of course assuming that the game goes for a long time, and japan doesn’t mop up the pacific with ease as both the uk and us are focused on europe, right?
tin_snips,
First some stipulations:
1. The Allies commit totally to Europe.
Yes. We neglect Japan completely. This isn’t any different as per KGF strategy. However, instead of making pertinent decisions, all the UK is doing is sending bombers to Berlin like a mindless gobot.
The Pacific rim falls and Japan takes Moscow. But the Allies should be able to contain and expunge Germany. UK then turns its bomber force to Moscow, making it inhospitable to the Japanese.
God, I’m sounding like Churchill already.
i can see how you enjoy the statistical side of things, but it just doesn’t seem like a very good strategy. it isn’t fun, and japan could quite easily afford to repair any damage to its industry in captured moscow. So soon enough germany is liberated, and it becomes a long war of attrition
think of the fun side of things! devoted german player :cry:
Good point. This strategy actually came from my sister, TM. In the old days, after Germany had fallen, she would relentlessly bomb the heck out of Moscow (Japanese controlled). It made life hell for the Axis player (me) because even though Moscow was worth 8 IPCs, I was losing 20-30 IPCs a turn to her wing!* Not even the Japanese could afford to lose that much each turn!
However, because of rule changes, the damage cap on Moscow is set at 12 IPCs (A&A:50). Perhaps the UK may actually have to do something useful like build a landing navy. Infantry backed up 6-7 bombers is still scary.
I like having fun too, but if I had to play 2-player game (where keeping track of 3 nations can be overwhelming), this is a worthwhile strategy.
yeah, got to hate those players who always get the good roles haha
There is one thing that’s different with the AAR bombing the hell out of you strategy:
Germany won’t lose more than 20 ipc a turn and that’s only if she wants the maximum production in Germany which means 10 inf at the cheapest, so Germany will only start thinking about repairing for 20 ipc when she cashes 50 ipc or more.
In reality Germany will probably repair between 10-20 ipc a turn, depending on how much cash she has. Let’s say around 38 ipc on hand. That would mean repairing 17 ipc of damage and still buying 7 inf a turn. Not much, but don’t forget there is one country less fighting you on the land = UK.
This is of course without taking tech into account (if Germany repairs 2 at 1 IPC bombing is hardly effective) plus Germany might also have an IC in France which means you need to bomb 32 damage each turn on France + Berlin to get the maximum. That’s 9 bombers… With UK income going down the drain each turn I am not sure UK can keep that air force flying.
If Japan goes to America instead Moscow, USA is tied to that fight so they cannot aid Africa or Europe. Japan will get enough money to make both american and asian campaigns or try a own SBR campaign over USA.
And rolling land techs is a simple counter, as someone said
Driel310,
Germany won’t lose more than 20 ipc a turn and that’s only if she wants the maximum production in Germany which means 10 inf at the cheapest, so Germany will only start thinking about repairing for 20 ipc when she cashes 50 ipc or more.
In reality Germany will probably repair between 10-20 ipc a turn, depending on how much cash she has. Let’s say around 38 ipc on hand. That would mean repairing 17 ipc of damage and still buying 7 inf a turn. Not much, but don’t forget there is one country less fighting you on the land = UK.
True. Though I think it’s optimistic to believe Germany is earning 38 IPCs at turn. In this case, none of the Allies are doing anything right. A more realistic estimate would be ~25 IPCs a turn. That’s roughly 7 Inf a turn, which like you said, means Germany has to repair up to 17 IPCs per turn.
You send 5 bombers to Germany, expecting one gets shot down to AA. That’s 14 IPCs per turn. You avoid damage runoff this way (any damage beyond 20 is lost) and damage to the factory is residual, unless Germany pays to repair it. The cost is 12 IPCs per turn (that one UK bomber), though that expected number is actually less. 14 IPCs of damage per turn is half of Germany’s economy.
To create this bomber fleet UK has to invest in 5 bombers (60 IPCs / 3 turns), plus one extra to replace the bomber lost each turn. The UK also makes ~25 IPCs per turn, meaning once it’s set up it’s bomber fleet, it pockets about 16 IPCs per turn. That 16 IPCs could be used on another bomber for an Italian campaign.
So yes, UK is removed from the mainland, but (1) it deals a significant portion of damage to Germany’s wartime economy (2) it has enough money left over to start an Italian SBR campaign as well.
This is of course without taking tech into account (if Germany repairs 2 at 1 IPC bombing is hardly effective) plus Germany might also have an IC in France which means you need to bomb 32 damage each turn on France + Berlin to get the maximum. That’s 9 bombers… With UK income going down the drain each turn I am not sure UK can keep that air force flying.
Germany investing in tech to solve the SBR is generally not a good idea for reasons I’ve explained.
What if Germany counters by building a factory in France? In a vacuum, a France IC is a German misstep. A simple counter is for the UK is to drop this strategy for something more conventional and divert their fleet to Italy, where they can still deal damage.
Funcioneta,
If Japan goes to America instead Moscow, USA is tied to that fight so they cannot aid Africa or Europe. Japan will get enough money to make both american and asian campaigns or try a own SBR campaign over USA.
Answering SBRs with SBRs. Awesome idea :evil: I’ve also been experimenting with a Alaska strategy for Japan (not just for SBR but for KGF in general), though I believe it just creates a Western Canada/Alaska dead zone. I have not arrived at a conclusion to see which side benefits more.
On the other hand, a full on amphibious invasion of Western USA is a very BAD idea.
A little off topic, but: Has anyone found an India IC (for the UK) to be useful? Or do the Japanese take India too easily?
I’ve thought of a hybrid strategy to BoB titled BoR (Bombs Over Rome). It involves calculating the distance of a few airline routes, which I thought was quite “fun.”
It’s a bit difficult to explain, so let me put it in the most simplistic turns
1. First turn: UK builds a bomber and a IC in India.
2. Second turn: The UK bomber SBRs Berlin and lands in Ukraine (assuming it’s under Russian control), while simultaneously building 3 inf (9 IPCs) a turn in India.
3. Third turn: The UK bomber SBRs Rome and lands in the Caucasus.
4. Forth turn: The UK bomber and combined UK infantry force storm Burma. The UK bomber lands in Caucasus.
5. Fifth turn on: The UK bomber can continue to bomb Rome, create a Burma deadzone, or eventually bomb Berlin again going the Caucasus -> Gibraltar -> Berlin -> United Kingdom route. Also from its Caucasus airstrip the bomber can raid the Italian navy! :evil:
The best part is the bomber is always doing something active! The bad thing is this relies on several things happening, including Ukraine in Russian hands and that the Japanese don’t overrun India (which I fear after the first time BoR is employed, will ALWAYS happen).
But think of the frequent flier miles! Join the RAF, See the World! 8-)
Anyways food for thought…
@TG:
If Japan goes to America instead Moscow, USA is tied to that fight so they cannot aid Africa or Europe. Japan will get enough money to make both american and asian campaigns or try a own SBR campaign over USA.
Answering SBRs with SBRs. Awesome idea :evil: I’ve also been experimenting with a Alaska strategy for Japan (not just for SBR but for KGF in general), though I believe it just creates a Western Canada/Alaska dead zone. I have not arrived at a conclusion to see which side benefits more.
In Revised, the dead zone meant allies cannot reinforce Africa very much to fight against Japan and reduced USA to 35 IPCs (assuming soviets don’t defend China). I think this gives advantage to axis, and if you can take and hold wcan as Japan you can collect 55 IPCs easily. SBR on un-aa gunned Eusa … priceless …
Not sure how it will work in AA50 (USA gets 40 because of NO, but Japan get’s more than 60). I wish it will work well or I’m stuck to play allies if I want avoid KGF :|
TG Moses VI:
my analysis of this is much simpler than yours:
taking aside any strategic considerations, I do the following cost-benefit analysis:
The Net Benefit of SRB is: Expected Gain (IPCs taken from the enemy) - Expected Cost (cost of loosing the BB)
Expected Gain (EG) = Average Damage Yield by SBR * Probability of BB surviving the AA
In numbers: EG = (1+2+3+4+5+6)/6 x 5/6 = 2.92
Expected Cost (EC) = BB Cost * Probability of Being Shoot Down by AA
In numbers: EC = 12 * 1/6 = 2
So, in AA50: SRB Next Benefit is: 2.92 - 2 = 0.92
If you’re risk neutral, you should bomb
In Revised, the numbers for EC were: 15 * 1/6 = 2.5
Hence EG - EC = 2.92 - 2.5 = 0.42
So it was still a ‘rational’ choice, only that you’re expected gain was smaller
comments? thoughts? Am I missing something?
Yes, that’s another correct way of looking at it. It’s more similar to casino odds.
To add on these numbers, what is the expected gain of a bomber attacking the following units?
1 Bomber vs 1 Infantry = (4/6 * 3) - (2/6 * 12) = -2.0 IPCs
Bomber vs Battleship (2 hits) = (4/6 - 20) - (4/6 * 12) - (4/6 * 12) = -2.67 IPCs
Bomber vs Tank = (4/6 * 5) - (3/6 * 12) = -2.67 IPCs
Bomber vs Fighter = (4/6 * 10) - (4/6 * 12) = -1.33 IPCs
Bomber vs AA Gun (SBR) = +0.92 IPCs
Bomber vs Destroyer = (4/6 * 8) - (2/6 * 12) = +1.33 IPCs
Bomber vs Cruiser = (4/6 * 12) - (3/6 * 12) = +2.0 IPCs
Bomber vs Aircraft Carrier = (4/6 * 13) - (3/6 * 12) = +2.67 IPCs
Bomber vs Factory (without AA) = +3.5 IPCs
Bomber vs Transport = +7 IPCs
Whoever knew the two greatest fears of a bomber were attacking tanks and battleships – two of their favorite targets during the war? :wink:
This UK bomber only strategy implies a 2 player contest because I can’t imagine anyone sitting down for 4 hours and only making SBR dice rolls. yawn The game is supposed to be fun! If I’m UK I’m building a S. Africa, India, or Australia IC and defending expanding my empire! Axis and Allies is best played 1 player per nation in my opinion.
TG you need to review the changes for AA50 a bit more. Now when you purchase a tech dice you get to roll it every turn until you get the tech. I can not see why the US would not be involved in a SBR campaign as they now start with 2 bombers in '41 and 3 bombers in '42. There is also Italy to consider bombing back into the stone age. They make limited money and are the weakest Axis power.
And my personal take on SBRs is all that cost analysis is just an exercise for amusement. It does not take into consideration where the damage is done and how that affects an opponent.
