Strategic Bombing Raids Don't Work

[Guest]

Where did you come up with the 15ipc damage from the original thread?

If you say the average roll of a 6 sided die is a 3 then we need some math lessons. It is 3.5 because you cann’t roll a 0.

That means you do 18.5 wirth of damage (on average) if yuo get hit on the 6th SBR before you fire. Kinda’ like having 2.3 kids I guess.

Dan

[Ozone27]

As is so often the case, SUD is correct. :wink: A slightly more succinct way of putting it would be that SBRs are a gamble, but the gamble sometimes pays off. The key is the gamblers’ credo: never gamble what you don’t want to lose. If you can’t afford to lose a BMR–don’t SBR! For instance, I like the idea of using both the Japan & Germany BMRs early in the game to joint SBR USSR. Your starting BMRs cost you nothing & if you don’t hurt USSR early, then you may never! Try flying the Japan BMR to Western Europe afterwards. The opportunity to do even more damage with it later may present itself…

On the other hand, I dislike the strategy of buying all BMRs for a turn and using them to SBR. This is a big investment and if you lose the BMRs, you lose big. Plus you may find an opportunity to invade a territory wasted later due to insufficient manpower. Vs. the opportunity to sieze a territory, SBRing loses big. Think INF first, SBR waay later…

Basically consider SBRing tactically, not strategically. Do it on a turn by turn basis and when the situation changes, cancel it. I believe strategic bombing is only worth it in situations where the target is vulnerable; that is, when they need every last dime to get what they need for the next turn. Germany is usually in such a state. Any power that is losing ground & falling back defensively may also be vulnerable. What you DON’T want to do is rely on a strategy of SBRs to win you the game. You may win some spectacular victories, but the strategy will eventually fail more often than it succeeds…

If you’ve got Rocket Power, the situation changes somewhat. Small SBRs on the same power you are Rocketing yield bigger dividends than normal due to the additional rocket damage. Consider this fact before moving…

Ozone27

[mike_105]

boming raids work very well for every ipc that germany loses thats one ipc the ruskies wont be fighting against.

[Guest]

Ah’m waiting for TG Moses VI to speak up about the evils of SBR.

He should know, KA-BOOM! His evil sister(?) did it to him several times,
if my perusal of these records was correct :P .

[Guest]

I’m not sure why you guys keep talking about how much damage the bomber would do by the 6th turn. On average, it’ll die on the 3.5th turn. And doing 3.5 damage per turn, means that it will inflict 12.25 IPC of bombing cost, not 15, or 18.5 or whatever.

Well, that’s just my 12.25 cents anyway.

[Xi]

Averaging, Kev, averaging!
And I don’t think 12.25 fits the bill.
If you atttack and average 3.5 IPCs in three turns your opponent will lose 10 or 11 IPCs. Whereas he will lose 14 IPCs by turn 4.
As you didn’t buy the BMR it.

Oh, ****! Where are those stats again? :roll:

[Guest]

The probability for not get a hit from an AA gun during 6 runs is actually a bit more then 33% so I think that’s a risk well worth to take.

[BigBlocky]

Kev, actually, it’s incorrect to say the bomber will die by the 3.5th turn. There is only a 16.67 % chance to lose a bomber. The best assumption to make is if you send 6 bombers you lose 1. Each bomber does on average 3.5 IPC times 5 bombers means statistically you can do 17.5IPC for each 15IPC you spend on bombers. I’ve written computer simulations where the attacker starts with 6 bombers, builds a bomber then does an attack with the intial 6 bombers against a IC with an AA. I ran 10, 000 trials and the average IPC total was 17.48 IPCs. Take from that what you may.

BB

[Guest]

My brothers and I play a lot of A&A (online) and we have noticed that we get a lot of 5’s and almost never lose a bomber. I bet 3 of 4 rolls are 5’s. I have seen 1,3,6 only a few times in maybe 500 SBR’s and have seen only slightly more 2 & 4’s. We have had to limit the total numbers of bombers owned by a country because they never get hit and do way to much damage.

Anyone else encounter this problem (well it’s not a problem when you are the one doing the bombing)?

[BigBlocky]

The more dice your roll the more the odds work out to an even distribution. There is no magic or supernatural force, in time the odds work out. If you count on ‘dice’ to win then you never lose by somebody else’s superiour strategy, you merely always lose because of dice. Good players rarely win or lose based on the dice rolls.

BB

[C_F]

I don’t want to be rude, but I can pretty much gurantee you that if you rolled 500 times for AA that about 1/6 of your bombers died. The ones that made it through did almost exactly 3.5 IPC’s of damage per bomber. If you want to bet that 3 of 4 of your rolls are 5’s. I will give you 100 to 1 , we can roll 500 times, and I would put every dime I own on it.

[Guest]

Most people argue that doing SBR results in the loss of 1/6 bombers and the bombed player will loose 5/6*3.5 IPCs. This costs the attacker 2.5 and the defender approximatly 3. Hence mass SBRs should work.
I think this is the correct answer to the wrong question. The more interesting question is:
How long does it take for a bomber to pay off?
If you are going to SBR your enemy you have to spend 15 IPCs, but before you knocked 15 IPCs out of you oponent the game might be over.
Actually the game would have to last 11 rounds of SBR for an estimated damage bigger than 15. The chances for hitting at least 15 within 3 rounds are mere 5%. The chances of hitting at least 15 within 4 rounds are 15%.
Buying a bomber for SBRs is certainly not a good idea, using a bomber you allready posses might be reasonable, but their might be better thing to do with it.

The Math:

1st: (5/6)^1 * 3.5 ~ 3.0 (overall 3.0)

2nd: (5/6)^2 * 3.5 ~ 2.4 (overall 5.4)

3rd: (5/6)^3 * 3.5 ~ 2.0 (overall 7.4)

4th: (5/6)^4 * 3.5 ~ 1.7 (overall 9.1)

5th: (5/6)^5 * 3.5 ~ 1.4 (overall 10.5)

...

On the long run it pays off, but you won’t live long enough to see the long run.

[BigBlocky]

On average a bomber does 3.5 IPC so it should pay off in 4-5 rounds not 11, factor in the 1/6 loss issue and its about 5-6 rounds.

An issue that nobody mentions with SBR is the effect of ‘over bombing’. Obiously the goal is to bring the enemy close to zero IPC. In order to ‘average’ this sometimes the enemy gets over-bombed, doing 35 IPCs and the enemy having less. I’m not sure how often that occurs as I rarely use SBRs as as tactict. I often find that using bombers in my many battles pays off more by getting battles over quicker and thus losing less peices. This often has the effect of making the surviving force just that much stronger and often means too strong to counter-attack in a cost effective mannor.

BB

[Ozone27]

As I stated before & after looking at the numbers it seems to me that SBRs are something you utilize on a medium scale (2-4 Bombers) spreading the risk among as many of your friends as possible on a turn-by-turn basis ONLY. That is, you & your Allies have available BMRs (that is, BMRs not required to achieve that round’s objectives) within range of an enemy that cannot afford to lose the troops it can be expected to purchase next turn. The way I see it, this means an enemy already reeling, but having enough IPC’s to make a nuisance of themselves the next turn (or the following turn) w/ what they purchase. For instance if USSR had just lost a major battle vs. the Axis, but had enough cash on hand to buy a lot more troops. In this case, a 2 BMR series of raids by Germany & Japan might yield good results with less risk than if they attacked from a position of weakness. It’s a gambler’s choice…

But it’s NOT a strategy…

Ozone27

[Guest]

If you could be sure your bomber survived 5 rounds this would result in 5 * 3.5=17.5 expected damage, but you can’t be sure. The probablitiy that your bomber will be present in the n-th attack is (5/6)^n. So you have to multiply this probability with the expectaion value of 3.5. This results in the given figueres. On the long run this, geometric, series will converge to
(5/6)/(1-5/6) * 3.5 = 5 * 3.5 = 17.5
The ratio 15 / 17.5 is the same as
(5/6 * 3.5) / (1/6 * 15)
mentioned in other posts.
But it will take 11 turns for reaching 15.
((5/6)^12 - 5/6)/(5/6 - 1) * 3.5 = 15.1

For information on the geometric series see
http://www.wikipedia.org/wiki/Geometric_series

[BigBlocky]

A geometric series is not the proper tool for this. I think you’d need to use a stochastic model, it’s been years since I got my B.Sc in Computer science so I don’t have any links to back it up.

Why make things complicated when simplicity will do.

Premise #1:
I think we can all agree if you had 6 bombers on a raid, statistically speaking, you should lose 1 bomber.

Premise #2:
Each surviving bomber will do 3.5 IPC

Premise #3:
5*3.5=17.5

Conclusion
If you spent 15 IPC per turn for a bomber, started with 6 bombers, you on average will do 17.5IPC per round.

This is called a sound argument. If all the premises are true then the conclusion must also be true. Prove 1 of my premesis wrong and my conclusion is not logically true.

However it is statistics. Did you hear about the three statisticians who went on a hunting trip? They see a deer, the first statistician shoots and misses 5 feet to the left, the second statistician shoots and misses 5 feet to the right. The third statistician yells out “BULLSEYE!!!”……

The 15:17.5 payout ratio does not take into effect what those bombers could have done if they were used in a land or naval battle instead. They do not take into acount the cost of losing your only bomber. Losing your only bomber means your reach is less and your enemy has less to defend against. 1 bomber plays havoc with plans requiring a 1-2 transports to move through it’s area of reach.

I totally agree with Ozone, SBR are not a strategic, merely a usefull tactic in some situations when the opportunity or need presents itself. Using SBR has a strategy locks you into 1 mode of attack.

BB

[Guest]

@BigBlocky:

A geometric series is not the proper tool for this. I think you’d need to use a stochastic model, it’s been years since I got my B.Sc in Computer science so I don’t have any links to back it up.

I find it makes sense. :)

Conclusion
If you spent 15 IPC per turn for a bomber, started with 6 bombers, you on average will do 17.5IPC per round.

This is called a sound argument. If all the premises are true then the conclusion must also be true. Prove 1 of my premesis wrong and my conclusion is not logically true.

What you missed in your premises then is that you have to buy 5 bombers first to get to your total number of 6.
This is an investment of 60 IPCs, that you have to “refinance”. Therefore you suddenly need so much more turns.
Assuming that you already have the six bombers you need is too much and the reason for the turn difference IMO.

[BigBlocky]

On second thought, I see how the geometric series works, Meijing’s number agrees with what I stated in this thread on March 15th when describing my stochastic simulation. 15 IPCs gets you 17.5 on SBR.

I’m not sure what Meijing means with this:
But it will take 11 turns for reaching 15.
((5/6)^12 - 5/6)/(5/6 - 1) * 3.5 = 15.1

F_alk, you state the obvious, and I didn’t miss the premise you have to start with 6 bombers, I stated it…… I think you’re missing the point. I merely showed a different way to agree with what I said earlier and what Meijing eloquently proved with the geometric series. It’s merely that 15 gives 17.5 in SRB’s on average. I also stated that didn’t take into consideration what the bombers could have done instead. Your point is true as well, the cost of having bombers instead of say transports and land units is not factored into the so-called payoff ratio.

I never use SBR as a strategy outright, I do however find the opportunity to SBR with bombers that aren’t better used elsewhere.

BB

[Guest]

@BigBlocky:
Your reasoning is perfectly right. It answers the question, whether to use a bomber not used for something else for an SBR. I would do so, but only after making sure I couldn’t use it for something else.
I’m adressing the question, whether to buy a bomber for making SBRs. This answer is clearly no. As F_alk pointed out the 15 IPCs you have spend won’t pay back while the game lasts.

[Guest]

BB,

i am kind of right and wrong. Just as you stated the “steady state”, i mentioned the process of getting there.