Strategic Bombing Raids Don't Work


  • 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.


  • 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


  • 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


  • 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


  • 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


  • @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.


  • 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


  • @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.


  • BB,

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

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