SBR revisited - some new algebra



  • In a previous thread, it was discussed whether SBR was worthwhile. Here is some algebra that may make you think again.

    Probability a bomber is shot down = 1/6 (denoted F)
    Probability a bomber survives = 5/6 (denoted S)
    Average IPC damage (providing bomber is not) = 3.5

    As correctly pointed out, the expected (average) IPC damage a bomber will do before being shot down is 17.5 IPC’s.

    However, the calculation that follows determines the probability that the bomber will make a profit (ie cause more than 15 IPC’s of damage before dying).

    Shot down__Profit/Loss_Probability
    on round
    1__________-15_________0.1667
    2__________-11.5_______0.1389
    3__________-8.0________0.1157
    4__________-4.5________0.0965
    5__________-1.0________0.0804
    Sum____________________0.5982

    6__________+2.5________0.0670

    6_________+21_________0.3349
    Sum____________________0.4019

    It should be noted that any one bomber has a 59.8% chance of surviving less than 4 rounds, and thus making a net loss of IPC’s.

    The expectation value is scewed by the high profit if the bomber is not shot dwon by round 6, but as you can see, the probability of this happening is rather low (1/3).

    This is an interesting facet of SBR not highlighted by many people. So, unless you have a large number of bombers to average out the results, you only have a percentage chance of making a profit.

    Hope that helps

    Stu

    PS sorry about the table - hope that works.

    [ This Message was edited by: Desert_Viper on 2002-03-28 05:56 ]

    [ This Message was edited by: Desert_Viper on 2002-05-13 13:16 ]



  • whoa, very good! I could of not figured that out…I like history, not math!



  • i dont see how you can look at it that way, i mean really. Suddenly you have to be Spock to bomb somebody.

    [ This Message was edited by: Mr Ghoul on 2002-03-28 15:53 ]



  • 59.8% sounds great, but it’s still a little too low for my taste and investments. The table was nicely done and it really is great for calculating probability on a turn by turn basis. Howevers, actually rolling the dice are a different factor altogether, but hey, what can you expect?



  • yes, people who play craps don’t rely purely on luck.



  • That is so true. Before I learned to play Craps, I thought it was this “no strategy involved game” (sort of the Keno or Slotmachines) where all the money rode on whether or not you could hit the magic number. However, after I learned craps, I found it was an intricate and complex game (seriously craps is like 3 games in one) that required years of pratice and skill to master. Now whenever I walk by a craps table, I know you don’t have to be the one rolling the dice to win (or lose) money.



  • On 2002-03-28 14:54, Mr Ghoul wrote:
    i dont see how you can look at it that way, i mean really. Suddenly you have to be Spock to bomb somebody.

    LOL! 😁

    …really though, keep in mind that the Allies, if they work together, don’t really have to necessarily get perfect “value” out of each piece like the Axis do: might be one reason why SBR seems to work better for them than the Axis–though I am still partial to German-Japanese joint bombing of USSR.

    Also, 4 of the 5 countries start the game w/ a BMR–this could be counted as “free” to whomever’s keeping score…

    Cool way of looking at this…thanks for the info…

    Ozone27

    [ This Message was edited by: Ozone27 on 2002-03-28 21:13 ]



  • Well the only way for the Axis to take away Russian IPCs and territorial gains would be through SBRs by Germany and Russia. And since bombers have a range of 6, it allows you with the versatility of choosing to either SBR or just make regular attacks.



  • yes, it sucks if you attack somewhere with 5 aircarft and you lose three.



  • Just losing any amount of aircraft for Germany or Japan is bad enough. This usually never happens since German fighters should always be protected by inf. in a land attack and by subs in a naval battle. A lot of the time you’ll just see ftrs. as a deterant to an attack.

    There are a lot of times though (especially in A&A:CD) where transports or AA guns will score an unholy amount of hits on fighters. So be sure to watch out for this.



  • Germany and Japan’s 5 fighters are vital. There is no way they could replace them any time soon.

    That’s why that one stinkin’ AA gun in karelia is so annoying!



  • Yeah, that AA gun in Kerilia is a real killer. In this one A&A game I played (and this was in the CD version), I [Germany] lost 3 out of 4 fighters (along with my only bomber) due to AA gun hits! After that battle (which I was defeated on all turns), I refrain from placing my Luftwaffe in any unnecessary danger.


    Never before have we had so little time in which to do so much

    [ This Message was edited by: TG Moses VI on 2002-03-30 21:53 ]



  • What if you move the AA gun in Karelia out? I assume you can’t move the gun on your Non Com move the turn you take Karelia (though that’d be cool if you could!), but if Karelia were untenable after a round or 2 you could move the AA gun back to Eastern Europe where it’d do you a lot of good and the Russians none…

    Ozone27



  • that’s what i do, but usually russia can muster a good counter attack.

    you seem damned if you don’t use aircraft on the attack against karelia, thous extra 3 and 4s or lesses do a lot.



  • I would say hitting Kerilia with ftrs. is a must since you can still fly all the way from Western Europe to your target. But in the CD-ROm game, I’ll just make sure I won’t.



  • you got a major grudge against that game!

    i guess they wanted to “balance” it.



  • Balance it!? Yeah like the Germans don’t have any other problems the way it is. Oh well at least when the play A&A:CD I see the Russians getting screwed a lot. I swear Russian inf. can’t defend for carp.



  • BMRs are better used as part of a INF/ARM/FTR land attack…especislly where there are no AAGs. However, as stated previously, the Allies can afford to lose BMRs in more SBR scenarios than the Axis(BUT, a combined Axis SBR bombing of Russia is ideal!)


Log in to reply
 

Suggested Topics

  • 8
  • 8
  • 8
  • 6
  • 6
  • 5
  • 5
  • 17
I Will Never Grow Up Games
Axis & Allies Boardgaming Custom Painted Miniatures
Dean's Army Guys

62
Online

14.6k
Users

35.2k
Topics

1.4m
Posts