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Author Topic: Strategic Bombing: Calculating odds  (Read 3386 times)
clarkc
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« on: March 12, 2002, 09:55:00 am »
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I wrote a computer program to confirm my statistical calculations on whether it is worthwhile to buy bombers to wear down an opponent with strategic bombing. First, some people in various discussions have said the bomber takes away 3 IPCs from the victim on each average roll. This should be 3.5 IPCs (average of the 6 values of a die). Second, you have a simple converging series that shows the expected value of a bomber:

1/6 chance of having a value of 0 (got hit by AA on 1st try). 5/6 * 1/6 chance of having a value of 1 die roll (got hit by AA on second round). 5/6 * 5/6 * 1/6 chance of having a value of 2 die rolls (got hit by AA on 3rd round), etc. This is a simple geometric series that sums to (converges to) 5, meaning 5 die rolls, meaning a value of 5 * 3.5 = 17.5 IPCs taken away from the enemy. This is balanced against the 15 IPC cost of the bomber, meaning that each decision to buy a bomber and devote it to strategic bombing will take away 2.5 IPCs more from your opponent than it will take away from you, and it will take an average of 6 turns to do so. That is a VERY SLOW way to wear down an opponent. Note that using the incorrect value of 3 per die roll, instead of 3.5, makes the bomber purchase a wash.

Now, if you are Germany and you are hemmed in and just waiting for rescue by Japan, and you have a bomber with which you started the game and have no good way to use it any more (Africa totally fortified by USA/UK, Finland/Norway captured by USA/UK, no paratrooping opportunities, Allied fleet too big to attack, etc.), then you might as well consider the bomber to be worthless and use it on strategic bombing against USSR. That helps Japan gain ground on USSR, and your net expected benefit is the reduction of 17.5 IPCs from the USSR before it gets shot down. Once it gets shot down, you are certainly not going to replace it; 5 infantry are much more sensible.

For groups of bombers, the math is exactly the same on a per-bomber basis.

For heavy bombers, the expected value is (3 * 17.5) minus the 15 IPC cost, rather than 17.5 - 15. So, instead of 2.5 IPC net over 6 turns, it is 37.5 net over 6 turns, a factor of 15 improvement in wearing down an opponent.

Fo regular bombers, only use bombers you already have and have no other use for them in the long run. Consider also that you lose 15 IPCs right now, when you buy the bomber, and it takes 5-6 turns to extract that many from your opponent. Time is very valuable in this game. Earlier IPCs are better than later ones.

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Usul513
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« Reply #1 on: March 12, 2002, 10:05:00 am »
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You are overlooking a very basic thing about bombers, they are not restricted to only doing SBR's.  If you get a bomber and use it for a turn or two to SBR, you may then take it the next round and take advantage of its high attack roll. I agree that buying bombers simply for the purpose of SBRs is a waste of money(unless you got heavies).  I prefer to use Germany's bomber to support attacks on ships, especially against the US East Coast. My point is, if you stick to a rigid method of only using each bomber for one purpose, you lose room to maneuver.
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clarkc
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« Reply #2 on: March 12, 2002, 10:29:00 am »
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I was just addressing one question in isolation: Buying bombers for strategic purposes. Lots of people seem to be advocating it as if it were obvious that it pays off. Some make it sound like it is devastating.

Also, if you plan to do strategic bombing for 2 turns and then use it for attacks, there is about a 30% chance that the bomber will be gone. You could have had three tanks for your attack (three tanks beat 1 bomber in ground attacks) or 5 infantry (even these are better than 1 bomber in an attack!)

Economically, planes only make sense when their range is required, or when the presence of fighters on an aircraft carrier is required. For antagonists sharing a continent, attacking each other from bordering territories, infantry and tanks are the only purchases that work out, along with an AA gun to defend a new factory. It's boring to buy nothing but infantry and tanks, I realize, but until range becomes an issue, the numbers are all on their side.
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HortenFlyingWing
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« Reply #3 on: March 12, 2002, 12:14:00 pm »
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an average roll is 3.  a flak gun will hit a bomber one out of 6 times (by chance.

strat bombing is a gamble, because if everything happened perfectly, you lose equal to the amount you spent on the bomber.  strat bombing must be done to a country that is running out of ways to make money, or otherwise it is almost a waste of time.
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Candyman67
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« Reply #4 on: March 12, 2002, 12:27:00 pm »
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Your numbers don't lie but many of the countries in A&A have multiple enemies that need to use the seas.  How are you gonna take out a naval fleet or unprotected transports with tanks or AA guns?  That is another importance of an airforce.
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dezrtfish
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« Reply #5 on: March 12, 2002, 01:00:00 pm »
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Horten,
1+2+3+4+5+6=21
21/6=3.5


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dezrtfish
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« Reply #6 on: March 12, 2002, 01:13:00 pm »
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using this logic I belive it can be a good I dea for the US to buy bombers though because trading IPCs with Germany can upset the ballence in europe in favor of the Allies.

If for instance the US bought 1 bomber a turn for strategic bombing they would begin to slowly strangle germany starting on turn two while britain could lend aid in the form of troops to Russia.  The US would still have a minimum of 17 IPC to assist the British navy to recovery.
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HortenFlyingWing
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« Reply #7 on: March 12, 2002, 02:29:00 pm »
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ok... it is about a 3 smiley  good rollers make it even harder to strat bomb.

Don't getme wrong, i'm an airforce kind of guy.  but only for fleets and defense.  i would rather buy a tank for land.
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Candyman67
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« Reply #8 on: March 12, 2002, 02:33:00 pm »
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I agree Red.  I guess I should address you as Mr. Red sir.  Hah.
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TG Moses VI
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« Reply #9 on: March 12, 2002, 04:15:00 pm »
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By the time USA polishes off Africa, I could see America investing in a large bomber force.  Hey, it worked in history and you don't have to deal with pesky fighters.  
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clarkc
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« Reply #10 on: March 12, 2002, 04:57:00 pm »
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Red has a good point, that the USA can trade IPCs with Germany using strategic bombers, which is a win for the Allies, since it leaves UK and USSR versus Japan. The other good thing about buying bombers is that it takes no imagination and you can start doing it now, without worrying about whether your navy can survive after your first round of purchases (or do I need to save up and buy 2 rounds worth of navy on one turn, to survive an air attack?)

Bombers can always be bought and used without much calculation. They are just about a trade-off, though, whereas other purchases might be better than that.
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Candyman67
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« Reply #11 on: March 12, 2002, 05:37:00 pm »
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It worked marginally in WWII, may I add.  Why not emulate history by having the British build a large bomber force and blow up the joint?
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TG Moses VI
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« Reply #12 on: March 12, 2002, 06:51:00 pm »
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The problem with buy bombers for both UK and USA is that the Allies run the danger of risking too much for too little.  For the Allies bombers will mostly be spent just for strat bombing as Germany lacks undefended heavily undefended territories or a Navy and Japan is too far to hit effectively.  Strat bombing is basically just an investment for the feature.  As said before it'll take 5-6 turns before a bomber's worth can truely be felt and by time the Axis may already have one the game.  If you're looking for something for new for USA instead of just building up for D-Day, why go for the Pacific.  You'll probably make more money conquering islands than bombing.        
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Candyman67
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« Reply #13 on: March 13, 2002, 09:09:00 am »
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Though I here what you are saying, the key I think is to take as many IPC's away from Germany as fast/much as possible.  Do I think industrial bombing will completely turn the tide?  No, not really unless one gains heavy bombers.  But I do think industrial bombing over time will lead to a stalemate on the Eastern Front.  

Let's figure: Germany has less IPC's meaning less forces to buy, plus Germ. needs to send forces to defend Western Europe from an invasion.  Russia builds its forces places them in Karelia.  Plus, Britain is sending in a few transports of infantry each turn plus a fighter now and then.  That is a recipe for stalemate and that is the best thing that could happen to the Allies.
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dezrtfish
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« Reply #14 on: March 13, 2002, 09:51:00 am »
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I'm going to type up my American Strat and post it for you guys to try to trash, this bombing Idea is a big part of it.

As for you Candyboy when ever you ready to be thrashed by an ond man just let me know.
tongue
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