Posts made by 03321

@Rakeman:

Law of large numbers.

I’d hardly call the 30 rolls involving a long-term SBR campaign against Italy over the course of an entire game ‘large numbers.’  Compared to regular battles, SBR involves very few die.  I agree, though, that the average net gain more than doubling from Revised to AA50 will cause SBR to be used more extensively (as I already said).

@Rakeman:

What’s to stop the Axis from using the same bomb-to-death strategy against the UK?  Russia.

What’s to stop the Axis from using the same bomb-to-death strategy against Russia?  The UK.

Germany can buy 1 bomber every turn or 2 in Revised and get away with it until US comes in on a full KGF.  Why wouldn’t they be able to in AA50?  The question is more about whether US will actually need to pay attention to Pacific, which I (and I think 1 or 2 others) said a long time ago in another thread.  If they don’t then they should be the one to employ the all-out SBR tactic, imo.

And by the way, if UK purchases nothing but bombers to try bombing Italy into submission, they’ll have basically no navy after UK1.  They’ll have to wait until UK2 to buy some of that navy, and by i2 Italy should easily have taken Egypt.  So now Italy is pushing through Africa, while UK probably can’t even land in Algeria yet, due to Germany’s air.  Though maybe they’d have enough combined with help from US.  On the other side of the world this means Japan should be able to take India without much trouble as UK didn’t reinforce it.  So UK’s down to what, a low-20s income?  And then they lose the rest of Africa and drop into the teens.  I tend to think it’s going to be a bit more trouble for them than simply bombing Italy to submission and swatting them out of Africa.  Certainly, I think that supporting a conquest of Africa with bombing against Italy will be helpful…game-breaking, I don’t think so.  But hey, I could definitely be wrong.

They played that game without national objectives, so that would make some difference.  And I’m pretty sure the people playing Axis admitted they didn’t play well.

@marechallannes:

Bombers are expensive!

Not anymore.

At 12 IPC bombers offer more offensive punch/cost than fighters, it seems bombers will be all over the place (maybe even some Russian bombers!), and because they cost less SBR is now a better investment for your money.

As for bombing Italy to death…consider a scenario where Italy takes out Egypt early and claims the rest of Africa.  UK’s going to be as low if not lower than Italy in income.  So, what’s to stop the Axis from using the same bomb-to-death strategy against UK?  Or Russia for that matter.  Personally, I think SBR will be used more extensively in AA50, possibly even with full strategies centered around bombing one power to a point that it can barely defend itself.  But I don’t think it will break the game.

So…after much wasted time.  This list shows exact probabilities for losing a certain number of bombers after 3 consecutive rounds bombing with exactly 6 bombers per round, as well as the average amount of SBR damage done, IPC loss worth of bombers, and the net gain for the Axis.

Bomber Losses Probability Average Damage Done IPC Loss in Bombers Net IPC Gain
0                    3.76%                 63                       0                       63
1                   13.52%                59.5                    15                     44.5
2                   22.99%                 56                     30                       26
3                   24.52%                52.5                    45                      7.5
4                   18.39%                 49                     60                     -11
5                   10.30%                45.5                    75                    -29.5
6                    4.46%                 42                      90                     -48
7                    1.53%                38.5                    105                    -66.5

This includes all possibilities for AA losses in a single round.  All outcomes of 8 bomber losses or more were below 1% probability (about .5% cumulative) so I left them out.  Anyway, I still don’t think it’s incredibly relevant since I’m not sure how realistic it is to bomb with exactly 6 bombers every round.  Whatever, it does show that in a situation like that you will have a negative net outcome just over 1/3rd of the time.

P.S. these numbers are once again without capping SBR damage

@Rakeman:

(there is a way to do it by directly getting the percent of success, but that’s more difficult because getting two 6’s and getting 1 six both yield the same result… can’t remember how to do it that way).

You take the chance of getting a hit on exactly that roll (meaning every roll before it missed) and add it to the chance of getting a hit on every other roll before it.  In other words:  (1/6) + (1/6)(5/6) + (1/6)(5/6)^2 + … + (1/6)*(5/6)^n where n+1 = number of rolls.

About the direct chance of getting rockets in AA50.  If you spend 5 IPC on tech in one round you will continue to roll an attempt to achieve a tech every turn thereafter.  So eventually 5 IPC will get you a tech, at which point it becomes a 1/6 chance to get rockets if that’s the tree you go into.  But yeah, on any given roll it’s 1/36.

@Rhineland:

I think that until someone crunches the numbers for 3 turns out for the probabilites then one can tell if this is luck strategy or actually viable.

What do you want calculated out to 3 turns?

If you want the probability for all possible #'s of bomber losses versus the average damage you’d do when you bomb with exactly 6 bombers every turn for 3 consecutive turns…that would be easy to do, but probably not very relevant.  For instance, in a round where you lose 3 bombers chances are you won’t be bombing with 6 bombers on your next round.

If you want the same probabilities for 3 consecutive turns when you start the 1st turn with 6 bombers (3 each Germany and Japan) and don’t buy any bombers after that…then that would be a little tougher and more time-consuming.  The same could also be done in a state where you buy 1 bomber any time one of the Axis drops below 3 bombers, though that would be even more time-consuming.

I could tell you right now that if you considered all outcomes (meaning anywhere from 0 to 6 aa hits in a round), without capping SBR damage, and bombing with 6 bombers every turn for 3 turns… your average net gain totalled over the 3 rounds would be 7.5 IPCs, with an average loss of 3 bombers (45 IPC-worth) and 52.5 IPCs of bombing damage done (17.5 per round).  However, it seems that we’ve come to an agreement to exclude at least outcomes involving 4 to 6 aa hits in a single round as being too uncommon to consider, which makes things a bit more cumbersome.

And, putting some more thought into the whole strategy, there seems to be more luck that I hadn’t thought of…where (assuming KGF), if Germany takes heavier bomber losses than Japan you will probably be in a worse position than if the opposite is true, since Japan can afford to replace their bombers more than Germany.  But if Germany takes light losses and Japan takes heavy losses you could have a more easily sustained bombing campaign.  Then again Germany’s IC is closer to Russia than Japan’s so maybe I’m just spewing garbage.

Alright, I hope you aren’t taking anything I’m saying as hostile bashing on this idea.  I’m really just trying to help explore the mathematical side of it.  As for the argument that people will take a 75% chance for victory, I see SBR as being different.  First, you’re not really just taking 1 SBR into account, you’re planning your entire strategy around it lasting for several turns at least, which means that 75% won’t hold up very long.  Second, the 25% downside can be pretty harsh (possible to lose 3-4x the IPC value of what you can deal to the opponent) with no way to ‘retreat’ from AA gun losses the way you can retreat from a normal battle.  I don’t think I would take a 75% chance to win a battle when trading territories over and over, which is more along the lines of what I see a constant SBR campaign as rather than just one 75% battle.

I was stupid about my calculation for the net positive outcome for bombing runs with 6 bombers, and wrote it in a somewhat confusing manner.  I believe your way of coming about it in the beginning was also wrong, though.  The “13” that I was talking about is the gain the Axis gets out of bombing (dmg done - bombers lost) assuming the outcome lands somewhere in the top 75% (0 or 1 bombers lost).  It is the solution to the same problem as your “8” which was 19 dmg done - 11 IPC lost.  It’s a faulty number, though, so forget it.

To lay it out.  Taking only the top 75% (approx) of outcomes into account, I’m trying to find the actual average IPC gain (bombing done - worth of bombers lost).  And this is assuming NO cap on SBR damage.

So, we have a 33.5% chance to lose 0 bombers.  This gives a positive net outcome of 21 IPC (21 avg. dmg. - 0 IPC of bombers lost).
Then we have a 40.2% chance to lose 1 bomber.  This gives a positive net outcome of 2.5 IPC (17.5 avg. dmg. - 15 IPC of bombers lost).

Now combining those 2 outcomes to find the total positive net outcome would be:
[(21*.335)+(2.5*.402)]/(.335+.402) = 10.91

So, assuming no cap to SBR damage, your average net gain (SBR dmg - IPC value of bombers lost) is 10.9 IPC the top 73.7% of the time.  That is certainly substantial, and it’s nice to know that the majority of the time you’ll get a solid return for your bombers.

However, I still don’t believe you can just rule out over 25% of the outcomes simply because MOST of the time you’ll have a positive return.  Now, I’m fine with taking out the outcomes that are like 1/100 because most games wouldn’t deal with them.  Although I’d note that in those types of games whoever was using the SBR strat would most likely lose if those types of losses were taken in the first round or two of SBR (1-in-58 chance).  Anyway, get rid of outcomes with 4 to 6 AA hits.  You still have a 20.1% chance to lose 2 bombers, which brings the net gain down to 5.1 IPC.  And you have a 5.4% chance to lose 3 bombers, bringing the net gain down to 3 IPC.

Now, my thing is that you’re planning to continue to bomb Russia with 6 bombers for at least 4 or 5 turns, right?  Taking a string of rounds with 6 SBRs per round, the chances that you end up losing 2 or more bombers in at least one of the rounds is:
26.3% after 1 round.  45.7% after 2 rounds.  60% after 3, 70.5% after 4, 78.3% after 5, and 84% after 6.

So, after just 2 rounds, it’s already nearly a 50% chance to lose 2 or more bombers in one of those rounds.  I don’t see that as something you can simply ignore.

But again, this is still not taking into account the fact that bombing runs against Caucasus will always be capped at 4, thus averaging 3 points of damage instead of 3.5, or that bombing runs against Moscow will be capped at 4/bomber if neither bomber is shot down by AA, and so average somewhere between 3 and 3.5 dmg.  It looks like the average net gain per round would be something more like 4 IPC/round when taking only 0, 1, or 2 AA hits into account, with a net gain of about 2 IPC/round when taking anywhere from 0 to 3 AA hits into account.

As for setting up a map, it’s too late now (1 AM : /), and tomorrow I’m working all day, so maybe Monday or something.  Those gains for Japan seem a bit optimistic for only 2 rounds, but I guess it depends how Russia played.  Japan definitely wouldn’t be able to get a bomber purchased on round 2 to bomb Russia on J3…unless it’s landing adjacent to Moscow somehow or Japan purchased an IC on J1.

by the way, attached an excel file with the exact probabilities for losing bombers to aa guns when making SBRs with 6 bombers and some other numbers I’ve been playing with

Mass Bombing (6 per turn).xls

Okay, I see what you’re saying now, but it still seems misleading to me to just ignore 25% of outcomes.

Yes, 75% of the time you’ll average a positive outcome.  But your math is incorrect for the amount of IPC-loss in bombers you sustain when losing 0 or 1 bomber.  You took 75% of 15 IPCs, combining the chance that you would both lose 0 and 1 bomber, when really it’s only 40% of 15 IPCs - the chance that you lose exactly 1 bomber.  So 75% of the time you’re going to average more like +13 IPC net damage.

But 25% of the time you’ll average a negative outcome of about 21 IPC (taking between 2 and 4 AA hits into account).  That is statistically relevant, and 25% is quite often.

I am equally pessimistic about the ineptitude of both my AA guns and my bombers, and the other player’s good luck with both.

@ncscswitch:

Of course, I do no go more than 4 mph over the posted limit…  but that does seem to work.

I generally do 50 in a 35, up to 80 to 90 in a 55 to 65 and have never gotten a ticket.  Speed limits should be raised by 10 MPH, right now they serve as minimums not maximums.  If someone is doing the speed limit everyone behind generally wants to pass them.  But then again I live down here in uncivilized South Cackalacky (Carolina).  I have done a bit of driving up in your beloved NC, though, and haven’t seen much difference.

Uhh…How are you getting those numbers?

On average out of 6 bombers you will lose 1 per round (15 IPC).  On average you will do 17.5 IPC of damage with bombers that don’t get shot down. (5/63.56) (chance-to-not-get-shotavg.-dmg#-bombers)  Right?

The strategy depends a lot more on a lot less dice, though, which allows for a lot more statistical deviation.  The problem is that you won’t be rewarded so much for the upside of this deviation (not losing bombers to AA+doing above average dmg), while still being fully penalized for the downside assuming LHTR.  This is because your damage is capping at 4 IPC/bomber, not much higher than the 3.5 average (2 for 8 in Moscow, 1 for 4 in Cauc), so above average damage won’t lend you much more than average.  However, when you get shot down or have a streak of low damage rolls you’re going to feel the full effects, and have trouble making up for it because your good dice are again going to be capped.

By the way, the average damage of a bomber vs. Caucasus is 3 ignoring AA (3/64 + 1/63 + 1/62 + 1/61), and 2.5 taking AA into consideration with an average loss of 2.5 IPC worth of bomber (15/6).  So really you’re not gaining much of anything on a 1:1 Allies vs. Axis IPC advantage, the strength seems to be simply that you are focusing all of the effort on Russia’s IPCs directly, dropping it to something like 6-12 IPC of buying power per turn, and Russia is the one Ally that can put units directly into Europe or Asia.  I don’t think it’s a very solid strategy, though, unless you like to depend on luck even more than you need it in a game with a more orthodox strategy.

@Cmdr:

Do we have an eta on release date and when someone will scan the rules into PDF?

An underground police force has been formed to keep all PDFs off the internets until after you have played at least one game FTF.  :evil:

I seem to remember reading Oct. 23rd as the scheduled release date.

@Lynxes:

Formosa Sz- Phil. I. Sz: 1 BB (naval attack), 1 CA (bombard)

I don’t believe you can exclude the cruiser from naval combat to get off a bombardment, unless the rule changed for some reason for Ann.  This puts you with 1inf/1arm vs. 2 inf on Philippines.

Heavy bombers get a 2nd roll @4, while jet fighters go from 3 to 4…laughable

Saw a guy buy a carrier for Japan round 1, claiming he was going to put pressure on US, then didn’t kill the Pearl fleet.  He ended up making a stupid move to take Alaska, giving US the Pacific islands, then had his entire navy wiped out about the same time the US made landings in mainland Asia.

@Hobbes:

Yup, that’s the correct spelling. But it is spelled ‘Afganistan’ on the board. Check it http://www.boardgamegeek.com/image/362552?size=original

Yup, you’re right, making incorrect corrections is fun : /.

Also, the Egypt territory is just ‘Egypt’, no Anglo.

dante’s right about Czech Hungary not bordering Ukraine, and I think that the other Ukraine territory is ‘Eastern Ukraine’ not ‘Northern Ukraine’.  Whatever it is it should border the Russia territory instead of being cut off by Belorussia.

Some of the names are a bit off.  shrug

Should be: French Madagascar, Solomon (no a) Islands, Anglo-Egypt Sudan, Panama, Saudi Arabia, Italian Africa, French Equa(a not i)torial Africa, Egypt, Afghanistan (stst), Gibraltar (a not e).  Not sure how nit-picky you wanted…Oh, and you left out a name for Switzerland!  Haven’t noticed any problems with sea zones, yet.

Libya shouldn’t be touching Anglo-Egypt Sudan.

<– using XP, Triple A works  shrug :|

@squirecam:

I dont think the allies can just “ignore” Japan. That was the whole point of the pacific VC and the bonus system. You will be forced to spend $ in the pacific, or you will lose.

That seems to be much more the effect of National Objectives and the new Chinese rules/territories than any need for Pacific VCs.

If Japan is able to take and hold W. US, I still don’t think VCs really matter.  Assuming Japan has every Eastern VC including India and all Pacific VCs…In that situation, the Axis would win by VCs (13-win) if Germany/Italy can take and hold either Leningrad or Stalingrad, or if Japan can take Ottawa or Washington.  If Germany/Italy are still in a position to take Len/Stalingrad with Japan established in W US, the Allies are done.  US would soon fall to Japan anyway in this situation because of the huge disparity in income, and the fact that UK can’t help US that much because they already seem to be having trouble containing Germany/Italy.  If Japan takes Washington for the win, you’ve once again won with a capital.  If Japan is able to take and hold Ottawa to win, then once again it seems they have a large enough force to soon overwhelm the US in Washington.  This whole scenario was brought about in the first place by National Objectives, though, not VCs.

@squirecam:

However, at 13 you dont need Ottawa or London, and I think 13 VC will end up the “standard”, just like 9 was for revised.

Sure, but that still pretty much means Axis has to take Moscow.  Unless you think Japan can dominate US in the Pacific so much that they’re able to hold Hawaii, never mind everything else.  If US holds Hawaii, Axis has to take Moscow.  And that’s at the lowest VC condition possible, it just seems pointless.  And I’m afraid 12 VC victory would screw up the balance, especially since Allies could win '41 after J1 failing to take Philippines :P.  Ottawa being in Egypt or SAF instead seems like it might actually make a 13 VC game interesting from the VC perspective.