Rhineland,

I think it could work but like you with one axis player vs. two.  I think it is safe to say this would have to be a KGF game.  Japan would need those FTR’s or IPC’s if the US came full bore at Japan.

I also think that Japan hade better hope that Germany can keep INF at the space Japan will be using as an air base.  Yeah FTR’s have a good defence but I would attack 4 FTR’s with 2 INF and 2 ART or ARM b/c Japan would loose more in the fight.

LT

On Germany 1, a good player tried buying 5 tanks and an IC in Ukraine after I had bad dice on R1. Didn’t work out in that game however.

Honestly, I really have not play tested the 6 bomber strategy against Russia.

I think it would probably work better in a KJF game because it would take America a turn just to catch up to Japan and then Japan would get defensive advantage anyway.  But that’s just my personal opinion on the matter.

As for “luck” I believe it would be safe to say that if you budget a loss of 9 IPC a round (33 Bombers) to do 12 IPC a round in damage (43 Bombers) you should be able to recuperate your losses when they occur.  But yes, it seems pretty obvious that 100% accurate AA Guns or 100% inaccurate AA Guns would impact the strategy and there is just no way around that in an ADS (using Actual Dice vs LL) game.

The sticking point would really be whether or not it is better for Germany to buy the one bomber on Germany 1 or both bombers.  Technically, Germany can easily afford 2 bombers (especially if you have 42 IPC on Round 1 because of a bid allowing 2 Bombers, 4 Infantry) but it may be better to stagger the purchase over two rounds. (With replacements every few rounds which can be saved up by spending 5 IPC less than your income each round.)

Just my opinion on the matter.  I do happen to like the theory behind this because it would limit the amount of money you need to dedicate to feet on the street (infantry) and maximize your resistance to America and England.  Of course, America and England can retaliate against Germany with their own bombers topping damage at 32 IPC a round vs the 24 Russia would be taking.

Well, to be honest, all gambit moves really depend on how round 1 (especially Russia 1) went.

If Russia tried for the hat trick (Belarus, W. Russia and Ukraine) and got stomped big time, then the all tank gambit might be the way to go.

If the allies put up zero resistance to German attacks, and you are like me and routinely purchase a bomber on Germany 1 anyway, the SBR campaign gambit might work

If your opponent is cocky, ahem, and there are a few on these boards, the Canadian Shield gambit might work.

Really, the game is turning into reading your opponent and luck and less into strategy for me now.  That’s why this is my year of really weird things.  Like against Uffish in my league game, I have purchased Artillery, 4 Armor with Russia on Russia 1. (I was going to get 2 fighters and an artillery, but the calculators said I would lose Caucasus.  my other idea was abandoning Caucasus and going with 3 submarines in SZ 16 or 2 destroyers or something, just to REALLY screw with his head!)

But the odds of success per round are:

No Bombers shot down: 33.14%
1 Bomber shot down (or less): 74.42%

That means, almost 75% of the time, you will do more damage to Russia than you will sustain to either Germany or Japan.  Mathematically/statistically speaking, the theory is sound.  At 15 IPC per bomber and only a 25.58% chance of losing more than one bomber, you are looking at a loss of 11 IPC on average to the axis.

Meanwhile, you are looking at a mean result of 3.5 IPC in damage done per bomber.  6 Bombers * 3.5 IPC in damage is 21 IPC.

So you, theoretically, do 21 IPC in damage to Russia each round and take 11 IPC in damage each round (and that 11 IPC is split evenly between Japan/Germany, so figure 5.5 IPC to each Axis but a full 21 to Russia.)

Now, I am not going to sit here and tell you that statistics is 100% accurate all the time.  Sure, I’ve experienced the event when 3 bombers attacked an AA Gun and 3 bombers were shot down by the AA Gun.  But assuming a normal distribution of results, rolled on a fair die, the potential damage to Russia far outweighs the potential risk to the axis - on paper.

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.

Actually, what I did to get the chance of a bomber shot down was to run 6 bombers against an AA gun on Frood.  (for one round of combat)

34.36%6 Bomno units.0 IPCs
40.02%5 Bom1 Bom15 IPCs
19.59%4 Bom2 Bom30 IPCs
5.1%*******3 Bom3 Bom*45 IPCs
0.83%2 Bom4 Bom60 IPCs
0.1%1 Bom*****5 Bom75 IPCs

Now, technically, just because you have a 1 in 6 chance to shoot down a bomber does not mean you will always get a positive result for every six bombers attacking.  The chances are actually 6 take 1 or 100%- 6 take 5 that you will score a hit.  On any given roll you have a 16.67% chance of hitting a bomber, but it does not scale like that in statistics.

Therefore, letting Frood run the numbers for me, so I don’t have to go through the binomial distribution to figure them out for myself!, the odds of losing 1 bomber or no bombers is the odds of losing no bombers + the odds of losing one bomber or:

34.36%+40.02% = 74.38%.

74.38% of 15 IPCs = 11.157 IPCs, but since you cannot lose 0.157 IPCs, we round to the nearest number, which is 11 IPCs.

To get the average damage done by 6 bombers we can determine the mean result and multiply that by the number of rolls.  The mean (or the expected value of Y) is the sum of all possible results divided by the number of possible results.  In this case, 1+2+3+4+5+6= total, total/6 = mean of Y.  Therefore the mean of Y is 3.5 IPC per bomber.  Since this is a mean and not the actual damage done we can have a partial IPC.

So we know that 74.38% of the time we have 5 or 6 bombers surviving their SBR runs.  Therefore, we can calculate the damage done by doing the following:

Number of Bombers (5) * Mean (3.5) = Total Damage (17.5 IPC)
+
Number of Bombers (6) * Mean (3.5) = Total Damage (21 IPC)

Total Damage/2 (for two results) = 38.5/2 = 19.25 IPC in damage.

Now we clear the partial IPC since you cannot surrender only a part of an IPC in this game.

The total damage we can expect to do, in one round, with 6 bombers attacking, 74.38% of the time, is 19 IPC and the total damage we can expect to take, in one round, with 6 bombers attacking 1 anti-aircraft cannon is 11 IPC.

This is an 8 IPC per round advantage to the alliance performing the strategic bombing runs.  In this case, it is much more significant as it is 11 IPC inflicted on the axis powers (roughly 5 or 6 IPC each) vs 19 IPC damage done to Russia each round.  Considering Russia is only earning between 18-30 anyway, this seriously weakens their ability to maintain a defensive posture forcing them to fall back sooner.

Of course, that’s the theory, and how I derived the numbers I was using.

In case anyone wonders, I am using result for 5 or 6 bombers because the odds of losing two or more bombers to anti-aircraft fire becomes prohibitively small.  However, it would be valid to run the numbers using 4 bombers as a possible result as this would happen 25.52% of the time.  I just prefer to be a little more optimistic about my bombers and pessimistic about my anti-aircraft cannons.

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.

I don’t think your calculations represent what really happens though.

Most of the players I play with are happy if they can get a 75% chance to win any given battle, especially ones with serious amounts of IPC in play. (Most of us will also take the 40% chance of winning a capital fight, since the upside far out weighs the downside.)

However, let’s look at your numbers.

Loss of 0 or 1 bombers results in 50% the cost of a bomber, which is 7.5 not 13 as you claimed.  This is still more accurate than LL which says 2.5 IPC lost per bomber (6 bombers would be 15 IPC.)

If you’d like to put it to a proof, tell you what, come up with a realistic map in round 3 where Germany purchased 1 bomber in Round 1, 1 Bomber in Round 2 and Japan purchased 1 bomber in Round 1 and 1 bomber in Round 2.

It’s round 3, therefore, all 6 bombers are in range of Caucasus and Russia.

No special gambits.  Africa’s owned mostly by Germany, like normal, and Japan has sunk the Pearl fleet and conquered Sinkiang, China, Yakut, Buryatia, SFE and India like normal.

Let’s see if my model or your model proves more accurate.

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

Apology accepted.  I can buy a 13 IPC gain for the axis on the bombing campaign over their losses, which is very significant if you think about it.

24 IPC collected - 13 IPC in SBR damage - Loss of Units trading territories is almost assuredly a negative income for Russia very early in the game.

That’s +11 IPC to buy units and you almost have to send at least 4 infantry out to take territories back so -12 IPC in lost units there.  that’s assuming Germany and Japan don’t go with heavy armies on the front lines in which case you won’t be collecting 24 IPC you’ll more likely be collecting closer to 14-18 IPC.

Either way, it appears that the Axis bombing campaign, all things being equal, could be a game winner.

But as you said, do you want to hope for luck?

In a game like my current Tournament match with Bo where we have had about 20 straight SBR runs w/o any BOM shot down by Gamer/Mateooo, it might be viable.

But that has been a very abnormal game, and I would not wager my Axis strat on that kind of luck…  :mrgreen:

I doubt this could be a game winner, not because of mathemathics, but because the allies would send more stuff to occupy land that belong to the axis powers, or other reasons… However, since this theory have not been tested in reality it could be overlooked by the AAR community, so it’s not impossible. Any game can be won by luck, but a good strat is a good strat regardless of good or bad dice.

To test this axis SBR strat it has to be used in several games between decent/experienced players, I would say 10-15 games.

I would be very, very suprised if it worked better than usual strats, that is inf+tanks+art+ftrs+some navy etc… send everything to Moscow  :lol:  and the allies stuff all shipped to Europe  :wink:

Thing is, Subotai, we know that an allied SBR campaign can give the allies a strong chance to win.  (4 Bombers for England + 4 Bombers for America assuming 1-2 bombers lost still gives you 21 IPC on average, but there’s also a good shot at taking up to 32 IPC from Germany.)

The question is if the Axis can also pull the same gambit.  I would think that Russia would be far more susceptible to German and Japanese bombing raids than Germany is to English and American bombing raids. (Heck, it’s almost common to see Germany and Japan send their solo bomber in every round just to do 7 IPC damage on average, if 7 is good, 21 is thrice as good, right?)

As for the allies getting anything more than normal, I just don’t see it really.  2 Bombers for Germany is No carrier on Germany 1, plus three less tanks on Germany 2.  2 Bombers for Japan is no Industrial Complex on Japan 1, and no ships on Japan 2.  reasonable sacrifices that should have no major impact on the game. (Honestly, I don’t even build Industrials with Japan until I am maxing out Japan every round with 4 Infantry, 4 Armor and I have 15 IPC left over.)

Don’t forget, this strategy starts you off with 2 free bombers at game start.  So we’re talking about Russia needing at least 2 hits before the axis even loses a single IPC worth of equipment.  The odds of 3 hits or more is less than 6% in one round.

Meanwhile, bombers have a big utility in forcing the allies to invest more in surface ships to protect their transports.  This alone could offset any increase in allied potency for a few rounds at least. (I assume it would take an AA Gun at least 10 rounds to kill all 6 bombers, but that’s just a guess.  )

I think this is a viable strategy and plan on testing it this week in my face to face game. I plan on giving Japan a transport bid allowing me to purchase 2 bombers on Japan 1. I feel Japan has enough infantry laying around to get away with this. I also plan on making Japan the primary bomber of the Axis and work up to and maintain 5 bombers per turn at Russia (3 Russia, 2 Caucasus). I think Germany needs to probably be played more conventionally and plan on buying an additional bomber round 1 and probably 3. I don’t think Germany will need to worry about maxing out damage to Russia, just maintain a slight pressure with some bombing. I plan to trade and exert pressure on the ground also with the Germans. The Japanese should have no real problems buying bombers as they are generally not threatened and if they are it should be from the US with Navy. 5 or 6 bombers with Japans starting ships could very well neutralize this threat for some time.