Most Surprising First Round purchases you have seen?

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.

To make such test I recommend using LL, even if most of you prefer ADS, with LL it means playing less games to determine if this is a better strat than other options.

The reason I think its inferior, is because we haven’t seen much of it.

If you are right, then AAR gameplay will change radically after other players also discover and use the SBR strat. FYI, SBR is not much used by allies (or axis) in most games, bombers are usually not bought…
SBR is used sometimes by bombers you start with, not often I see them bought by the top players.

Low Luck is an inferior testing tool, especially in terms of the way it handles SBR’s.

LL SBR’s bear no resemblance to reality.  Indeed LL SBR is one of the BIGGEST flaws with LL.

In TripleA (LL setting) SBR is handled like this, if you have 1 bmr, then AA gun rolls @1, if AA gun misses then the bmr rolls 1 die, this means in the long run will average around 3,5, but it could be 1 ipc damage, or 6 ipc damage.

If you have 5 bmrs doing SBR, AA gun rolls 1D@5, so 5 or less is a good chance to shoot down a bmr, and lets assume the AA gun rolled 5 or less, then the 4 remaining bmrs roll 4 dice, which could mean 46=24 ipc, or 41=1 ipc.

IF you have 6 bmrs doing SBR, or attacking any territory with AA gun then one bmr is lost automatically.

With 7 bmrs, one bmr is lost and AA gun shoots @1, 11 bmrs, 1 bmr is lost to AA gun, AA gun rolls @5 or less, so if you got lucky to escape AA gun with 11 bmrs, you loose only 1 bmr, rolls for 10 bmrs, and can do 60 ipc damage…

@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.

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

Assuming all things equal then 3 rounds of SBRing with 6 bombers without replacement would result in:

(6 Bombers)(1/6 Chance of Loss to AA Fire)(6!/6 average damage)(# of Surviving Bombers) + (5 Bombers)(1/6 Chance of Loss to AA Fire)(6!/6 average damage)(# of Surviving Bombers) + (4+5/6 Bombers)(1/6 Chance of Loss to AA Fire)(6!/6 average damage)(# of Surviving Bombers)

Therefore:

Round 1:  5 Bombers * 3.5 IPC = 17.5 IPC Damage done, (1 Bomber lost)
Round 2:  4.1667 Bombers Surviving * 3.5 IPC = 14.58 IPC Damage Done, (1.833 bombers lost)
Round 3:  3.6944 Bombers Surviving * 3.5 IPC = 12.93 IPC Damage Done, (2.305 bombers lost)

Damage Done to Russia = 45.01 IPC in 3 Rounds
IPC lost in attacking equipment = 34.575 IPC in 3 Rounds (note this cost is divided between the two axis powers.)

Now, that said, realistically speaking, you could not run the numbers like that because the data of subsequent sets is dependant on the results of previous tests.

I played two test games this week. The first was going to be an obvious Axis victory after round for so we decided to run it again. Now while my Allied opponent isn’t the best Allied player even after Germany had a horrid start in the first game it was decided very early. In the second things were going so well I decided to spread the Joy to England as well since by the time this is doable there income is already not so hot. I would say that barring some absolutely horrible dice this is a solid strategy for the Axis.

Still surprise me most everytime Japan buys 2 IC´s R1

Pineapple pizza is a very surprising first round purchase. ~ZP

Well i have done (usually do) a lot of “different” first round purchases.

Im seeing a lot of new people here so you prob don´t know who i am or if im shit or not  :wink:

But things that do work:

4 figs G1.

alt, 3 figs ,1 bmb with bids.

or 2 figs , 1 bmb, 1 arm.

depends a little bit.

Also i have succesfully deployed the IC in WEU.

Rationale is if your doing the “hold the line” tactics with Germany, while coming in with the save with japan.

Mixes very well with the AF strat, and rationale is the same.  When Allied Fleet build up is to much to handle, retreat figs from sea, and let the carriers die.

And it gives you a huge striking distance for the navy,

Allthought a IC in WEU should be used in combination with a bif for a Sub in SZ7? (with the other sub in atlantic)

For a strike on uk fleet on g1.

Also:

IC on Australia on UK1, combined either with a US build of warships on USA1, or a IC in sinkiang.

This works best with a 6 inf stack in bury and 2 arms of to Yakut, and a UK strike on FIC on UK1.

@Nix:

Also:

IC on Australia on UK1, combined either with a US build of warships on USA1, or a IC in sinkiang.
This works best with a 6 inf stack in bury and 2 arms of to Yakut, and a UK strike on FIC on UK1.

Australia plus z55 is not surprising to me. Australia plus IC sin but not z55 fleet is pretty surprising