• @Granada:

    Sorry, I think my logic is correct here, since while the first bmb dies on the 3rd-4th roll of dice, it will take 6 more rolls to get you to the 3rd-4th roll of the second half dozen of rolls. Of course, we work with averages because average is what is likely to happen most often: there is no mean when rolling a dice; and it is exactly between the 3rd and 4th roll when the cummulative likelihood you roll 1 exceeds 50 %.

    Mathematics doesn’t agree:
    “average” != “what is most likely to happen”. What is most likely to happen is an event with the biggest chance, given a set of events and a probability function over the events. For instance, let’s take the set of chances of a bomber dieing in raid N. For N=1, this is 1/6. For N=2, this is 5/6 (not dieing raid 1) * 1/6 (dieing raid 2). For N=3, it is 5/65/61/6. So the chance of dieing in raid N = 5/6^(N-1)*1/6 = the probability function. Dieing in raid 4 has a chance of 9.6%. As told, dieing in raid 1 has a chance of 16.7%. So according to your own definition (“most likely to happen”), it should be the first turn, which contradicts your conclusion of 3rd/4th turn.
    Ofcourse, you can use other sets of events. I’ll indulge you, and define the set you mean, which is cumulative: chance of getting shot down before raid 5, and chance of getting shot down on or after raid 5. Not getting shot down before raid 5=(5/6)^4=48%. Chances of getting shot down before raid 5 = chances of opposite = 1-48% = 52%. The result we can extrapolate is it is more probable to get shot before the 5th raid than after the 4th raid. But also: it is almost equally likely to get killed before the 5th raid as after the 4th raid (52%~=48%). Anyway, this is probably what you mean with “between 3rd and 4th”, only it should be “between 4th and 5th”.
    The problem with this definition of the set of events however is that it doesn’t tell you at what raid the bomber will probably die (you need my first definition of the set to do this). It only tells you before or after what raid the bomber will probably die. Which is utterly pointless in the purpose of determining average damage. As is the first definition too…

    Anyway, enough chit-chat, strategy talk.

    USA 1: buy 3 bmr. Gives 4 bmr total. After that, buy 2/3 of a bmr every round. This way you’ll always have 4 bmrs pounding Germany from round 3 upwards.
    Germany has an income of about 40. Let’s assume it needs 10 units each turn. So its best bet is to only repair Germany fully, giving you 20 IPC’s a turn to shoot at. With 4 bmrs, this will seldomly (=in less than 1.5% of cases) be overkill (chances of getting >20 are (5/6)^4 -getting past AA with 4 bmrs- * 2.7% -throwing 21 or more, see http://anydice.com/-  < ~1.5%).

    Using this strat, your land troops arrive one turn later, with 1 inf 1 arm (=8 IPC’s = 2/3 of a bmr) less each turn. This is the drawback.
    What do you get in return? From turn 4 onwards (3rd turn you’re shooting at Italy, which doesn’t get repaired) Germany is denied 12 IPC’s worth of units, or 4 infantry. You always have 4 bmrs to support an invasion. You need less transports (remember, 1 less inf+arm means less units to shuttle). You start hindering Germany from turn 3, which is faster than you can do with any newly built land army + fleet (the invasion of Africa is done with the starting army + fleet). Lastly, Germany cannot use Italy as a building point (for instance to build fleet or troops for Africa).

    The initial investment is high (3 bmr turn 1, 1 bmr turn 2 etc.), but what strategy with USA hasn’t got a high initial investment? After this investment you trade 8 IPC’s for 12 IPC’s each turn. It is a decent trade-off, possible in 1942 because bmrs are cheaper. Can you show me a strategy with US that trades IPC’s faster?

    All I am saying it is a “prayer” based method, not a strategy.

    It is not a prayer, but a decent strat, the quickest one I know to trade American IPC’s with Germany. I hope my point is more clear now.


  • @HolKann:

    All I am saying it is a “prayer” based method, not a strategy.

    It is not a prayer, but a decent strat, the quickest one I know to trade American IPC’s with Germany. I hope my point is more clear now.

    I agree with Granada - it is a ‘prayer’ based strategy because it is heavily dependent on dice results (both the AA and the damage inflicted^). And it only takes a bit of luck for the side being bombed for the strat to come apart and the more bombers you add, the greater the chances of that happening.

    Taking the example of 1 bomber and when it should die, you get 17% on round 1, then 31%, 42%, 52%, 60%, 67%…

    The thing is, real dice doesn’t care about these odds. The bomber may die on round 1 right away and you just wasted it. Or it may not but you’ll never know when it will die, it may survive the entire game happily bombing your opponent while he curses his luck. And if you bought a 2nd bomber you might as well see it shot again on the 1st bombing - the math may give you low odds for that to happen, but dice doesn’t care because dice has no memory! It doesn’t remember any previous throws, so the result is not dependent on any previous rolls. Of course, this also means that the 2nd bomber may as well live happily the rest of the game bombing the enemy, but you really have no way of knowing it because you can’t predict what will happen exactly, only have an idea of what might happen. And pray that you get decent dice.

    What about the 4 US bombers strat? Well, assuming the initial bomber didn’t get shot on the 2 round before the other 2 arrive, then those 4 may be lucky and only lose 1 bomber each round to the AA (which is replaced) or even not lose any bomber at all. However, you may also lose 2 or 3 or all bombers to the AA on a single raid, depending on how the dice is feeling today.
    It can be argued that the odds of losing all 4 are very low? Sure, but it can still happen and if it does your entire strat comes crashing down to earth. Or you may just lose 3 or even 2, but the odds for both are greater and for each bomber that you lose it, the less damage you deal to the enemy and more of your IPCs are blown out off the skies.

    @HolKann:

    The initial investment is high (3 bmr turn 1, 1 bmr turn 2 etc.), but what strategy with USA hasn’t got a high initial investment? After this investment you trade 8 IPC’s for 12 IPC’s each turn. It is a decent trade-off, possible in 1942 because bmrs are cheaper. Can you show me a strategy with US that trades IPC’s faster?

    Again, math doesn’t show everything. If the US buys 3 bombers then it won’t be able to establish a ‘shuck-shuck’ to Europe until at least round 5:
    *If it sends the ships on SZ10 to land on Africa on US1, they will be sunk and it will have to wait until round 2 for replacements.
    *If it doesn’t send them to SZ10 then Africa remains on Axis hands for a bit longer, making up for any initial losses due to bombing (and meanwhile the UK suffers from reduced income).
    *If the US didn’t land on Africa on US1, the UK will either have to go for Africa or Norway on UK2. If it goes to Norway then either the US sacrifices its initial fleet to land on Algeria to liberate Africa or the Axis keep it. If it goes to Africa then Germany keeps control of Norway a little longer.
    *If G buys a bomber on G1 and sinks the SZ2 fleet, then it will have 2 subs, 2 bombers and 3/4 fighters against the Allied fleet from G2 onwards. The Allies should have on UK2: 1 carrier, 2 fighters, 2 destroyers, 1 Russian sub and 1 US cruiser. Which means that if the UK wants to land on Europe it will need more defense to its fleet. That’s money that the UK should not be spending - the quicker it gets 4 transports the better it can pressure Germany and force it to defend several territories (W. Eur, Germany and E. Eur).
    *Since the US now builds ships on US2, it means that it won’t be until round 4 that they can reach SZ7, 6 or 3. So if the UK wants to land on Europe on round 2 or 3 they will need to buy a 2nd carrier or an additional destroyers/cruiser since they’ll have almost no help from the US fleet.

    So, the trade-off is not just 8 IPCs vs. 12. It is also about delaying the US shuck on Europe and having the UK spend more on navy and slowing down its transport fleet build up. Meanwhile G can fortify Europe and make up for the initial bombing losses by retaining Norway/Africa. And on the top of that, you have the possibility that the AA will get lucky and shoot down more bombers that you can afford. It may sound a decent strat to some (specially if the Axis don’t know how to deal with it), but having faced it quite a few times (and winning most of them) I call it a ‘prayer’ one.

  • 2024 2023 '22 '21 '20 '19 '18 '17

    @HolKann:

    Germany has an income of about 40. Let’s assume it needs 10 units each turn. So its best bet is to only repair Germany fully, giving you 20 IPC’s a turn to shoot at. With 4 bmrs, this will seldomly (=in less than 1.5% of cases) be overkill (chances of getting >20 are (5/6)^4 -getting past AA with 4 bmrs- * 2.7% -throwing 21 or more, see http://anydice.com/  < ~1.5%).

    Germany wouldn’t repair the German IC completely in that case, because that would only leave 20 IPC’s to actually buy those units. In general, Germany could adapt to the SBR strategy by planning it’s purchases in a specific way, provided that it can afford to do so.
    Suppose that Germany has an income of around 36, assuming that some progress has been made by the Allies. Regardless of whether the German or Italian IC is repaired, it’s impossible to buy more that 6 units with that money. Now if Germany desperately needs those units right away, it may be compelled to do so - for instance, repair Italy, buy 3 inf 3 tanks.
    But that’s a pretty expensive option, and gives the US bombers something useful to do next round. So Germany can consider whether it’s viable to wait for one round and just try and hold with what they have, in order to repair the German IC next round and then buy their units in a more cost-effective way, especially when there’s no other clear objective for the US bombers.
    I’m not saying that such a response negates the entire idea, but you’d have to consider that Germany may adapt to the SBR’s by means of a specific purchasing strategy.


  • @HolKann:

    @Granada:

    Sorry, I think my logic is correct here, since while the first bmb dies on the 3rd-4th roll of dice, it will take 6 more rolls to get you to the 3rd-4th roll of the second half dozen of rolls. Of course, we work with averages because average is what is likely to happen most often: there is no mean when rolling a dice; and it is exactly between the 3rd and 4th roll when the cummulative likelihood you roll 1 exceeds 50 %.

    Mathematics doesn’t agree:
    “average” != “what is most likely to happen”. What is most likely to happen is an event with the biggest chance, given a set of events and a probability function over the events. For instance, let’s take the set of chances of a bomber dieing in raid N. For N=1, this is 1/6. For N=2, this is 5/6 (not dieing raid 1) * 1/6 (dieing raid 2). For N=3, it is 5/65/61/6. So the chance of dieing in raid N = 5/6^(N-1)*1/6 = the probability function. Dieing in raid 4 has a chance of 9.6%. As told, dieing in raid 1 has a chance of 16.7%. So according to your own definition (“most likely to happen”), it should be the first turn, which contradicts your conclusion of 3rd/4th turn.
    Ofcourse, you can use other sets of events. I’ll indulge you, and define the set you mean, which is cumulative: chance of getting shot down before raid 5, and chance of getting shot down on or after raid 5. Not getting shot down before raid 5=(5/6)^4=48%. Chances of getting shot down before raid 5 = chances of opposite = 1-48% = 52%. The result we can extrapolate is it is more probable to get shot before the 5th raid than after the 4th raid. But also: it is almost equally likely to get killed before the 5th raid as after the 4th raid (52%~=48%). Anyway, this is probably what you mean with “between 3rd and 4th”, only it should be “between 4th and 5th”.
    The problem with this definition of the set of events however is that it doesn’t tell you at what raid the bomber will probably die (you need my first definition of the set to do this). It only tells you before or after what raid the bomber will probably die. Which is utterly pointless in the purpose of determining average damage. As is the first definition too…

    Fair enough. I have suspected there was a catch in my primitive math and thanks for correcting that. I am sure there must be a way how to count in such a sophisticated way what is the relative damage the bomber causes before dying. I am pretty sure the balance stays negative but definitely less then 3.5, so the burden on the bomber is lower, perhaps much lower, could be around 1 IPC, I guess.

    @HolKann:

    Anyway, enough chit-chat, strategy talk.

    USA 1: buy 3 bmr. Gives 4 bmr total. After that, buy 2/3 of a bmr every round. This way you’ll always have 4 bmrs pounding Germany from round 3 upwards.
    Germany has an income of about 40. Let’s assume it needs 10 units each turn. So its best bet is to only repair Germany fully, giving you 20 IPC’s a turn to shoot at. With 4 bmrs, this will seldomly (=in less than 1.5% of cases) be overkill (chances of getting >20 are (5/6)^4 -getting past AA with 4 bmrs- * 2.7% -throwing 21 or more, see http://anydice.com/-  < ~1.5%).

    Using this strat, your land troops arrive one turn later, with 1 inf 1 arm (=8 IPC’s = 2/3 of a bmr) less each turn. This is the drawback.
    What do you get in return? From turn 4 onwards (3rd turn you’re shooting at Italy, which doesn’t get repaired) Germany is denied 12 IPC’s worth of units, or 4 infantry. You always have 4 bmrs to support an invasion. You need less transports (remember, 1 less inf+arm means less units to shuttle). You start hindering Germany from turn 3, which is faster than you can do with any newly built land army + fleet (the invasion of Africa is done with the starting army + fleet). Lastly, Germany cannot use Italy as a building point (for instance to build fleet or troops for Africa).

    The initial investment is high (3 bmr turn 1, 1 bmr turn 2 etc.), but what strategy with USA hasn’t got a high initial investment? After this investment you trade 8 IPC’s for 12 IPC’s each turn. It is a decent trade-off, possible in 1942 because bmrs are cheaper. Can you show me a strategy with US that trades IPC’s faster?

    All I am saying it is a “prayer” based method, not a strategy.

    It is not a prayer, but a decent strat, the quickest one I know to trade American IPC’s with Germany. I hope my point is more clear now.

    I am glad you have come to these specifics, because I say this strategy is doomed to fail unless you are exceptionally lucky, and maybe even in such a case.

    1. You cannot assume Germany needs 10 units a round. It may easily build a fig a round and less inf/tnk.

    2. It will always use up its capacity on SEU, so it will only repair to 3-5 production capacity on Germany.

    3. Thus you would be sending 4 bmbs on 13-15 pray, reducing your 0.9 damage per raid to about 0.7.

    4. US is not loosing just tnk/inf, it is not that easy.

    Let us look at the proceedings more closely:

    R1. US builds 3bmb and 2 inf most likely, collects 40. R2 US builds bmb, AC, 2trn, collects 38. R3 US builds a bmb, 2trn 4inf, collects 38. R4 US builds a bmb, trn, art, 5 inf, collects 38. R5 (first round when it can likely safely not build a bmb and a trn, since it has 8 already) so it builds 4tnk, 4inf and 2 extra inf, collects 38. R6 US builds bmb, moves 8 units EC, 4trn SZ 1, merges fleets SZ6, may try to offload on Norway which has been trading or taken already. But then it comes to get really interesting.

    What if Germans seeing the strategy try to make the most of it and after an all inf buy R2, from R3 on they build a fig a round. If they have build a bmb on R1 which many people including myself usually do and they lost 2 figs R1 they will have 2 bmb plus 8 fig on R6. If US leaves something on SZ 2 to protect the transit to UK (and it must be the bb plus a dd to be safe), the Allies can only move SZ 3/6 with 2 AC, 4 fig, dd, cru (if UK bb died R1, build AC, 2 dds R1 and lost none ). This would get killed.

    OK, UK can build more ships and figs for cover. But than if the Japan air has been flown in it fixes your fleet on one spot unless the US decides to invest more on ships.

    So here is the choice. With your strategy you get your first regular offload with a good punch (4tnk, 4 inf) on Norway R8, and you will have a stack able to present a threat on Germany R11 the earliest. Or you will protect your ships so that they can manouver seperately and thus get to the very best SZ5. But then you will most likely not be coming with 8 units a round, but rather with 6 units a round, thus most likely bringing Germany into a danger even later.  And we are not taliking about US trying to contest Africa or doing anything in Pacific, so after it will lose Hawaii (around R6), it can even be on 37 for a few rounds.

    cause for all that chit-chat it is neither the air, nor the ships that win the war. Infantry and tanks do. US needs tanks in Europe and cannot afford them with the bombing strategy.

    Now what is going on in the bombed Germany for all that time? It uses approx. 10 IPCs a round to offset the bombing, stacks KAR if feasible to deter any early NOR landings, otherwise trades it together with bel and ukr, stacks WEU with plenty of air, keeps just enough on ger, sends a couple of inf on ee for trades every round. Produces 6 on SEU, 2-5 on Germany and most likely never drops under 40 in income unless it is too late for Allies to exploit.

    While Japan is round by round making sure that R and UK income drops steadily while building up (and building up infantry and tanks for that matter) to take Mosc.

    Thank you, come again.

  • '12

    A bombing raid ‘on average’ will do 5/6 of 3.5 when an AA is present.  When you do many samples, the average ‘converges’ towards this number.  By using 6 bombers it becomes a bit easier to demonstrate the math.  The ole ‘on average’ provides for 5 surviving bombers @ 3.5 ea for 17.5 IPC damage for the 6 starting bombers.  So the average becomes 17.5/6 is 2.916 repeating or 5/6 of 3.5.  So we all know this math, so what.  Well, I wrote a ‘toy’ computer program.  I started the ‘trial’ with no bombers.  Then once per round 1 bomber was added to the fleet, then a bombing raid carried out against an AA guarded IC.  As one would expect, the bomber fleet converged on 6 starting bombers and 5 after the raid.  I forget exactly when this average of 6 bombers occurred, obviously no sooner than round 6, I suspect around round 8-9 most of the convergence had occurred……on average and in an isolated example.  However, isolated simulations do at least validate mathematical techniques.

    But the game is not based on averages.  In particular, small scale battles involving expensive equipment often does not allow for statical anomalies to be smoothed out with many trials.

    Its been awhile since I have written code, but if there actually is a curiosity and demand for a toy program like that it wouldn’t take much effort to find a development environment and whip up a program for free distribution.  Better yet, maybe somebody more motivated/skilled could do it :-)  Perhaps a list of comma delineated integers representing initial size of bomber fleet, initial purchases of bombers for first few turns then a steady state value of IPCs invested in new bombers.

  • '16 '15 '10

    Interesting discussion.

    Outside of the 6 bomber low luck tactic that Hobbes mentioned, I tend to agree strat bombing isn’t the greatest Allied strategy.  Or at least it isn’t a good strategy for me…because it’s so dicey.  Bombers are likely a better investment for the Axis because they have use for them each turn, and every Axis bomber means more Allied investment guarding transports.

    However I’d hesitate write off a mostly bomber or mostly air USA strategy just yet.

    One factor not necessarily taken into consideration in the discussion above is that if USA is buying these bombers and placing them in WUSA, then Japan could be in trouble if they don’t respond appropriately.  So an early investment in bombers is not just good for getting an early start on bombing Germany…it can also be a threat that causes Japan to buy surface navy early in the game, potentially slowing them down.

    Another factor is that if USA has a big bomber stack then it can impact Japan’s ability to get Africa Ipcs, due to the USA threat to its fleet units.

    So I think if Allies go with a heavy USA air strategy then they have to position these units appropriately early in the game in order to get the most use out of them.

  • '12

    In second addition I fell into a strategy, it wasn’t planned but rather was an opportunity.  For the US I had invested heavily in bombers, light investment in fleet and KGF.  I built additional bombers and did a rapid switch to the pacific.  Japan had just invested heavily in ground forces and an IC, perhaps two.  The idea was that I caught him in a position where he could not protect his ICs and preserve his Navy.  It was never a strategy I planned to spring, but was always on a lookout to do such a thing.  Mind you it was long ago against players not as well rounded as they are now and in a version of the game no longer played it seems.

  • '16 '15 '10

    @MrMalachiCrunch:

    In second addition I fell into a strategy, it wasn’t planned but rather was an opportunity.  For the US I had invested heavily in bombers, light investment in fleet and KGF.  I built additional bombers and did a rapid switch to the pacific.  Japan had just invested heavily in ground forces and an IC, perhaps two.  The idea was that I caught him in a position where he could not protect his ICs and preserve his Navy.  It was never a strategy I planned to spring, but was always on a lookout to do such a thing.  Mind you it was long ago against players not as well rounded as they are now and in a version of the game no longer played it seems.

    Going hard with bombers is an easy way to destroy an inexperienced player.  Back in the early days of 41 I loved the all bomber strat for USA.  If Japan didn’t leave itself open, then I took the bombers to Europe and strat bombed them as soon as the med and/or baltic fleets were finished off.

    All bombers USA1 is very effective in the 42 scenario of aa50.  Japan starts off with a weak navy so a few bombers on USA1 essentially forces Japan to buy surface navy…surface navy that serves little use once those bombers make for Europe.

    The same factors are in play in Spring 42–Japan is relatively weaker.  The board is even smaller than aa50 so theoretically bombers are even more dominant in Pac war.  It’s easy to destroy a novice with KJF if you can use that USA air.

    The problem is the same problem anyone who plays KJF in 42 (or aa50 42 for that matter) runs into…if you really want to take out Japan you can but in that case a good German player will rout the Soviets…


    The all strat bombing strategy faces a different problem.  If you use strat bombing instead of building up a USA ground force to invade Europe, then Germany will often survive longer than it would have if you were investing in boots on the ground.

    However, bombers are multi-faceted and their presence affects enemy moves (and buys) in varied ways.  It would be a challenge to quantify these factors and assign them numerical values within the larger context of weighing the virtues of strat bombing campaigns against those of a conventional investment in navy and fighters and gear.


  • I don’t have the same problems with Strat bombing as everybody else has…

    For all that has been said about the “IPC / bmb raid” ratio not being worth it, I don’t agree.

    Let’s be generous, and say that the net result is 0,5 IPC. That would actually be great. If I could play a game where German income = 0 and USA income = 0. I’d do it, and win every time.

    My problem is S. EU. industrial complex. If I bomb Germany and S. EU to hell (to hell means all the way down to twice their production capacity), it still only needs to spend 12 IPC to be able to produce 6 units, which is not much, but might be enough to withstand the Allied assaults unitl Japan arrives.

    And before we get to that point, it’ll be G4, since US1 bmb buys won’t bomb Germany/S.EU before US3.

    So start bombing will only be effective against a G player that has not invested mainly in ground troops on G1 (let’s say he buys 1 FTR + 1 BMB).


  • Stratbombing looks really cool on the first sight. Only I have not seen it worked. I actually have based the post on my personal experience. I have played many players who stratbombed me and almost all of them complained bad luck in the process. I recalled the old CaspSub paper and decided to check out whether what they say was still relevant for Spring 1942.

    And my conclusion was that “bad luck” is nothing that happens to a stratbombing player but something he should expect, bad luck is what stratbombing brings. If you are happy with 0.5 damage inflicted per a raid, than you better think twice about what are the damages you are not inflicting because of strat bombing.

    As for the build of bmbs on WUS, I cannot see a calm Japanese player to be forced into buying anything, maybe a dd just to remove even the faintest hope of succes. 4bmbs would stand just 28 % chance of winning against bb, AC, 2 figs; with a dd it drops to 8 % (assuming the first dd killed the sub, in case the sub has retreated there is even less need for building an extra dd). And some people buy two dds J1 anyway. So the southern fleet would not be even necassary to add to the forces on the japanese sea on turn 2, and they can make it there usually turn 3 leaving any air attack on japanese fleet all but impossible.

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