@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.