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