An analysis of tech Heavy Bomber tech:
Each tech roll gives a 16.7% chance of scoring a tech. But added rolls are not cumulative but rather diminishing.
The math goes as follows:
16.7% = 1 tech roll.
16.7 + (16.7 x .833 (which is 1 - .167) = 30.6% = 2 tech rolls.
30.6 + (16.7 x .694 (which is 1 - .306) = 42.2% = 3 tech rolls
42.2 + (16.7 x .578 (which is 1 - .422) = 51.9% = 4 tech rolls
51.9 + (16.7 x .481 (which is 1 - .519) = 59.9% = 5 tech rolls
59.9 + (16.7 x .411 (which is 1 - .599) = 66.6% = 6 tech rolls
66.6 + (16.7 x .334 (which is 1 - .666) = 72.1% = 7 tech rolls
Multiply this % by .167 to determine you chances of getting a single specific tech (like heavy bombers).
Multiply by .333, .5, .666 and .833 for your chances of getting one tech in 2, 3, 4 or 5 techs respectively.
So for instance, if you make 7 tech rolls you have a 72.1 x .167 (or 12%) chance of getting heavy bombers.
Now if we can determine the IPC value of Heavy Bombers vs.we can a make cost analysis. Since heavy bombers attack twice, their cost is best compared to simply buying a second bomber…
Heavy bombers cannot undertake separate missions, roll two ones or take two hits on defense. But if we are just comparing their SBR capacity: heavy bombers take neither an extra AA gun hit nor do they offer a second target, compared to a second bomber. Since AA guns have less than a 50% chance of hitting, this makes heavy bombers worse by (16.7% - 16.7%) or 2 IPCs. Thus heavy bomb tech is worth 10 per existing bomber
So given the choice with 36 IPCs to buy 3 bombers or 5 tech rolls what is the proper choice? Three bombers is worth exactly 36. But as we’ve seen 7 tech rolls only has a 12% chance per turn to get heavy bombers. (Granted it has a 72% chance per turn to get some tech, but 35 for any OTHER tech is ludicrous).
Even if we already have 10 bombers on the board and we get a tech this turn, we still only have a 16.7% of heavy bombers. So the bombers are worth 36 and the tech is worth 16.7 IPCs at most.
I hope this conclusively proves that any money invested into securing a specific tech in a tournament length game (or probably even a marathon game) is wasted.
As an aside this means that rolling to get one of the two SBR mitigation techs (AA guns and Factory upgrade) isn’t really a strong option either.
Finally, it is worth noting that any financial commitment to SBR precludes at least SOME lack involvement in the traditional theaters of combat. This has the effect of letting the Axis gain money through more easily achieved national objectives and marginal IPC territories (such as those found in Africa). It also denies the allies (mostly England) progressively more IPCs. It is for this reason that I think SBRs, while definitely a sound strategy, appear to be more game-breaking than perhaps they really are.