I wrote a computer program to confirm my statistical calculations on whether it is worthwhile to buy bombers to wear down an opponent with strategic bombing. First, some people in various discussions have said the bomber takes away 3 IPCs from the victim on each average roll. This should be 3.5 IPCs (average of the 6 values of a die). Second, you have a simple converging series that shows the expected value of a bomber:
1/6 chance of having a value of 0 (got hit by AA on 1st try). 5/6 * 1/6 chance of having a value of 1 die roll (got hit by AA on second round). 5/6 * 5/6 * 1/6 chance of having a value of 2 die rolls (got hit by AA on 3rd round), etc. This is a simple geometric series that sums to (converges to) 5, meaning 5 die rolls, meaning a value of 5 * 3.5 = 17.5 IPCs taken away from the enemy. This is balanced against the 15 IPC cost of the bomber, meaning that each decision to buy a bomber and devote it to strategic bombing will take away 2.5 IPCs more from your opponent than it will take away from you, and it will take an average of 6 turns to do so. That is a VERY SLOW way to wear down an opponent. Note that using the incorrect value of 3 per die roll, instead of 3.5, makes the bomber purchase a wash.
Now, if you are Germany and you are hemmed in and just waiting for rescue by Japan, and you have a bomber with which you started the game and have no good way to use it any more (Africa totally fortified by USA/UK, Finland/Norway captured by USA/UK, no paratrooping opportunities, Allied fleet too big to attack, etc.), then you might as well consider the bomber to be worthless and use it on strategic bombing against USSR. That helps Japan gain ground on USSR, and your net expected benefit is the reduction of 17.5 IPCs from the USSR before it gets shot down. Once it gets shot down, you are certainly not going to replace it; 5 infantry are much more sensible.
For groups of bombers, the math is exactly the same on a per-bomber basis.
For heavy bombers, the expected value is (3 * 17.5) minus the 15 IPC cost, rather than 17.5 - 15. So, instead of 2.5 IPC net over 6 turns, it is 37.5 net over 6 turns, a factor of 15 improvement in wearing down an opponent.
Fo regular bombers, only use bombers you already have and have no other use for them in the long run. Consider also that you lose 15 IPCs right now, when you buy the bomber, and it takes 5-6 turns to extract that many from your opponent. Time is very valuable in this game. Earlier IPCs are better than later ones.