How do I defend against heavy bombers?

Thanks for the help guys

it is well known that the expected value for damage on an SBR is 3.5 IPCs (given the bomber survives AA fire and given the territory is 6 IPCs or more).  there are a few posts taking a stab at the distribution for heavy bombers in LHTR, but no one has formulated it correctly.  the work below shows the average SBR damage is 5.472 IPCs per heavy bomber.

in LHTR, heavy bombers roll 2 dice, take the max, add one, limit to the territory value, and that’s the IPC damage inflicted.

let A and B be independent random variables corresponding to the two dice rolled.  they are distributed as:
P(A=a) ={ 1/6  a=1,2,3,4,5,6
        { 0    otherwise

P(B=b) ={ 1/6  b=1,2,3,4,5,6
        { 0    otherwise

let C be the derived random variable defined as:
C = max(A,B) + 1

Theorem: C is distributed as:
P(C=c) ={  1/36    c=2
        {  3/36    c=3
        {  5/36    c=4
        {  7/36    c=5
        {  9/36    c=6
        { 11/36    c=7
        { 0        otherwise

Proof:
note: <= is the less-than-or-equal-to operator
note: E is the summation operator
P( C<=c ) = P( max(A,B)+1 <= c )

6
      = E  P( max(A,b)+1 <= c | B=b ) P(B=b)
          b=1

6
      = E  P( max(A,b) <= c-1 ) P(B=b)
          b=1

c-1
      = 1/6 * E  P( A <= c-1 )      c<=7
                b=1

c-1 c-1
      = 1/6 * E  E  P(A=a)          c<=7
                b=1 a=1

c-1 c-1
      = 1/36 * E  E  1              c<=7
                  b=1 a=1

= 1/36 * (c-1)^2              c<=7

and
P(C=c) = P(C<=c) - P(C<=c-1)
      ={  1/36    c=2
        {  3/36    c=3
        {  5/36    c=4
        {  7/36    c=5
        {  9/36    c=6
        { 11/36    c=7
        { 0        otherwise

Analysis:
note: E is the expectation operator
so, if one were heavy SBR’ing a 7 (or more) territory, the expected damage is:
E© = 21/36 + 33/36 + 45/36 + 57/36 + 69/36 + 711/36 = 197/36 = 5.472 IPC

so is the extra ~2 IPC per bomber worth the investment?  i’d like to know what other analysts think now that i’ve quantified the difference.

Interesting take.

Destroyers can be better then fighters, if you have combined arms, in that case.  Att/Def at 3 + Bombard @3 in opening fire.  Not too bad if Fighters are nerfed.

Though, I agree, fighters can defend on land and sea, that gives them flexibility.

You would still have the BOM available for naval combat, that would remain unchanged.  You just get rid of the 600 pound gorilla of how to make Heavy Bombers not unbalance the naval campaigns while still allowing the Allies to use a CBO offensive against Germany.

another way of doing this is to allocated an attacker chosen hit from any artillery or fighters rolling a one, and allowing tank hits to go against enemy armor or artillery first.

This is balanced and its been tested in my own games, but its an old idea since the 80’s.

Bombers cant do this because they are carpet bombers, while the other units are designed for targeted attacks.

You can have a sub do this on ones too as well as the battleship.

At least it would be easy to remember.

Germany cannot hold Caucasus early in the game.

If it tries, all Russia has to do is take Ukraine with West Russia forces, cutting off any reinforcements, and take Caucasus with combined West Russia and Russia forces.

On the other hand, Germany has a very easy time smashing Karelia early.  If Russia reinforces in Karelia, I think the Axis have an excellent chance of winning, as Germany smashes the Karelia stack with the Baltic transport, Norway, Eastern Europe infantry plus assorted tanks.  West Russia will not have enough to counterattack (since so many units were in Karelia in the first place), and the Germans have seriously damaged Russia’s ability to trade territories from W. Russia - the Germans can even secure Ukraine with that weak of a Russia.

Leave Archangel and Karelia open with Russia; do not defend.  That’s my recommendation.

Thanks man - that does help!

I think it is a perfect match to let the Germans have Jagd Panzers (Tank Destroyers) to counter the Russian Assault Gun advantage, not vice versa since now the Russian player control the game! When I say “control the game”, I mean that the Russian player can choose when and were the German Jagd Panzer advantage will come in to play! The attacker always has the initiative! But at the same time the German player may safe his advance against counter-attacks on his way into Russia!
:wink: