SBR rule question

@mozkaynak:

So, My understanding is that  fighters and bombers can attack submarine by themselves and submarine can not fire back.
Please confirm that.

Correct.

@mozkaynak:

So how does submerging work here?

Subs may submerge at the end of any round of combat if there are no opposing destroyers in the battle at that point (as long as the battle is not over).  They have no effect on other units while submerged, and are ignored.  They resurface at the end of the noncombat movement phase, having no effect on enemy units in the sea zone at that point.

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.

Welcome, Miket2424!

You could try reducing transports’ defense value.  If a transport rolls a 1, roll again and only hit on a 3 or less.  This would effectively halve their defensive capability.

You could also try using the transport rules from the new Anniversary game (see pages 13-16, 18-19, 21 and 31).  This is a bit more radical approach, and may require tweaking the setup a bit to counter the reduction in combat strength of some fleets.

Wow!
Were bombers flying around the world?
I’d love to play a game like that.

Spend like crazy!

Two exceptions:

1.  Sometimes, you need to go pure defense with Russsia.  When doing so, if you have 17 IPC, you spend 15 to get 5 infantry, and save 2 IPC.  Next turn, with another 17 IPC income, you will have 19 IPC, allowing you to get 6 infantry.

2.  Sometimes, you want to be able to switch fronts with the US.  So you don’t spend a lot first turn, then second turn, you commit to either Atlantic or Pacific.  (If you do spend in the Atlantic on US1, it takes TWO turns to sail to the Pacific, and vice versa).

In general, it is not a good idea to save.

UNLESS UR JESUS!

@Gamer:

@ncscswitch:

It would also skew the hell out of Europe.

Imagine Germany’s 6 FIGs and BOM backed up by a large stack of INF…  Throw in an ARM or seven…

Can you say “steamroll” anyone?

I prefer baked rolls.

When you download the file, change the ending to .map or .aam.  If it is a 2nd edition game, change it to .map.  If it is an AAR game change it to .aam.  Then you will be able to open the file from your “file” menu in AABattlemap.

SS

Sankt is correct.  The SUB may still chose to leave the SZ in COMBAT movement phase of their upcoming turn.  However, if the SUB does not combat mvoe out, then Comabt will occur with the new fleet.