Topics created by bigchris

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.

the thing i like about tripleA is that i have a history in a saved game file.  after entering all the moves (and editing), i can go back R1, step through each move and purchase and study the position.  once i see the clever moves in round 4-5, i can go back and see how they were setup.

i pretty much have to do it this way since many of the allies moves aren’t obvious at first glance.  it takes a few turns of the allies coordinating together (for me) to see why things were done several turns ago and why certain things were not done.

can abattlemap do that for me?  or will i just have to use my memory?

The attacker retreats before the defender submerges, in both OOB and LHTR.

This is clearly spelled out in the LHTR rules.  However, since the sequence is never specifically stated in the OOB rules, the general principle that the attacker acts first must be applied.

@Granada:

oh well, i have just tried the strategy against an experienced player and i was destroyed terribly. SZ 12 IS NOT A SAFE PLACE R1. You would not have 2 UK trans in most cases. I played against bid 9 so there was one sub more from the start and an AC on G1. Any kind of convoying system is necessary for US but next time i am going to make sure that i control the atlantic solidly first. I made some childish mistakes too, but if the germans put an effort to contesting the atlantic you cannot just build trannies. You have to sink their ships first and you have to do it quick and as cheap as possible.

Btw if the convoying system is to work smoothly you need for US actually three sets of transport ships, two wount do.

Early allied shipping losses can really hamper your game plan. It is always vital to protect not only the transports, but that British battleship! If Germany invests 24 ipcs in the water, you will have to wait a round or two to be safe, however, thats all right, as Germany took away 24 ipcs from the Russian campaign, you have time to get going.

they did, only the tank in the south even survived, –in the north, a couple infantry, an ART and the tank.  Allies should have dumped more into Bastogne and surrounding area i guess. 
  And since nothing else survived, the tank was cut off from supplies and allies didn’t bring any more up to allow it to even move.