N00b school: Pearl Heavy v. Pearl Light

@ponef In regards to what? This thread kind of wound up diverting itself in like 3 different directions:

Whether UK should retake Egypt B1 Vs. send the FTR from the India Carrier over to the US Pearl Harbor Fleet. Whether Japan should attack the Pearl Harbor Fleet, the UK India Fleet, or both on J1. Whether UK should attack Borneo B1 or not.

The answer to basically all of these boiled down to some combination of “it depends on how the dice went G1” and “are you playing under WBC Rules or not”. Seeing as WBC no longer runs tournaments for Revised (or any A&A, for that matter), we’re left to assume all games being played will be OOB rules (or at least LHTR), in which case Egypt suddenly becomes much less of a priority in the grand scheme of things.

Personally, I got to try the strategy out at the 2018 WBC in one of my games. It worked well for me, as Japan was routinely baited into attacking the USN, losing the TT and the DD in the process. This allowed me to wipe out the remaining IJN Fleet A1 (Bomber from East USA + FTR from West USA + Navy from US West Coast + FTR from Hawaii). This crippled the IJN and let me rapidly come to dominate the Pacific.

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.

Because a destroyer is cheaper.

You cannot buy 2 transports and a carrier on Japan 1.  That means trading in a transport to get a carrier, not a trade I want, or getting two transports (3 or 4 total available on Japan 2) and a destroyer thus not tying up your fleet on such non-sense as transport protection duty.

Not to mention, when I go after the American fleet with Japan, I always wish I had another destroyer.  I never wish I had another transport.  (Talking rounds 12+ when Japan goes after the Allied fleet to protect S. Germany)

They are both a good time but watching your buddy spill his tenth beer all over himself while he flips the board in the air after rolling a few 666’s at 3 am can’t be beat!

I think we could probably devote a whole board to the sub rules. I think in Classic (bot many games of Classic under the belt went to that backwards via Europe) subs could come into a zone, shoot, and leave without being shot at. Not sure on that though.

Our problem was we were not conducting opening fire every round that subs were still on the battle board. We would have opening shots then treat them just like any other naval units.

The sub rules are different in all four versions of the game with subs that much I’m very clear on. The sub rules for Revised I’m very clear on because I think they are the cleanest.

sure, I’d play ya IRL.  But I’m in NYC and you’re around Chicago, I think, yes?

OH wellz, what can ya do?

So, like I mentioned before:

most people make up their USA strategy after J has made his first move:

@Axel:

A) if you do a Pearl attack: Most of the USA players would leave the Pacific and do a KGF…
B) if you don’t do a Pearl attack: Most of the USA players stay in the Pacific…

So, if you are J: make your discission: do you want to let USA stay in the Pacific? or do you want to let the USA mess with G?

and almost every post I read regarding this subject so far has made the USA strategy depending on J1!
So Japan has to make up his mind and in that way determines USA strategy most of the times…

I think this poll has made his point :-)

Well Kaladesh, have you tried the opening fire variant yet? :D I find it balanced and use it every time!