N00b school: Pearl Heavy v. Pearl Light

In my group we generally skip the tech development. To my opinion too it is unbalancing the game for one player. It feels more like a fair fight to play without the tech development.

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)

@nuno:

@ncscswitch:

In LL, you end up with Agent Smith’s who have years of work with sims to lock down specific strats that always work.

Once again ncscswitch couldn’t pass an opportunity to bait me…

Not-so-welcome back Agent Smith.  Glad you finally publicly admitted who you are, now we do not have to pussy foot around with you any longer.

I see you have not changed in the slightest… still all talk and bluster, with absolutely NO substance.  One of those unfortunate souls who refuses to put up or shut up.

@nuno:

Now go entertain yourself censoring/banning me, like you love so much to do.

Actually, you are the only one who is working at getting you banned.  You already expounded on how you were banned from another gaming site.  And you were previously banned in several of your other incarnations from this site.  Eventually you may grow up enough to figure out that it is not the entire A&A gaming world that is out to get you, but that you are just an asshole and that no one wants to have to put up with your shit.

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.

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 :-)

If the UK fig is flown in for defense, then Bury is skipped.

Thanks, Tri- this is the crux of what I was trying to say. I even put it in bold in my last post to make it clear :-D

But I’ll do it again because it’s fun.

Russian and British choices dictate whether Japan can even think about Buryatia or not.

Buryatia is only possible if the right conditions exist. An extra British fighter in China means the right conditions do not exist. And if you do choose to do it, you build accordingly (3 transports), which deals with the U.S. threat.

To every question of “well what if _______ and what if________”,  I answer- don’t attack Buryatia.