N00b school: Pearl Heavy v. Pearl Light

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.

If the attacker retreats and there is no more CV for the planes involved in the defense, all defending figs get one movement point to escape to friendly territory or SZ (if there is a carrier with capacity handy). Since Hawaii is US/Allied control, both the US fig and the Brit fig can land there.

The same would apply in any other cases - say germans attack allied fleet in north sea protected by US planes. If CV is sunk then germans retreat, US planes could escape to UK (or any other adjacent allied territory) on germany’s turn.

@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.

How does US counter Japan’s Pearl?

Simple answer:  KGF.

If you really want to go KJF, you either go Ssinkiang and Indian ICs, or you build Pacfleet on US1 threatening attack on Pearl US2 (Japan shouldn’t be strong enough to wipe out the US2 fleet), or you can try Alaska transport chain.  Buncha things you can do really.  I note you already mentioned the LRA option.

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.

Thanks man - that does help!

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.

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