Newsgroups: rec.games.board
Date: Mon,  9 Nov 1992 21:09:23 -0500 
From: "Jonathan T. Moore" <jmci+@andrew.cmu.edu>
Subject: Re: A&A - Can Allies ever win (IIa)
Distribution: world

Excerpts from netnews.rec.games.board: 9-Nov-92 A&A - Can Allies ever
win (.. Ingolf Markhof@ls12r.inf (4021)

>keith@cco.caltech.edu (Keith Allan Schneider) writes:
>
>> Ukraine does not boarder Moscow.
>
>Sorry. You're right. I used the wrong area in my text. In fact I mean the
>area in the west of Moscow and in the south of Karelia. I guess this is the
>Caucasus. Russia will get big problems once germany has placed a large >force
>(e.g. 15 tanks, 10 Infantry and some fighters) in the Caucasus.
>
>tw1r+@andrew.cmu.edu (Timothy C. Worsley) writes:
>
>> 	Infantry are much better for defending than Fighters are.  Even in
>> attack (of only one space) infantry gives you 4 ones instead of one 3,
>> which is MUCH better.  Fighters are only really good if you need to >move
>> quickly or fight on land and sea.
>
>From this point of view, your're right: An attacking fighter will >eliminate
>1*(3/6)=0.50 units (average), while four attacking infantry will hit
>4*(1/6)=0.66 units. And if you are defending, it's 1*(4/6)=0.66 for the
>fighter, and 4*(2/6)=1.33 for the infantry.
>
>But there are several things you should keep in mind:
>
>1) As infantries probability for a hit (0.16) is much smaller than the
  > prbability for fighters (0.5) in the attacking case, the actual number
   >of hits varies very much for infantry.
>   Example: If you attack with 8 infantry, you can expect to get
>   8*(1/6)=1.33 hits. But the possibility to get no hit at all is still
>   (5/6)^8=0.23 !!! 
>   And as infantries probability for a hit (0.16) is much smaller than the
>   probability for a miss (0.83), the variation is not symmetrically:
  > Look at the previous example: The probability to get 8 hits is
   >(1/6)^8=0.000000595 !!!
   >This is not true if you're attacking with fighters. Here, the probality
   >for a hit is 0.5, so the probablity for a miss is 0.5, too. If you
   >attack with 4 fighters, you can expect to achieve 4*0.5=2 hits. The
   >chance to get not hits is only 0.5^4=0.625, but this is exactly the
   >chance to get even 4 hits, too.
   >Sumary: Attacking with fighters is more deterministic and desasterous
   >variance of the dice results are not as often as with infantry. (Of
   >course not must not attack with fighters, only. You'll need some >infantry
  > for your casualties!)
>
>2) If you attack with infantry only, your attacking power will decrease
  > each round of attack. If you are attacking by a force of fighters and
   >infantry, a major part of your attacking power will come from the
>fighters.
  > But for casualities, you'll remove some infantry, of course. So, you're
>   attacking power will not decrease so much.
>
>3) If you attack with infantry only, you'll need a lot of them. Let's say
>   gemany has 3 infantry in the Caucasus, and you're going to attack >these.
>   The defending infantry will hit in average 3*(2/6)=1 of your units. If
  > you want to do this, you need 6 infantry: 6*(1/6)=1. But due to the 
  > variance (see 1), you might better send 8 or 9 infantry. This is more
  > than Russia can build in a turn! And this infantry will not defend
  > the Caucasus. Let's say you'll eliminate the 3 german units and there
  > are 5 of your units left. Germany will kill them by a combined infantry
  > and fighter attack! You have lost all 8 or 9 infantry to stop germany!
 >  
>4) Fighters are double effective: You can use them to attack one area and
 >  send them back to defend another. So, Russia can destroy german forces
 >  in the Caucasus and defend Karelia with its fighters!
>
>Comments?
>
I've got some comments, sure. You are missing the point: at no time
should you be overly aggressive with Russia, except perhaps on the first
turn, as beyond that first turn, your opportunities for high gain:loss
ratios dwindle to approximately nil. The only purpose to the first round
Eastern Europe attack is to buy time. This effectively eliminates an
effective assault on Karelia by Germany in the first turn. As for after
that, you basically just want to churn out the infantry and hold tight.
If you can hold out in Karelia for a couple turns, the U.S. and Britain
will be tightening the screws on Germany and you can relax somewhat.
Just keep in mind that either way, infantry or fighters, your forces are
better on DEFENSE. Make Germany come to you. His infantry will be half
as good as yours, his fighters only .75 as good (minus any AA
casualties); he will really have to grind it out for at least a good
three turns before he can get you. However, by then, if he's just done
that, Britain and the U.S. will be knocking on Berlin anyway. Another
thing, about the probabilities and variances, I haven't had prob and
stat in a while, but the variance shouldn't matter that much. Over the
course of the game, barring extraordinary luck, you will be rolling
enough dice to achieve close to the averages anyway. In my opinion, it
all evens out in the end (which is rotten luck for the Axis).

Hope I shed some light on the subject.

Jon


-----------------------------------------------
Jon Moore             (jmci@andrew.cmu.edu) 
 "What have I got in my pocket?" --Bilbo     
 "Let the truth of love be lighted,          
  Let the love of truth shine clear." --RUSH 
-----------------------------------------------

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