From: markhof@ls12r.informatik.uni-dortmund.de (Ingolf Markhof)
Newsgroups: rec.games.board
Subject: A&A - Can Allies ever win (IIa)
Date: 9 Nov 1992 14:28:03 GMT
Organization: CS Department, Dortmund University, Germany
Distribution: world
NNTP-Posting-Host: ls12r
Keywords: Axis & Allies

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?

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