Newsgroups: rec.games.board
Date: Tue, 10 Nov 1992 07:10:13 -0500 
From: Erik Lauer <el0g+@andrew.cmu.edu>
Subject: Re: A&A - Can Allies ever win (IIa)
Distribution: world

markhof@ls12r.informatik.uni-dortmund.de (Ingolf Markhof) writes:

>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.
Well, lets sum it up this way:  you can buy 4 inf or 1 fighter.  Chance
of fighter missing: .5 chance of 4 inf missing: .48.  Fighter can not
get more than 1 hit, inf can.  So inf are more likely to generate the
hit, and can generate multiple hits.

>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!)

Well, attacking with fighters is more deterministic, for any number of
hits your chance of getting that number or higher is better if you
bought all inf instead.  I guess you would rather be pretty sure you get
2 hits rather than be more sure you get 2 hits, and risk getting more.

>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.

Well, if I have the 4 inf backing up for each fighter you would have, I
average more hits every round, and I am more sure of getting those hits,
plus if I get unlucky I have the inf to lose while the fighter would die
in 1 hit.  If I lose 1 of those inf, your bonus is you lose your fighter.

>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!

Well, the Caucuses are not the problem, since you can take Ukraine too,
but you have finally gotten to one of the big advantages of the fighter!
 Yes, you can attack and not end up there.  You can move 4.  You can
attack naval pieces.

>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!

Correct again.

>Comments?
You were correct about the fighters being more flexible.  As far as
winning a single land battle though, there can be no doubt that inf are
mre effective.  When attacking a mix of roughly 3 tanks per 5 inf is
optimal (more inf if you have air pieces).  Russia, however, should
build 8 inf in Karelia the first turn, it already has the two fighters
to use, and must put as much preassure on Germany as it can, indirectly
helping the allies retake Africa.  I am not sure how often the Allies
will win if Russia start building planes on turn 1.

>------------------------------------------------------------------------------
>      ____                                                             
      
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Erik
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