Newsgroups: rec.games.board
Date: Tue, 10 Nov 1992 00:43:32 -0500 
From: Thomas Omar Smith <ts2a+@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.

This is only a problem if Germany is able to spend several turns
building this force, and does not face a solid defensive force from
> Russia.

> 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!)

But, it costs 4x as much to attack or defend with 4 fighters.  For your
4 fighter, you could have had 16 infantry defending.  16 Infantry
defending will stop the 10 tanks your opponent could have bought for the
> same money.  4 fighters won't.

> 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.

True, but the same argument can be made for armor and infantry, and the
armour is much more cost effective.  5 tanks, attacking or defending,
> will beat 2 fighters.  And the cost is practically the same.

> 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!
>    
You're assuming that Russia should attack.  But what if instead you
leave those 9 infantry in a defensive position, forcing the Germans to
> advance.  They'll take more that their value out of the German assault.

> 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!

This is the real advantage of the fighter.  It can move where support is
needed very well.  However, the fighter is a reserve unit, not a main
unit.  Defensively, infantry is better than any other troop dollar for
dollar.  Offensively, tanks are best.  You seem to be thinking in terms
of unit effectiveness instead of dollar effectiveness.  Doing this will
give you nice pieces, but not enough to counter your opponents better
> bought pieces.

> Comments?

> ------------------------------------------------------------------------------
>       ____                                                                    
>   UniDo  /  Ingolf Markhof  University of Dortmund, LS Informatik XII         
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