From: duelge@schaefer.math.wisc.edu (Jason Duelge)
Subject: Re: A&A - Can Allies ever win (IIa)
Keywords: Axis & Allies
Reply-To: duelge@schaefer.UUCP (Jason Duelge)
Organization: Univ. of Wisconsin Dept. of Mathematics
Date: Mon, 9 Nov 92 22:26:08 GMT

In article <1dlshjINN6m7@fbi-news.Informatik.Uni-Dortmund.DE> markhof@ls12r.informatik.uni-dortmund.de (Ingolf Markhof) 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!)
>
This is pretty bad probability application.
Lets look at cost.  You can buy 8 infantry or 2 fighters.
The probability of getting 0 hits with 8 infantry is about 23%
The probability of getting 0 hits with 2 fighters is 25%.  So, for
the same price, you have a GREATER chance of getting 0 hits with
fighters.
Now, with 2 fighters you have a 50% chance of getting 1 hit.  With
8 infantry you have (8)(1/6)(5/6)^7 = 37% chance.
With 2 fighters you have a 25% chance of getting 2 (or more) hits.
With 8 infantry, you have a 40% chance of getting 2 or more hits.
So, no matter how you look at it, for defense the infantry are better.
This completely ignores the fact that it takes 4 hits to destroy a
12 ipc infantry 'block', whereas it takes only one hit to destroy a
12 ipc fighter.

>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 russians aren't really concerned much with attacking.  They
have two fighters, which will be sufficient in the attacks they need to
make.

>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!
>
Russia has 2 fighters!  Use them.
   
>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?
>
You continue to miss the point.  The game is heaviliy weighted in favor
of the allies, but not if the Russian's play stupidly.  For Russia to
build anything but infantry is pretty stupid.

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| Jason Duelge                                                              |
| 141 Lakewood                                                              |
|  Gardens ln                                                               |