Re: [risk] defending vs attacking?

[Richard Rognlie <rrognlie@gamerz.net>]

I've done some rough calculations on classic Risk[tm] odds for 
attack v. defense  (Odds Table attached)

You'll note that the odds are skewed dramatically towards the
defender 
    AL(e) == expected loss for Attacker
    DL(e) == expected loss for Defender

in the even attack cases

1v1 == 1.4:1 defender favor
2v2 == 1.56:1 defender favor

Perhaps we should (in cases of invasion) "credit" the defender with
additional armies.  And if they lose armies, it is in proportion
to this "virtual" total.

e.g.  I have 5 armies defending against 8 invaders.  I get a "credit"
of 50% (pulling an easy number from the air).  5 + 2.5 (round down)
== 7.  I lose, but take 7 with me.

Another example.  6 defenders vs.  7 invaders.  I get 3 credit.
9 v. 7.    I lose 7 == 7/9 of my force.   (put another way, I 
save 2/9 of my original force of 6)  6 * 2/9 == 1.333 (round down)
== 1.


I could easily see this as working.  (scary thought).   But is it 
too hard to view things that way?

Richard



Odd Table (as calculated by richard)
------------------------------------
att 1 v. def 1  (36)
   att lose 1 = 21      58.3%
   def lose 1 = 15      41.7%

att 2 v. def 1  (216)   
   att lose 1 = 91      42.1%
   def lose 1 = 125     57.9%

att 3 v. def 1  (1296)
   att lose 1 = 441     34.0%
   def lose 1 = 855     66.0%

att 1 v. def 2  (216)
   att lose 1 = 161     74.5%
   def lose 1 = 55      25.5%

att 2 v. def 2  (1296)          AL(e) = 1.22  DL(e) = 0.78
   att lose 2  = 581    44.8%
   lose 1 each = 420    32.4%
   def lose 2  = 295    22.8%

att 3 v. def 2  (7776)          AL(e) = 0.92  DL(e) = 1.08
   att lose 2  = 2275   29.2%
   lose 1 each = 2611   33.6%
   def lose 2  = 2890   37.2%

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