[risk] DIceless Combat

[Richard Rognlie <rrognlie@gamerz.net>]

In _New Rules for Classic Games_, Schmittberger proposes a simple
algorithm for diceless combat between two players...

	A v. B

If both forces are the same, complete annihilation (unless once of the
forces in defending [say A attacks B] in which case, 1 defender is left
stadning).

Otherwise, the larger force wins.  It loses the same number of pieces as
the smaller force, less the difference in size.  W=W-(L-(W-L)) e.g.,

	A5 -> B3. 

	A loses 3 minus the difference of 2 == 1.  So A loses 1.

This has the side affect of:  If you attack with a force of twice the
defender or more, you win without losing a piece.

As long as only 2 players are involved, this works fine.  But when we
try to scale up to multiple players, it gets ugly quickly.  e.g.

	A4 ->  B3  <- C1

	if we think in terms of a combined attack we get (5 v. 3)  The
	aggressors would lose 1.  But who loses it?  A or C?  if the 
    larger force A then A3 and C1 survive.  they fight, and A3 takes
	the territory.  If C loses the army, A4 survives to take the 
	territory unopposed.  And I can see arguments either way.

It gets ugly ugly very quickly.


To combat this, I created the algorithm currently in use.

Take all the forces' values, and look at the top two values.  If 
they're equal, mutual annihilation occurs (unless one of them is
the defender... then 1 of his survives).  If unequal, the largest 
force survives, losing the number of armies as the next larger.  All
others are lost.  in the above example, A loses 3 but wins.  B and C 
are eliminated.  It's clean, but suffers from the drawback Bob
mentioned this morning...

What if A and C are working together?  in the above example, C gains
nothing from attacking.  If he wants to help A, he could attack on 
an earlier turn, reducing B to 2, *then* A attacks only losing 2,
not the 3...  But that requires careful coordination.

I'm still open to suggestions.  It is beta afterall!  8^)

Richard

-- 
 /  \__  | Richard Rognlie / Sendmail Consultant / Sendmail, Inc.
 \__/  \ | URL:    http://www.gamerz.net/rrognlie/   
 /  \__/ | Give a man a fish, and he'll be hungry tomorrow.  Teach a
 \__/    | man to fish, and he'll be at the river all day drinking beer.